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console.error(err); throw err; };\n\n \tvar jsonpArray = window[\"webpackJsonp\"] = window[\"webpackJsonp\"] || [];\n \tvar oldJsonpFunction = jsonpArray.push.bind(jsonpArray);\n \tjsonpArray.push = webpackJsonpCallback;\n \tjsonpArray = jsonpArray.slice();\n \tfor(var i = 0; i < jsonpArray.length; i++) webpackJsonpCallback(jsonpArray[i]);\n \tvar parentJsonpFunction = oldJsonpFunction;\n\n\n \t// add entry module to deferred list\n \tdeferredModules.push([0,\"chunk-vendors\"]);\n \t// run deferred modules when ready\n \treturn checkDeferredModules();\n","module.exports = __webpack_public_path__ + \"img/blue_background_with_illustration@2x.51fbcce5.svg\";","import mod from \"-!../node_modules/mini-css-extract-plugin/dist/loader.js??ref--6-oneOf-1-0!../node_modules/css-loader/index.js??ref--6-oneOf-1-1!../node_modules/vue-loader/lib/loaders/stylePostLoader.js!../node_modules/postcss-loader/src/index.js??ref--6-oneOf-1-2!../node_modules/cache-loader/dist/cjs.js??ref--0-0!../node_modules/vue-loader/lib/index.js??vue-loader-options!./App.vue?vue&type=style&index=0&lang=css&\"; export default mod; export * from \"-!../node_modules/mini-css-extract-plugin/dist/loader.js??ref--6-oneOf-1-0!../node_modules/css-loader/index.js??ref--6-oneOf-1-1!../node_modules/vue-loader/lib/loaders/stylePostLoader.js!../node_modules/postcss-loader/src/index.js??ref--6-oneOf-1-2!../node_modules/cache-loader/dist/cjs.js??ref--0-0!../node_modules/vue-loader/lib/index.js??vue-loader-options!./App.vue?vue&type=style&index=0&lang=css&\"","module.exports = __webpack_public_path__ + \"img/logo_stedi_nav_bar_sl.b797606c.svg\";","module.exports = __webpack_public_path__ + \"img/logo_surs_sl.aff49f11.svg\";","module.exports = __webpack_public_path__ + \"img/orange_background_with_illustration@2x.7dffe17c.svg\";","module.exports = __webpack_public_path__ + \"img/Group_homepage3_mobile.6c642371.png\";","var render = function () {var _vm=this;var _h=_vm.$createElement;var _c=_vm._self._c||_h;return _c('div',{staticClass:\"homepage\"},[_c('homepage-navigation'),_c('div',{attrs:{\"id\":\"hero\"}},[_c('div',{staticClass:\"hero-background-image text-center\"},[_c('img',{attrs:{\"src\":require('@/images/New_homepage/Group_homepage.svg'),\"alt\":\"Pozadinska slika 1.1\"}})]),_c('div',{staticClass:\"hero-content\"},[_c('div',{staticClass:\"flex text-center\"},[_c('div',{staticClass:\"row row-first\"},[(_vm.language === 'en')?_c('div',[_c('logo-animation-en')],1):_vm._e(),(_vm.language === 'sl')?_c('div',[_c('logo-animation-sl')],1):(_vm.language === 'hr' || _vm.language === null)?_c('div',[_c('logo-animation-hr')],1):_vm._e()]),_c('div',{staticClass:\"row\"},[_c('p',{staticClass:\"homepage-hero-text\",domProps:{\"innerHTML\":_vm._s(_vm.$t('homepage.intro'))}})]),_c('div',{staticClass:\"row\"},[_c('div',[_c('router-link',{staticClass:\"btn btn-large btn-green\",attrs:{\"to\":\"/chapter-literature\",\"data-text\":\"→\"}},[_c('div',[_vm._v(_vm._s(_vm.$t('chapters_button')))])])],1)]),_c('div',{staticClass:\"row\"},[_c('div',{staticClass:\"hero-background-footer-image text-center\"},[_c('img',{attrs:{\"src\":require('@/images/New_homepage/Group_homepage_mobile.svg'),\"alt\":\"Pozadinska slika 1.2\"}})])])])])]),_c('div',{attrs:{\"id\":\"about\"}},[_c('div',{staticClass:\"container\"},[_c('div',{staticClass:\"about-title text-center\"},[_c('h2',{staticClass:\"homepage-title\",domProps:{\"innerHTML\":_vm._s(_vm.$t('about'))}})]),_c('div',{staticClass:\"flex\"},[_c('div',{staticClass:\"col col-left\"},[_c('p',{staticClass:\"homepage-sections-text\",domProps:{\"innerHTML\":_vm._s(_vm.$t('homepage.about_section.1'))}}),_c('p',{staticClass:\"homepage-sections-text\",domProps:{\"innerHTML\":_vm._s(_vm.$t('homepage.about_section.2'))}}),_c('p',{staticClass:\"homepage-sections-text\",domProps:{\"innerHTML\":_vm._s(_vm.$t('homepage.about_section.3'))}}),_c('p',{staticClass:\"homepage-sections-text\",domProps:{\"innerHTML\":_vm._s(_vm.$t('homepage.about_section.4'))}})]),_c('div',{staticClass:\"col col-right\"},[_c('p',{staticClass:\"homepage-sections-text\",domProps:{\"innerHTML\":_vm._s(_vm.$t('homepage.about_section.5'))}}),_c('p',{staticClass:\"homepage-sections-text\",domProps:{\"innerHTML\":_vm._s(_vm.$t('homepage.about_section.6'))}}),_c('p',{staticClass:\"homepage-sections-text\",domProps:{\"innerHTML\":_vm._s(_vm.$t('homepage.about_section.7'))}}),_c('p',{staticClass:\"homepage-sections-text\",domProps:{\"innerHTML\":_vm._s(_vm.$t('homepage.about_section.8'))}})])])])]),_c('div',{attrs:{\"id\":\"contact\"}},[_c('div',{staticClass:\"contact-background-mobile-image text-center\"},[_c('img',{attrs:{\"src\":require('@/images/New_homepage/Group_homepage2_mobile.svg'),\"alt\":\"Pozadinska slika 2.2\"}})]),_c('div',{staticClass:\"contact-background-image text-center\"},[_c('img',{attrs:{\"src\":require('@/images/New_homepage/Group2_homepage.svg'),\"alt\":\"Pozadinska slika 2.1\"}})]),_c('div',{staticClass:\"contact-title text-center\",attrs:{\"id\":\"contactTitle\"}},[_c('h2',{staticClass:\"homepage-title\",domProps:{\"innerHTML\":_vm._s(_vm.$t('contact'))}})]),_c('div',{staticClass:\"contact-content\"},[_c('p',{staticClass:\"homepage-sections-intro\",domProps:{\"innerHTML\":_vm._s(_vm.$t('homepage.contact.1'))}}),_c('p',{staticClass:\"homepage-sections-text\",domProps:{\"innerHTML\":_vm._s(_vm.$t('homepage.contact.2'))}}),_c('a',{staticClass:\"contact-btn-wrapper\",attrs:{\"href\":\"mailto:gp.surs@gov.si\"}},[_c('button',{staticClass:\"btn btn-small btn-orange\",attrs:{\"type\":\"button\",\"data-text\":\"→\",\"href\":\"mailto:gp.surs@gov.si\"}},[_c('div',[_vm._v(_vm._s(_vm.$t('homepage.contact.3')))])])]),_c('div',{staticClass:\"socials\"},[_c('a',{attrs:{\"href\":_vm.$t('socials.facebook'),\"target\":\"_blank\",\"title\":\"Facebook\",\"rel\":\"noopener noreferrer\"}},[_c('span',{staticClass:\"icon facebook-icon\"})]),_c('a',{attrs:{\"href\":_vm.$t('socials.instagram'),\"target\":\"_blank\",\"title\":\"Instagram\",\"rel\":\"noopener noreferrer\"}},[_c('span',{staticClass:\"icon instagram-icon\"})]),_c('a',{attrs:{\"href\":_vm.$t('socials.youtube'),\"target\":\"_blank\",\"title\":\"Youtube\",\"rel\":\"noopener noreferrer\"}},[_c('span',{staticClass:\"icon youtube-icon\"})])])]),_c('div',{staticClass:\"contact-background-mobile-image text-center\"},[_c('img',{attrs:{\"src\":require('@/images/New_homepage/Group_homepage3_mobile.png'),\"alt\":\"Pozadinska slika 2.3\"}})])]),_c('footer',{attrs:{\"id\":\"footer\"}},[_c('div',{staticClass:\"flex\"},[_c('div',{staticClass:\"col\"},[_c('div',[_c('span',[_c('router-link',{staticClass:\"footer-small-text\",attrs:{\"to\":\"/STEDy-and-cookies\"},domProps:{\"innerHTML\":_vm._s(_vm.$t('homepage.footer.1'))}}),_vm._v(\" | \"),_c('router-link',{staticClass:\"footer-small-text\",attrs:{\"to\":\"/accessibility\"},domProps:{\"innerHTML\":_vm._s(_vm.$t('homepage.footer.5'))}}),_c('br'),_vm._v(\" © \"+_vm._s(new Date().toISOString().slice(0, 4))+\" \"),_c('a',{attrs:{\"href\":\"https://www.dzs.hr/\",\"target\":\"_blank\",\"rel\":\"noopener noreferrer\"},domProps:{\"innerHTML\":_vm._s(_vm.$t('homepage.footer.2'))}})],1)])]),_c('div',{staticClass:\"col col-center\"},[_c('div',{staticClass:\"footer-logos\"},[_c('div',[(_vm.language == 'sl')?_c('a',{attrs:{\"href\":\"https://www.stat.si/statweb\"}},[_c('img',{attrs:{\"src\":require('../images/Homepage/logo_surs_sl.svg'),\"alt\":\"SURS logo\"}})]):_vm._e(),(_vm.language == 'en')?_c('a',{attrs:{\"href\":\"https://www.stat.si/StatWeb/en\"}},[_c('img',{attrs:{\"src\":require('../images/Homepage/logo_surs.svg'),\"alt\":\"SURS logo\"}})]):_vm._e(),_c('a',{attrs:{\"href\":\"https://www.dzs.hr/\"}},[_c('img',{attrs:{\"src\":require('../images/Homepage/dzs_logo@2x.svg'),\"alt\":\"DZS logo\"}})]),_c('a',{attrs:{\"href\":\"https://ec.europa.eu/eurostat\"}},[_c('img',{attrs:{\"src\":require('../images/Homepage/eurostat_logo@2x.svg'),\"alt\":\"Eurostat logo\"}})])]),_c('div',[_c('span',{staticClass:\"footer-smaller-text\",domProps:{\"innerHTML\":_vm._s(_vm.$t('homepage.footer.3'))}})])])]),_vm._m(0)])])],1)}\nvar staticRenderFns = [function () {var _vm=this;var _h=_vm.$createElement;var _c=_vm._self._c||_h;return _c('div',{staticClass:\"col col-end\"},[_c('div')])}]\n\nexport { render, staticRenderFns }","var render = function () {var _vm=this;var _h=_vm.$createElement;var _c=_vm._self._c||_h;return _c('div',{staticClass:\"navigation\",class:{'scrolled': _vm.isNotTop}},[_c('div',{staticClass:\"flex\"},[_c('div',{staticClass:\"col col-left\"},[_c('router-link',{attrs:{\"to\":\"/\"}},[(this.$i18n.locale == 'sl')?_c('img',{directives:[{name:\"scroll-to\",rawName:\"v-scroll-to\",value:('#hero'),expression:\"'#hero'\"}],attrs:{\"alt\":\"Stedy - Assistant in your statistical challenges\",\"src\":require('../images/Homepage/logo_stedi_nav_bar_sl.svg')}}):_vm._e(),(this.$i18n.locale == 'en')?_c('img',{directives:[{name:\"scroll-to\",rawName:\"v-scroll-to\",value:('#hero'),expression:\"'#hero'\"}],attrs:{\"alt\":\"Stedy - Assistant in your statistical challenges\",\"src\":require('../images/Homepage/logo_stedi_nav_bar_en.svg')}}):_vm._e(),(this.$i18n.locale == 'h1')?_c('img',{directives:[{name:\"scroll-to\",rawName:\"v-scroll-to\",value:('#hero'),expression:\"'#hero'\"}],attrs:{\"alt\":\"Stedy - Assistant in your statistical challenges - DZS\",\"src\":require('../images/Homepage/logo_stedi_nav_bar@2x.svg')}}):_vm._e()]),_c('button',{directives:[{name:\"scroll-to\",rawName:\"v-scroll-to\",value:({el: '#about', offset: - 68}),expression:\"{el: '#about', offset: - 68}\"}],staticClass:\"btn btn-ghost\",attrs:{\"type\":\"button\"},domProps:{\"innerHTML\":_vm._s(_vm.$t('about'))}}),_c('button',{directives:[{name:\"scroll-to\",rawName:\"v-scroll-to\",value:({el: '#contactTitle', offset: - 68}),expression:\"{el: '#contactTitle', offset: - 68}\"}],staticClass:\"btn btn-ghost\",attrs:{\"type\":\"button\"},domProps:{\"innerHTML\":_vm._s(_vm.$t('contact'))}})],1),_c('div',{staticClass:\"col col-right\"},[_c('div',{staticClass:\"social\"},[_c('a',{attrs:{\"href\":_vm.$t('socials.facebook'),\"target\":\"_blank\",\"title\":\"Facebook\",\"rel\":\"noopener noreferrer\"}},[_c('span',{staticClass:\"icon facebook-icon\"})]),_c('a',{attrs:{\"href\":_vm.$t('socials.instagram'),\"target\":\"_blank\",\"title\":\"Instagram\",\"rel\":\"noopener noreferrer\"}},[_c('span',{staticClass:\"icon instagram-icon\"})]),_c('a',{attrs:{\"href\":_vm.$t('socials.youtube'),\"target\":\"_blank\",\"title\":\"Youtube\",\"rel\":\"noopener noreferrer\"}},[_c('span',{staticClass:\"icon youtube-icon\"})])]),_c('select',{directives:[{name:\"model\",rawName:\"v-model\",value:(_vm.$i18n.locale),expression:\"$i18n.locale\"}],staticClass:\"select-ghost\",on:{\"change\":[function($event){var $$selectedVal = Array.prototype.filter.call($event.target.options,function(o){return o.selected}).map(function(o){var val = \"_value\" in o ? o._value : o.value;return val}); _vm.$set(_vm.$i18n, \"locale\", $event.target.multiple ? $$selectedVal : $$selectedVal[0])},_vm.changeLang]}},_vm._l((_vm.langs),function(lang,i){return _c('option',{key:(\"Lang\" + i),domProps:{\"value\":lang}},[_vm._v(_vm._s(lang.toUpperCase()))])}))])])])}\nvar staticRenderFns = []\n\nexport { render, staticRenderFns }","<template>\r\n  <div class=\"navigation\" :class=\"{'scrolled': isNotTop}\">\r\n    <div class=\"flex\">\r\n      <div class=\"col col-left\">\r\n        <router-link to=\"/\">\r\n          <img v-if=\"this.$i18n.locale == 'sl'\" alt=\"Stedy - Assistant in your statistical challenges\" :src=\"require('../images/Homepage/logo_stedi_nav_bar_sl.svg')\" v-scroll-to=\"'#hero'\">\r\n          <img v-if=\"this.$i18n.locale == 'en'\" alt=\"Stedy - Assistant in your statistical challenges\" :src=\"require('../images/Homepage/logo_stedi_nav_bar_en.svg')\" v-scroll-to=\"'#hero'\">\r\n          <img v-if=\"this.$i18n.locale == 'h1'\" alt=\"Stedy - Assistant in your statistical challenges - DZS\" :src=\"require('../images/Homepage/logo_stedi_nav_bar@2x.svg')\" v-scroll-to=\"'#hero'\">\r\n\t\t</router-link>\r\n        <button type=\"button\" class=\"btn btn-ghost\" v-scroll-to=\"{el: '#about', offset: - 68}\" v-html=\"$t('about')\"></button>\r\n        <button type=\"button\" class=\"btn btn-ghost\" v-scroll-to=\"{el: '#contactTitle', offset: - 68}\" v-html=\"$t('contact')\"></button>\r\n      </div>\r\n      <div class=\"col col-right\">\r\n        <div class=\"social\">\r\n          <a :href=\"$t('socials.facebook')\" target=\"_blank\" title=\"Facebook\" rel=\"noopener noreferrer\">\r\n            <span class=\"icon facebook-icon\"></span>\r\n          </a>\r\n          <a :href=\"$t('socials.instagram')\" target=\"_blank\" title=\"Instagram\" rel=\"noopener noreferrer\">\r\n            <span class=\"icon instagram-icon\"></span>\r\n          </a>\r\n          <a :href=\"$t('socials.youtube')\" target=\"_blank\" title=\"Youtube\" rel=\"noopener noreferrer\">\r\n            <span class=\"icon youtube-icon\"></span>\r\n          </a>\r\n          <!--<a :href=\"$t('socials.linkedin')\" target=\"_blank\" title=\"LinkedIn social icon\" rel=\"noopener noreferrer\">\r\n            <span class=\"icon linkedin-icon\"></span>\r\n          </a>\r\n          <a :href=\"$t('socials.github')\" target=\"_blank\" title=\"Github social icon\" rel=\"noopener noreferrer\">\r\n            <span class=\"icon github-icon\"></span>\r\n          </a>-->\r\n        </div>\r\n        <select v-model=\"$i18n.locale\" class=\"select-ghost\" @change=\"changeLang\">\r\n          <option v-for=\"(lang, i) in langs\" :key=\"`Lang${i}`\" :value=\"lang\">{{ lang.toUpperCase() }}</option>\r\n        </select>\r\n      </div>\r\n    </div>\r\n  </div>\r\n</template>\r\n\r\n<script>\r\n  export default {\r\n    name: 'HomepageNavigation',\r\n    data() {\r\n      return {\r\n        langs: ['en', 'sl'],\r\n        isNotTop: false\r\n      }\r\n    },\r\n    methods: {\r\n      sendToParent(id) {\r\n        this.$emit('scroll-to', id)\r\n      },\r\n      changeLang() {\r\n        window.localStorage.setItem('lang', this.$i18n.locale)\r\n      }\r\n    },\r\n    mounted() {\r\n      window.onscroll = () => {\r\n        this.isNotTop = (window.pageYOffset > 0) ? true : false\r\n      }\r\n    }\r\n\r\n  }\r\n</script>\r\n\r\n<style lang=\"scss\" scoped>\r\n.btn-ghost {\r\n  padding: 0.375rem 0.35rem !important;\r\n}\r\n</style>\r\n","import mod from 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\"./HomepageNavigation.vue?vue&type=style&index=0&id=74863973&lang=scss&scoped=true&\"\n\n\n/* normalize component */\nimport normalizer from \"!../../node_modules/vue-loader/lib/runtime/componentNormalizer.js\"\nvar component = normalizer(\n  script,\n  render,\n  staticRenderFns,\n  false,\n  null,\n  \"74863973\",\n  null\n  \n)\n\ncomponent.options.__file = \"HomepageNavigation.vue\"\nexport default component.exports","var render = function () {var _vm=this;var _h=_vm.$createElement;var _c=_vm._self._c||_h;return _c('div',{staticClass:\"hero-logo-svg\"},[_c('svg',{staticStyle:{\"white-space\":\"pre\"},attrs:{\"xmlns\":\"http://www.w3.org/2000/svg\",\"viewBox\":\"0 0 1440 1080\",\"text-rendering\":\"geometricPrecision\",\"shape-rendering\":\"geometricPrecision\"}},[_c('defs',[_c('symbol',{attrs:{\"id\":\"n0mf64hw6u0319epaxqfcen7\",\"preserveAspectRatio\":\"none\",\"width\":\"325\",\"height\":\"96\",\"viewBox\":\"0 0 325 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</g>\r\n</svg>\r\n</div>\r\n\r\n</template>\r\n\r\n<script>\r\nexport default {\r\n  name: 'LogoAnimationSl',\r\n  mounted() {\r\n    if(KeyshapeJS.version.indexOf('1.')!=0)throw Error('Expected KeyshapeJS v1.*.*');window.ks=document.ks=KeyshapeJS;(function(ks){\r\n    ks.animate(\"#jjmy0836g8k143in6en1ixui\",[{p:'mpath',t:[200,716],v:['0%','100%'],e:[[1,0,0,0,0.998968],[0]],mp:\"M-872.501,-2.68545e-06L-0.501007,-2.68545e-06\"},{p:'opacity',t:[2783,2800],v:[1,0],e:[[0],[0]]}],\r\n    \"#yj80ty6kexqdp4l5g2itpgpz\",[{p:'opacity',t:[2783,2800],v:[1,0],e:[[0],[0]]},{p:'strokeDashoffset',t:[883,1100],v:[353,0],e:[[0],[0]]}],\r\n    \"#ks285740h67oghvlxhf2se30\",[{p:'mpath',t:[416,716,866],v:['0%','87.181033%','100%'],e:[[1,0,0,0.58,1],[1,0,0,0.58,1],[0]],mp:\"M-0.500007,80.633L-0.500007,-14.3666L-0.500007,-0.398003\"},{p:'opacity',t:[416,716,2783,2800],v:[0,1,1,0],e:[[0],[0],[0],[0]]}],\r\n    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}\r\n}\r\n</script>","import mod from \"-!../../../node_modules/cache-loader/dist/cjs.js??ref--12-0!../../../node_modules/thread-loader/dist/cjs.js!../../../node_modules/babel-loader/lib/index.js!../../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../../node_modules/vue-loader/lib/index.js??vue-loader-options!./LogoAnimationSl.vue?vue&type=script&lang=js&\"; export default mod; export * from \"-!../../../node_modules/cache-loader/dist/cjs.js??ref--12-0!../../../node_modules/thread-loader/dist/cjs.js!../../../node_modules/babel-loader/lib/index.js!../../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../../node_modules/vue-loader/lib/index.js??vue-loader-options!./LogoAnimationSl.vue?vue&type=script&lang=js&\"","import { render, staticRenderFns } from \"./LogoAnimationSl.vue?vue&type=template&id=a2cc2db6&\"\nimport script from \"./LogoAnimationSl.vue?vue&type=script&lang=js&\"\nexport * from \"./LogoAnimationSl.vue?vue&type=script&lang=js&\"\n\n\n/* normalize component */\nimport normalizer from \"!../../../node_modules/vue-loader/lib/runtime/componentNormalizer.js\"\nvar component = normalizer(\n  script,\n  render,\n  staticRenderFns,\n  false,\n  null,\n  null,\n  null\n  \n)\n\ncomponent.options.__file = \"LogoAnimationSl.vue\"\nexport default component.exports","<template>\r\n\r\n  <div class=\"homepage\">\r\n    <homepage-navigation/>\r\n\r\n    <div id=\"hero\">\r\n      <div class=\"hero-background-image text-center\">\r\n        <img :src=\"require('@/images/New_homepage/Group_homepage.svg')\" alt=\"Pozadinska slika 1.1\">\r\n      </div>\r\n\r\n      <div class=\"hero-content\">\r\n        <div class=\"flex text-center\">\r\n          <div class=\"row row-first\">\r\n            <div v-if=\"language === 'en'\">\r\n              <logo-animation-en />\r\n            </div>\r\n\t\t\t<div v-if=\"language === 'sl'\">\r\n\t\t\t\t<logo-animation-sl />\r\n\t\t\t</div>\r\n            <div v-else-if=\"language === 'hr' || language === null\">\r\n              <logo-animation-hr />\r\n            </div>\r\n          </div>\r\n          <div class=\"row\">\r\n            <p class=\"homepage-hero-text\" v-html=\"$t('homepage.intro')\"></p>\r\n          </div>\r\n          <div class=\"row\">\r\n            <div>\r\n              <router-link to=\"/chapter-literature\" class=\"btn btn-large btn-green\" data-text=\"→\">\r\n                <div>{{ $t('chapters_button') }}</div>\r\n              </router-link>\r\n            </div>\r\n          </div>\r\n          <div class=\"row\">\r\n            <div class=\"hero-background-footer-image text-center\">\r\n              <img :src=\"require('@/images/New_homepage/Group_homepage_mobile.svg')\" alt=\"Pozadinska slika 1.2\">\r\n            </div>\r\n          </div>\r\n        </div>\r\n      </div>\r\n    </div>\r\n\r\n    <div id=\"about\">\r\n      <div class=\"container\">\r\n        <div class=\"about-title text-center\">\r\n          <h2 class=\"homepage-title\" v-html=\"$t('about')\"></h2>\r\n        </div>\r\n        <div class=\"flex\">\r\n          <div class=\"col col-left\">\r\n            <p class=\"homepage-sections-text\" v-html=\"$t('homepage.about_section.1')\"></p>\r\n            <p class=\"homepage-sections-text\" v-html=\"$t('homepage.about_section.2')\"></p>\r\n            <p class=\"homepage-sections-text\" v-html=\"$t('homepage.about_section.3')\"></p>\r\n            <p class=\"homepage-sections-text\" v-html=\"$t('homepage.about_section.4')\"></p>\r\n          </div>\r\n          <div class=\"col col-right\">\r\n            <p class=\"homepage-sections-text\" v-html=\"$t('homepage.about_section.5')\"></p>\r\n            <p class=\"homepage-sections-text\" v-html=\"$t('homepage.about_section.6')\"></p>\r\n            <p class=\"homepage-sections-text\" v-html=\"$t('homepage.about_section.7')\"></p>\r\n            <p class=\"homepage-sections-text\" v-html=\"$t('homepage.about_section.8')\"></p>\r\n          </div>\r\n        </div>\r\n      </div>\r\n    </div>\r\n\r\n    <div id=\"contact\">\r\n      <div class=\"contact-background-mobile-image text-center\">\r\n        <img :src=\"require('@/images/New_homepage/Group_homepage2_mobile.svg')\" alt=\"Pozadinska slika 2.2\">\r\n      </div>\r\n\r\n      <div class=\"contact-background-image text-center\">\r\n        <img :src=\"require('@/images/New_homepage/Group2_homepage.svg')\" alt=\"Pozadinska slika 2.1\">\r\n      </div>\r\n\r\n      <div id=\"contactTitle\" class=\"contact-title text-center\">\r\n        <h2 class=\"homepage-title\"  v-html=\"$t('contact')\"></h2>\r\n      </div>\r\n\r\n      <div class=\"contact-content\">\r\n        <p class=\"homepage-sections-intro\" v-html=\"$t('homepage.contact.1')\"></p>\r\n        <p class=\"homepage-sections-text\" v-html=\"$t('homepage.contact.2')\"></p>\r\n\r\n        <a href=\"mailto:gp.surs@gov.si\" class=\"contact-btn-wrapper\">\r\n          <button type=\"button\" class=\"btn btn-small btn-orange\" data-text=\"→\" href=\"mailto:gp.surs@gov.si\">\r\n            <div>{{ $t('homepage.contact.3') }}</div>\r\n          </button>\r\n        </a>\r\n\r\n        <div class=\"socials\">\r\n          <a :href=\"$t('socials.facebook')\" target=\"_blank\" title=\"Facebook\" rel=\"noopener noreferrer\">\r\n            <span class=\"icon facebook-icon\"></span>\r\n          </a>\r\n          <a :href=\"$t('socials.instagram')\" target=\"_blank\" title=\"Instagram\" rel=\"noopener noreferrer\">\r\n            <span class=\"icon instagram-icon\"></span>\r\n          </a>\r\n          <a :href=\"$t('socials.youtube')\" target=\"_blank\" title=\"Youtube\" rel=\"noopener noreferrer\">\r\n            <span class=\"icon youtube-icon\"></span>\r\n          </a>\r\n          <!--<a :href=\"$t('socials.linkedin')\" target=\"_blank\" title=\"LinkedIn social icon\" rel=\"noopener noreferrer\">\r\n            <span class=\"icon linkedin-icon\"></span>\r\n          </a>\r\n          <a :href=\"$t('socials.github')\" target=\"_blank\" title=\"Github social icon\" rel=\"noopener noreferrer\">\r\n            <span class=\"icon github-icon\"></span>\r\n          </a>-->\r\n        </div>\r\n      </div>\r\n\r\n      <div class=\"contact-background-mobile-image text-center\">\r\n        <img :src=\"require('@/images/New_homepage/Group_homepage3_mobile.png')\" alt=\"Pozadinska slika 2.3\">\r\n      </div>\r\n    </div>\r\n\r\n    <footer id=\"footer\">\r\n      <div class=\"flex\">\r\n        <div class=\"col\">\r\n            <div>\r\n                <span> <router-link to=\"/STEDy-and-cookies\" class=\"footer-small-text\" v-html=\"$t('homepage.footer.1')\"></router-link> | <router-link to=\"/accessibility\" class=\"footer-small-text\" v-html=\"$t('homepage.footer.5')\"></router-link> <br> &copy; {{ new Date().toISOString().slice(0, 4) }} <a href=\"https://www.dzs.hr/\" target=\"_blank\" rel=\"noopener noreferrer\" v-html=\"$t('homepage.footer.2')\"></a></span>\r\n            </div>\r\n        </div>\r\n        <div class=\"col col-center\">\r\n          <div class=\"footer-logos\">\r\n            <div>\r\n              <a v-if=\"language == 'sl'\" href=\"https://www.stat.si/statweb\"><img :src=\"require('../images/Homepage/logo_surs_sl.svg')\" alt=\"SURS logo\"></a>\r\n              <a v-if=\"language == 'en'\" href=\"https://www.stat.si/StatWeb/en\"><img :src=\"require('../images/Homepage/logo_surs.svg')\" alt=\"SURS logo\"></a>\r\n              <a href=\"https://www.dzs.hr/\"><img :src=\"require('../images/Homepage/dzs_logo@2x.svg')\" alt=\"DZS logo\"></a>\r\n              <a href=\"https://ec.europa.eu/eurostat\"><img :src=\"require('../images/Homepage/eurostat_logo@2x.svg')\" alt=\"Eurostat logo\"></a>\r\n            </div>\r\n            <div>\r\n              <span class=\"footer-smaller-text\" v-html=\"$t('homepage.footer.3')\"></span>\r\n            </div>\r\n          </div>\r\n        </div>\r\n        <div class=\"col col-end\">\r\n          <div>\r\n            <!--<a class=\"footer-small-text github-link\" href=\"#\">\r\n              <span class=\"icon github-icon\"></span>\r\n              <span v-html=\"$t('homepage.footer.4')\"></span>\r\n            </a>-->\r\n          </div>\r\n        </div>\r\n      </div>\r\n    </footer>\r\n\r\n  </div>\r\n</template>\r\n\r\n<script>\r\nimport HomepageNavigation from '@/components/HomepageNavigation'\r\nimport LogoAnimationEn from '@/images/Homepage/LogoAnimationEn'\r\nimport LogoAnimationHr from '@/images/Homepage/LogoAnimationHr'\r\nimport LogoAnimationSl from '@/images/Homepage/LogoAnimationSl'\r\n\r\nexport default {\r\n  name: 'home',\r\n  components: {\r\n    HomepageNavigation,\r\n    LogoAnimationEn,\r\n    LogoAnimationHr,\r\n\tLogoAnimationSl\r\n  },\r\n  computed: {\r\n    currentLanguage () {\r\n      return this.$i18n.locale\r\n    }\r\n  },\r\n  data() {\r\n    return {\r\n      language: null\r\n    }\r\n  },\r\n  beforeMount() {\r\n    this.language = this.$i18n.locale\r\n    document.title = this.$t('title_tag.homepage')\r\n  },\r\n  updated() {\r\n    this.language = this.$i18n.locale\r\n  },\r\n  metaInfo() {\r\n    return {\r\n      meta: [\r\n        {name: 'description', content: this.$t('meta_content.homepage')}\r\n      ]\r\n    }\r\n  }\r\n}\r\n</script>\r\n\r\n<style lang=\"scss\" scoped>\r\n.row-first {\r\n  @media (max-width: 765px) {\r\n    width: inherit !important;\r\n  }\r\n}\r\n</style>\r\n","import mod from \"-!../../node_modules/cache-loader/dist/cjs.js??ref--12-0!../../node_modules/thread-loader/dist/cjs.js!../../node_modules/babel-loader/lib/index.js!../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Home.vue?vue&type=script&lang=js&\"; export default mod; export * from \"-!../../node_modules/cache-loader/dist/cjs.js??ref--12-0!../../node_modules/thread-loader/dist/cjs.js!../../node_modules/babel-loader/lib/index.js!../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Home.vue?vue&type=script&lang=js&\"","import { render, staticRenderFns } from \"./Home.vue?vue&type=template&id=da914d72&scoped=true&\"\nimport script from \"./Home.vue?vue&type=script&lang=js&\"\nexport * from \"./Home.vue?vue&type=script&lang=js&\"\nimport style0 from \"./Home.vue?vue&type=style&index=0&id=da914d72&lang=scss&scoped=true&\"\n\n\n/* normalize component */\nimport normalizer from \"!../../node_modules/vue-loader/lib/runtime/componentNormalizer.js\"\nvar component = normalizer(\n  script,\n  render,\n  staticRenderFns,\n  false,\n  null,\n  \"da914d72\",\n  null\n  \n)\n\ncomponent.options.__file = \"Home.vue\"\nexport default component.exports","import Vue from 'vue'\r\nimport Router from 'vue-router'\r\nimport store from './store';\r\n\r\nimport Home from './views/Home.vue'\r\n\r\nVue.use(Router)\r\n\r\nconst router = new Router({\r\n  mode: 'history',\r\n  base: process.env.BASE_URL,\r\n  routes: [\r\n    {\r\n      path: '/',\r\n      name: 'home',\r\n      component: Home,\r\n      meta: {\r\n        title: \"translation.('meta_content.homepage')\"\r\n      }\r\n    },\r\n    {\r\n      path: '/chapter-literature',\r\n      name: 'chapter-literature',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/ChapterLiterature.vue')\r\n    },\r\n    {\r\n      path: '/about',\r\n      name: 'about',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/About.vue')\r\n    },\r\n    {\r\n      //path: '/privacy-policy',\r\n      //name: 'privacy-policy',\r\n      path: '/STEDy-and-cookies',\r\n      name: 'STEDy-and-policy',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/PrivacyPolicy.vue')\r\n    },\r\n    // lessons\r\n    {\r\n      path: '/opisivanje-podataka/podaci',\r\n      name: 'opisivanje-podataka-podaci',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/1-opisivanje-podataka/1-1-podaci.vue')\r\n    },\r\n    {\r\n      path: '/opisivanje-podataka/podaci/zadatak',\r\n      name: 'opisivanje-podataka-podaci-zadatak',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/1-opisivanje-podataka/1-1-podaci-zadatak.vue')\r\n    },\r\n    {\r\n      path: '/slucajna-varijabla/slucajna-varijabla',\r\n      name: 'slucajna-varijabla-slucajna-varijabla',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/3-slucajna-varijabla/3-1-slucajna-varijabla.vue')\r\n    },\r\n    {\r\n      path: '/slucajna-varijabla/slucajna-varijabla/zadatak',\r\n      name: 'slucajna-varijabla-slucajna-varijabla-zadatak-1',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/3-slucajna-varijabla/3-1-slucajna-varijabla-zadatak-1.vue')\r\n    },\r\n    {\r\n      path: '/slucajna-varijabla/diskretna-slucajna-varijabla',\r\n      name: 'slucajna-varijabla-diskretna-slucajna-varijabla',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/3-slucajna-varijabla/3-2-diskretna-slucajna-varijabla.vue')\r\n    },\r\n    {\r\n      path: '/slucajna-varijabla/diskretna-slucajna-varijabla/zadatak',\r\n      name: 'slucajna-varijabla-diskretna-slucajna-varijabla-zadatak-1',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/3-slucajna-varijabla/3-2-diskretna-slucajna-varijabla-zadatak-1.vue')\r\n    },\r\n    {\r\n      path: '/slucajna-varijabla/neprekidna-slucajna-varijabla',\r\n      name: 'slucajna-varijabla-neprekidna-slucajna-varijabla',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/3-slucajna-varijabla/3-3-neprekidna-slucajna-varijabla.vue')\r\n    },\r\n    {\r\n      path: '/slucajna-varijabla/neprekidna-slucajna-varijabla/zadatak',\r\n      name: 'slucajna-varijabla-neprekidna-slucajna-varijabla-zadatak-1',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/3-slucajna-varijabla/3-3-neprekidna-slucajna-varijabla-zadatak-1.vue')\r\n    },\r\n    {\r\n      path: '/slucajna-varijabla/funkcija-distribucije',\r\n      name: 'slucajna-varijabla-funkcija-distribucije',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/3-slucajna-varijabla/3-4-funkcija-distribucije.vue')\r\n    },\r\n    {\r\n      path: '/slucajna-varijabla/ocekivanje',\r\n      name: 'slucajna-varijabla-ocekivanje',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/3-slucajna-varijabla/3-5-ocekivanje.vue')\r\n    },\r\n    {\r\n      path: '/slucajna-varijabla/ocekivanje/dodatni-zadaci',\r\n      name: 'slucajna-varijabla-ocekivanje-dodatni-zadaci',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/3-slucajna-varijabla/3-5-ocekivanje-dodatni-zadaci.vue')\r\n    },\r\n    {\r\n      path: '/slucajna-varijabla/varijanca-i-standardna-devijacija',\r\n      name: 'slucajna-varijabla-varijanca-i-standardna-devijacija',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/3-slucajna-varijabla/3-6-varijanca-i-standardna-devijacija.vue')\r\n    },\r\n    {\r\n      path: '/slucajna-varijabla/varijanca-i-standardna-devijacija/zadatak',\r\n      name: 'slucajna-varijabla-varijanca-i-standardna-devijacija-zadatak-1',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/3-slucajna-varijabla/3-6-varijanca-i-standardna-devijacija-zadatak-1.vue')\r\n    },\r\n    {\r\n      path: '/distribucije/bernoulijeva-distribucija',\r\n      name: 'distribucije-bernoulijeva-distribucija',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/4-distribucije/4-1-bernoulijeva-distribucija.vue')\r\n    },\r\n    {\r\n      path: '/distribucije/bernoulijeva-distribucija/zadatak',\r\n      name: 'distribucije-bernoulijeva-distribucija-zadatak-1',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/4-distribucije/4-1-bernoulijeva-distribucija-zadatak-1.vue')\r\n    },\r\n    {\r\n      path: '/distribucije/binomna-distribucija',\r\n      name: 'distribucije-binomna-distribucija',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/4-distribucije/4-2-binomna-distribucija.vue')\r\n    },\r\n    {\r\n      path: '/distribucije/binomna-distribucija/zadatak',\r\n      name: 'distribucije-binomna-distribucija-zadatak-1',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/4-distribucije/4-2-binomna-distribucija-zadatak-1.vue')\r\n    },\r\n    {\r\n      path: '/distribucije/uniformna-distribucija',\r\n      name: 'distribucije-uniformna-distribucija',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/4-distribucije/4-3-uniformna-distribucija.vue')\r\n    },\r\n    {\r\n      path: '/distribucije/uniformna-distribucija/zadatak',\r\n      name: 'distribucije-uniformna-distribucija-zadatak-1',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/4-distribucije/4-3-uniformna-distribucija-zadatak-1.vue')\r\n    },\r\n    {\r\n      path: '/distribucije/normalna-distribucija',\r\n      name: 'distribucije-normalna-distribucija',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/4-distribucije/4-4-normalna-distribucija.vue')\r\n    },\r\n    {\r\n      path: '/distribucije/normalna-distribucija/zadatak',\r\n      name: 'distribucije-normalna-distribucija-zadatak-1',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/4-distribucije/4-4-normalna-distribucija-zadatak-1.vue')\r\n    },\r\n    {\r\n      path: '/distribucije/distribucija',\r\n      name: 'distribucije-distribucija',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/4-distribucije/4-5-distribucija.vue')\r\n    },\r\n    {\r\n      path: '/distribucije/studentova-t-distribucija',\r\n      name: 'distribucije-studentova-t-distribucija',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/4-distribucije/4-6-studentova-t-distribucija.vue')\r\n    },\r\n    {\r\n      path: '/statisticko-zakljucivanje/populacija-i-uzorak',\r\n      name: 'statisticko-zakljucivanje-populacija-i-uzorak',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/5-statisticko-zakljucivanje/5-1-populacija-i-uzorak.vue')\r\n    },\r\n    {\r\n      path: '/statisticko-zakljucivanje/populacija-i-uzorak/zadatak',\r\n      name: 'statisticko-zakljucivanje-populacija-i-uzorak-zadatak-1',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/5-statisticko-zakljucivanje/5-1-populacija-i-uzorak-zadatak-1.vue')\r\n    },\r\n    {\r\n      path: '/statisticko-zakljucivanje/procjena-proporcije-vjerojatnosti',\r\n      name: 'statisticko-zakljucivanje-procjena-proporcije-vjerojatnosti',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/5-statisticko-zakljucivanje/5-2-procjena-proporcije-vjerojatnosti.vue')\r\n    },\r\n    {\r\n      path: '/statisticko-zakljucivanje/procjena-proporcije-vjerojatnosti/zadatak-1',\r\n      name: 'statisticko-zakljucivanje-procjena-proporcije-vjerojatnosti-zadatak-1',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/5-statisticko-zakljucivanje/5-2-procjena-proporcije-vjerojatnosti-zadatak-1.vue')\r\n    },\r\n    {\r\n      path: '/statisticko-zakljucivanje/procjena-ocekivanja-i-varijance',\r\n      name: 'statisticko-zakljucivanje-procjena-ocekivanja-i-varijance',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/5-statisticko-zakljucivanje/5-3-procjena-ocekivanja-i-varijance.vue')\r\n    },\r\n    {\r\n      path: '/statisticko-zakljucivanje/pouzdani-interval-za-ocekivanje',\r\n      name: 'statisticko-zakljucivanje-pouzdani-interval-za-ocekivanje',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/5-statisticko-zakljucivanje/5-4-pouzdani-interval-za-ocekivanje.vue')\r\n    },\r\n    {\r\n      path: '/statisticko-zakljucivanje/pouzdani-interval-za-ocekivanje/zadatak',\r\n      name: 'statisticko-zakljucivanje-pouzdani-interval-za-ocekivanje-zadatak-1',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/5-statisticko-zakljucivanje/5-4-pouzdani-interval-za-ocekivanje-zadatak-1.vue')\r\n    },\r\n{\r\n      path: '/statisticko-zakljucivanje/pouzdan-interval-za-procjenu-i-vjerojatnost',\r\n      name: 'statisticko-zakljucivanje-pouzdan-interval-za-procjenu-i-vjerojatnost',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/5-statisticko-zakljucivanje/5-5-pouzdan-interval-za-procjenu-i-vjerojatnost.vue')\r\n    }, {\r\n      path: '/statisticko-zakljucivanje/pouzdan-interval-za-procjenu-i-vjerojatnost/zadatak',\r\n      name: 'statisticko-zakljucivanje-pouzdan-interval-za-procjenu-i-vjerojatnost-zadatak',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/5-statisticko-zakljucivanje/5-5-pouzdan-interval-za-procjenu-i-vjerojatnost-zadatak.vue')\r\n    }, {\r\n      path: '/statisticko-zakljucivanje/testiranje-statistickih-hipoteza',\r\n      name: 'statisticko-zakljucivanje-testiranje-statistickih-hipoteza',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/5-statisticko-zakljucivanje/5-6-testiranje-statistickih-hipoteza.vue')\r\n    }, {\r\n      path: '/statisticko-zakljucivanje/testiranje-statistickih-hipoteza/zadatak',\r\n      name: 'statisticko-zakljucivanje-testiranje-statistickih-hipoteza-zadatak',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/5-statisticko-zakljucivanje/5-6-testiranje-statistickih-hipoteza-zadatak.vue')\r\n    }, {\r\n      path: '/statisticko-zakljucivanje/jednostavna-linearna-regresija',\r\n      name: 'statisticko-zakljucivanje-jednostavna-linearna-regresija',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/5-statisticko-zakljucivanje/5-7-jednostavna-linearna-regresija.vue')\r\n    },\r\n    {\r\n      path: '/opisivanje-podataka/frekvencije-i-relativne-frekvencije',\r\n      name: 'opisivanje-podataka-frekvencije-i-relativne-frekvencije',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/1-opisivanje-podataka/1-2-frekvencije-i-relativne-frekvencije.vue')\r\n    },{\r\n      path: '/opisivanje-podataka/frekvencije-i-relativne-frekvencije/zadatak',\r\n      name: 'opisivanje-podataka-frekvencije-i-relativne-frekvencije-zadatak',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/1-opisivanje-podataka/1-2-frekvencije-i-relativne-frekvencije-zadatak.vue')\r\n    },{\r\n      path: '/opisivanje-podataka/stupicasti-dijagram-i-histogram',\r\n      name: 'opisivanje-podataka-stupicasti-dijagram-i-histogram',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/1-opisivanje-podataka/1-3-stupicasti-dijagram-i-histogram.vue')\r\n    },{\r\n      path: '/opisivanje-podataka/stupicasti-dijagram-i-histogram/zadatak',\r\n      name: 'opisivanje-podataka-stupicasti-dijagram-i-histogram-zadatak',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/1-opisivanje-podataka/1-3-stupicasti-dijagram-i-histogram-zadatak.vue')\r\n    }, {\r\n      path: '/opisivanje-podataka/prosjek',\r\n      name: 'opisivanje-podataka-prosjek',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/1-opisivanje-podataka/1-4-prosjek.vue')\r\n    }, {\r\n      path: '/opisivanje-podataka/prosjek/zadatak',\r\n      name: 'opisivanje-podataka-prosjek-zadatak',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/1-opisivanje-podataka/1-4-prosjek-zadatak.vue')\r\n    }, {\r\n      path: '/opisivanje-podataka/medijan',\r\n      name: 'opisivanje-podataka-medijan',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/1-opisivanje-podataka/1-5-medijan.vue')\r\n    }, {\r\n      path: '/opisivanje-podataka/medijan/zadatak',\r\n      name: 'opisivanje-podataka-medijan-zadatak',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/1-opisivanje-podataka/1-5-medijan-zadatak.vue')\r\n    }, {\r\n      path: '/opisivanje-podataka/minimum-maksimum-i-raspon',\r\n      name: 'opisivanje-podataka-minimum-maksimum-i-raspon',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/1-opisivanje-podataka/1-6-minimum-maksimum-i-raspon.vue')\r\n    }, {\r\n      path: '/opisivanje-podataka/minimum-maksimum-i-raspon/zadatak',\r\n      name: 'opisivanje-podataka-minimum-maksimum-i-raspon-zadatak',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/1-opisivanje-podataka/1-6-minimum-maksimum-i-raspon-zadatak.vue')\r\n    }, {\r\n      path: '/opisivanje-podataka/kvartili-i-interkvartilni-raspon',\r\n      name: 'opisivanje-podataka-kvartili-i-interkvartilni-raspon',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/1-opisivanje-podataka/1-7-kvartili-i-interkvartilni-raspon.vue')\r\n    }, {\r\n      path: '/opisivanje-podataka/kvartili-i-interkvartilni-raspon/zadatak',\r\n      name: 'opisivanje-podataka-kvartili-i-interkvartilni-raspon-zadatak',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/1-opisivanje-podataka/1-7-kvartili-i-interkvartilni-raspon-zadatak.vue')\r\n    }, {\r\n      path: '/opisivanje-podataka/kvartili-i-interkvartilni-raspon/dodatni-zadaci',\r\n      name: 'opisivanje-podataka-kvartili-i-interkvartilni-raspon-dodatni-zadaci',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/1-opisivanje-podataka/1-7-kvartili-i-interkvartilni-raspon-dodatni-zadaci.vue')\r\n    }, {\r\n      path: '/opisivanje-podataka/varijanca-i-standardna-devijacija',\r\n      name: 'opisivanje-podataka-varijanca-i-standardna-devijacija',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/1-opisivanje-podataka/1-8-varijanca-i-standardna-devijacija.vue')\r\n    }, {\r\n      path: '/opisivanje-podataka/varijanca-i-standardna-devijacija/zadatak',\r\n      name: 'opisivanje-podataka-varijanca-i-standardna-devijacija-zadatak',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/1-opisivanje-podataka/1-8-varijanca-i-standardna-devijacija-zadatak.vue')\r\n    }, {\r\n      path: '/opisivanje-podataka/kutijasti-dijagram',\r\n      name: 'opisivanje-podataka-kutijasti-dijagram',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/1-opisivanje-podataka/1-9-kutijasti-dijagram.vue')\r\n    }, {\r\n      path: '/opisivanje-podataka/kutijasti-dijagram/zadatak',\r\n      name: 'opisivanje-podataka-kutijasti-dijagram-zadatak',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/1-opisivanje-podataka/1-9-kutijasti-dijagram-zadatak.vue')\r\n    }, {\r\n      path: '/opisivanje-podataka/dijagram-rasprsenosti-i-standardna-devijacija',\r\n      name: 'opisivanje-podataka-dijagram-rasprsenosti-i-standardna-devijacija',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/1-opisivanje-podataka/1-10-dijagram-rasprsenosti-i-standardna-devijacija.vue')\r\n    }, {\r\n      path: '/opisivanje-podataka/dijagram-rasprsenosti-i-standardna-devijacija/zadatak',\r\n      name: 'opisivanje-podataka-dijagram-rasprsenosti-i-standardna-devijacija-zadatak',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/1-opisivanje-podataka/1-10-dijagram-rasprsenosti-i-standardna-devijacija-zadatak.vue')\r\n    }, {\r\n      path: '/osnove-vjerojatnosti/vjerojatnost',\r\n      name: 'osnove-vjerojatnosti-vjerojatnost',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/2-osnove-vjerojatnosti/2-1-vjerojatnost.vue')\r\n    }, {\r\n      path: '/osnove-vjerojatnosti/vjerojatnost/zadatak',\r\n      name: 'osnove-vjerojatnosti-vjerojatnost-zadatak',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/2-osnove-vjerojatnosti/2-1-vjerojatnost-zadatak.vue')\r\n    }, {\r\n      path: '/osnove-vjerojatnosti/uvjetna-vjerojatnost',\r\n      name: 'osnove-vjerojatnosti-uvjetna-vjerojatnost',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/2-osnove-vjerojatnosti/2-2-uvjetna-vjerojatnost.vue')\r\n    }, {\r\n      path: '/osnove-vjerojatnosti/uvjetna-vjerojatnost/zadatak',\r\n      name: 'osnove-vjerojatnosti-uvjetna-vjerojatnost-zadatak',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/2-osnove-vjerojatnosti/2-2-uvjetna-vjerojatnost-zadatak.vue')\r\n    }, {       \r\n      path: '/accessibility',\r\n      name: 'accessibility',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/Accessibility.vue')\r\n\t},\r\n\r\n\r\n\r\n\r\n    //mathjax example\r\n    {\r\n      path: '/mathjax-example',\r\n      name: 'mathjax-example',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/Mathjax.vue')\r\n    },\r\n\r\n\r\n\r\n    // chapters\r\n    {\r\n      path: '/opisivanje-podataka/',\r\n      name: 'opisivanje-podataka',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/1-opisivanje-podataka/Index.vue')\r\n    },\r\n    {\r\n      path: '/osnove-vjerojatnosti/',\r\n      name: 'osnove-vjerojatnosti',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/2-osnove-vjerojatnosti/Index.vue')\r\n    },\r\n    {\r\n      path: '/slucajna-varijabla/',\r\n      name: 'slucajna-varijabla',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/3-slucajna-varijabla/Index.vue')\r\n    },\r\n    {\r\n      path: '/distribucije/',\r\n      name: 'distribucije',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/4-distribucije/Index.vue')\r\n    },\r\n    {\r\n      path: '/statisticko-zakljucivanje/',\r\n      name: 'statisticko-zakljucivanje',\r\n      // route level code-splitting\r\n      // this generates a separate chunk (about.[hash].js) for this route\r\n      // which is lazy-loaded when the route is visited.\r\n      component: () => import(/* webpackChunkName: \"about\" */ './views/lessons/5-statisticko-zakljucivanje/Index.vue')\r\n    }\r\n\r\n  ],\r\n  scrollBehavior() {\r\n    return { x: 0, y: 0 };\r\n  }\r\n})\r\n\r\nwindow.localStorage.setItem('isReloaded', 'false')\r\n\r\nrouter.beforeEach((to, from, next) => {\r\n  store.commit('toggleLoader', true)\r\n  next()\r\n})\r\n\r\nrouter.afterEach((to, from) => {\r\n  setTimeout(() => store.commit('toggleLoader', false), 500)\r\n})\r\n\r\nrouter.afterEach((to, from) => {\r\n\tdocument.title = to.meta.title;\r\n});\r\n\r\n// SURS, fix da je ime aplikacije neodvisno od velikosti crk\r\nif (router.mode === 'history'){\r\n  router.history.getCurrentLocation = function() {\r\n    let path = window.location.pathname\r\n    let base = router.history.base\r\n\t\r\n\t// Removes base from path (case-insensitive)\r\n    if (base && path.toLowerCase().indexOf(base.toLowerCase()) === 0) {\r\n      path = path.slice(base.length)\r\n    }\r\n\t\r\n    return (path || '/') + window.location.search + window.location.hash\r\n  }\r\n}\r\n// SURS\r\n\r\nexport default router;\r\n","module.exports = __webpack_public_path__ + \"img/logo_surs.019f7731.svg\";","var map = {\n\t\"./af\": \"2bfb\",\n\t\"./af.js\": \"2bfb\",\n\t\"./ar\": \"8e73\",\n\t\"./ar-dz\": \"a356\",\n\t\"./ar-dz.js\": \"a356\",\n\t\"./ar-kw\": \"423e\",\n\t\"./ar-kw.js\": \"423e\",\n\t\"./ar-ly\": \"1cfd\",\n\t\"./ar-ly.js\": \"1cfd\",\n\t\"./ar-ma\": \"0a84\",\n\t\"./ar-ma.js\": \"0a84\",\n\t\"./ar-sa\": \"8230\",\n\t\"./ar-sa.js\": \"8230\",\n\t\"./ar-tn\": \"6d83\",\n\t\"./ar-tn.js\": \"6d83\",\n\t\"./ar.js\": \"8e73\",\n\t\"./az\": \"485c\",\n\t\"./az.js\": \"485c\",\n\t\"./be\": \"1fc1\",\n\t\"./be.js\": \"1fc1\",\n\t\"./bg\": \"84aa\",\n\t\"./bg.js\": \"84aa\",\n\t\"./bm\": \"a7fa\",\n\t\"./bm.js\": \"a7fa\",\n\t\"./bn\": \"9043\",\n\t\"./bn.js\": \"9043\",\n\t\"./bo\": \"d26a\",\n\t\"./bo.js\": \"d26a\",\n\t\"./br\": \"6887\",\n\t\"./br.js\": 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\"d6b6\",\n\t\"./hy-am.js\": \"d6b6\",\n\t\"./id\": \"5038\",\n\t\"./id.js\": \"5038\",\n\t\"./is\": \"0558\",\n\t\"./is.js\": \"0558\",\n\t\"./it\": \"6e98\",\n\t\"./it.js\": \"6e98\",\n\t\"./ja\": \"079e\",\n\t\"./ja.js\": \"079e\",\n\t\"./jv\": \"b540\",\n\t\"./jv.js\": \"b540\",\n\t\"./ka\": \"201b\",\n\t\"./ka.js\": \"201b\",\n\t\"./kk\": \"6d79\",\n\t\"./kk.js\": \"6d79\",\n\t\"./km\": \"e81d\",\n\t\"./km.js\": \"e81d\",\n\t\"./kn\": \"3e92\",\n\t\"./kn.js\": \"3e92\",\n\t\"./ko\": \"22f8\",\n\t\"./ko.js\": \"22f8\",\n\t\"./ky\": \"9609\",\n\t\"./ky.js\": \"9609\",\n\t\"./lb\": \"440c\",\n\t\"./lb.js\": \"440c\",\n\t\"./lo\": \"b29d\",\n\t\"./lo.js\": \"b29d\",\n\t\"./lt\": \"26f9\",\n\t\"./lt.js\": \"26f9\",\n\t\"./lv\": \"b97c\",\n\t\"./lv.js\": \"b97c\",\n\t\"./me\": \"293c\",\n\t\"./me.js\": \"293c\",\n\t\"./mi\": \"688b\",\n\t\"./mi.js\": \"688b\",\n\t\"./mk\": \"6909\",\n\t\"./mk.js\": \"6909\",\n\t\"./ml\": \"02fb\",\n\t\"./ml.js\": \"02fb\",\n\t\"./mn\": \"958b\",\n\t\"./mn.js\": \"958b\",\n\t\"./mr\": \"39bd\",\n\t\"./mr.js\": \"39bd\",\n\t\"./ms\": \"ebe4\",\n\t\"./ms-my\": \"6403\",\n\t\"./ms-my.js\": \"6403\",\n\t\"./ms.js\": \"ebe4\",\n\t\"./mt\": \"1b45\",\n\t\"./mt.js\": \"1b45\",\n\t\"./my\": \"8689\",\n\t\"./my.js\": \"8689\",\n\t\"./nb\": \"6ce3\",\n\t\"./nb.js\": \"6ce3\",\n\t\"./ne\": \"3a39\",\n\t\"./ne.js\": \"3a39\",\n\t\"./nl\": \"facd\",\n\t\"./nl-be\": \"db29\",\n\t\"./nl-be.js\": \"db29\",\n\t\"./nl.js\": \"facd\",\n\t\"./nn\": \"b84c\",\n\t\"./nn.js\": \"b84c\",\n\t\"./pa-in\": \"f3ff\",\n\t\"./pa-in.js\": \"f3ff\",\n\t\"./pl\": \"8d57\",\n\t\"./pl.js\": \"8d57\",\n\t\"./pt\": \"f260\",\n\t\"./pt-br\": \"d2d4\",\n\t\"./pt-br.js\": \"d2d4\",\n\t\"./pt.js\": \"f260\",\n\t\"./ro\": \"972c\",\n\t\"./ro.js\": \"972c\",\n\t\"./ru\": \"957c\",\n\t\"./ru.js\": \"957c\",\n\t\"./sd\": \"6784\",\n\t\"./sd.js\": \"6784\",\n\t\"./se\": \"ffff\",\n\t\"./se.js\": \"ffff\",\n\t\"./si\": \"eda5\",\n\t\"./si.js\": \"eda5\",\n\t\"./sk\": \"7be6\",\n\t\"./sk.js\": \"7be6\",\n\t\"./sl\": \"8155\",\n\t\"./sl.js\": \"8155\",\n\t\"./sq\": \"c8f3\",\n\t\"./sq.js\": \"c8f3\",\n\t\"./sr\": \"cf1e\",\n\t\"./sr-cyrl\": \"13e9\",\n\t\"./sr-cyrl.js\": \"13e9\",\n\t\"./sr.js\": \"cf1e\",\n\t\"./ss\": \"52bd\",\n\t\"./ss.js\": \"52bd\",\n\t\"./sv\": \"5fbd\",\n\t\"./sv.js\": \"5fbd\",\n\t\"./sw\": \"74dc\",\n\t\"./sw.js\": \"74dc\",\n\t\"./ta\": \"3de5\",\n\t\"./ta.js\": \"3de5\",\n\t\"./te\": \"5cbb\",\n\t\"./te.js\": \"5cbb\",\n\t\"./tet\": \"576c\",\n\t\"./tet.js\": \"576c\",\n\t\"./tg\": \"3b1b\",\n\t\"./tg.js\": \"3b1b\",\n\t\"./th\": \"10e8\",\n\t\"./th.js\": \"10e8\",\n\t\"./tl-ph\": \"0f38\",\n\t\"./tl-ph.js\": \"0f38\",\n\t\"./tlh\": \"cf75\",\n\t\"./tlh.js\": \"cf75\",\n\t\"./tr\": \"0e81\",\n\t\"./tr.js\": \"0e81\",\n\t\"./tzl\": \"cf51\",\n\t\"./tzl.js\": \"cf51\",\n\t\"./tzm\": \"c109\",\n\t\"./tzm-latn\": \"b53d\",\n\t\"./tzm-latn.js\": \"b53d\",\n\t\"./tzm.js\": \"c109\",\n\t\"./ug-cn\": \"6117\",\n\t\"./ug-cn.js\": \"6117\",\n\t\"./uk\": \"ada2\",\n\t\"./uk.js\": \"ada2\",\n\t\"./ur\": \"5294\",\n\t\"./ur.js\": \"5294\",\n\t\"./uz\": \"2e8c\",\n\t\"./uz-latn\": \"010e\",\n\t\"./uz-latn.js\": \"010e\",\n\t\"./uz.js\": \"2e8c\",\n\t\"./vi\": \"2921\",\n\t\"./vi.js\": \"2921\",\n\t\"./x-pseudo\": \"fd7e\",\n\t\"./x-pseudo.js\": \"fd7e\",\n\t\"./yo\": \"7f33\",\n\t\"./yo.js\": \"7f33\",\n\t\"./zh-cn\": \"5c3a\",\n\t\"./zh-cn.js\": \"5c3a\",\n\t\"./zh-hk\": \"49ab\",\n\t\"./zh-hk.js\": \"49ab\",\n\t\"./zh-tw\": \"90ea\",\n\t\"./zh-tw.js\": \"90ea\"\n};\n\n\nfunction webpackContext(req) {\n\tvar id = webpackContextResolve(req);\n\treturn __webpack_require__(id);\n}\nfunction webpackContextResolve(req) {\n\tvar id = map[req];\n\tif(!(id + 1)) { // check for number or string\n\t\tvar e = new Error(\"Cannot find module '\" + req + \"'\");\n\t\te.code = 'MODULE_NOT_FOUND';\n\t\tthrow e;\n\t}\n\treturn id;\n}\nwebpackContext.keys = function webpackContextKeys() {\n\treturn Object.keys(map);\n};\nwebpackContext.resolve = webpackContextResolve;\nmodule.exports = webpackContext;\nwebpackContext.id = \"4678\";","var render = function () {var _vm=this;var _h=_vm.$createElement;var _c=_vm._self._c||_h;return _c('div',{attrs:{\"id\":\"app\"}},[_c('cookies'),_c('loader',{class:{ 'active': _vm.isLoading }}),_c('transition',{attrs:{\"name\":\"fade\"}},[_c('router-view')],1)],1)}\nvar staticRenderFns = []\n\nexport { render, staticRenderFns }","var render = function () {var _vm=this;var _h=_vm.$createElement;var _c=_vm._self._c||_h;return _vm._m(0)}\nvar staticRenderFns = [function () {var _vm=this;var _h=_vm.$createElement;var _c=_vm._self._c||_h;return _c('div',{staticClass:\"loader\"},[_c('div',{staticClass:\"loader-overlay\"},[_c('div',{staticClass:\"lds-css ng-scope\"},[_c('div',{staticClass:\"lds-bars\",staticStyle:{\"width\":\"100%\",\"height\":\"100%\"}},[_c('div'),_c('div'),_c('div'),_c('div')])])])])}]\n\nexport { render, staticRenderFns }","<template>\r\n  <div class=\"loader\">\r\n    <div class=\"loader-overlay\">\r\n      <div class=\"lds-css ng-scope\">\r\n        <div style=\"width:100%;height:100%\" class=\"lds-bars\">\r\n          <div></div>\r\n          <div></div>\r\n          <div></div>\r\n          <div></div>\r\n        </div>\r\n      </div>\r\n    </div>\r\n  </div>\r\n</template>\r\n\r\n<script>\r\n  export default {\r\n    name: 'loader'\r\n  }\r\n</script>\r\n\r\n<style lang=\"scss\">\r\n.loader {\r\n  display: none;\r\n\r\n  &.active {\r\n    display: block;\r\n  }\r\n}\r\n\r\n.loader-overlay {\r\n  position: fixed;\r\n  top: 0;\r\n  right: 0;\r\n  left: 0;\r\n  bottom: 0;\r\n  z-index: 9999;\r\n  background-color: rgba(0, 0, 0, 0.8);\r\n\r\n  display: flex;\r\n  align-items: center;\r\n  justify-content: center;\r\n}\r\n\r\n@keyframes lds-bars {\r\n  0% {\r\n    opacity: 1;\r\n  }\r\n  50% {\r\n    opacity: 0.5;\r\n  }\r\n  100% {\r\n    opacity: 1;\r\n  }\r\n}\r\n\r\n@-webkit-keyframes lds-bars {\r\n  0% {\r\n    opacity: 1;\r\n  }\r\n  50% {\r\n    opacity: 0.5;\r\n  }\r\n  100% {\r\n    opacity: 1;\r\n  }\r\n}\r\n\r\n.lds-bars {\r\n  position: relative;\r\n}\r\n\r\n.lds-bars div {\r\n  position: absolute;\r\n  width: 35px;\r\n  height: 80px;\r\n  top: 60px;\r\n  -webkit-animation: lds-bars 1s cubic-bezier(0.5, 0, 0.5, 1) infinite;\r\n  animation: lds-bars 1s cubic-bezier(0.5, 0, 0.5, 1) infinite;\r\n}\r\n\r\n.lds-bars div:nth-child(1) {\r\n  left: 30px;\r\n  background: #2EADA7;\r\n  -webkit-animation-delay: -0.6s;\r\n  animation-delay: -0.6s;\r\n}\r\n\r\n.lds-bars div:nth-child(2) {\r\n  left: 70px;\r\n  background: #45348C;\r\n  -webkit-animation-delay: -0.4s;\r\n  animation-delay: -0.4s;\r\n}\r\n\r\n.lds-bars div:nth-child(3) {\r\n  left: 110px;\r\n  background: #F69B1F;\r\n  -webkit-animation-delay: -0.2s;\r\n  animation-delay: -0.2s;\r\n}\r\n\r\n.lds-bars div:nth-child(4) {\r\n  left: 150px;\r\n  background: #EE4269;\r\n}\r\n\r\n.lds-bars {\r\n  width: 200px !important;\r\n  height: 200px !important;\r\n  -webkit-transform: translate(-100px, -100px) scale(1) translate(100px, 100px);\r\n  transform: translate(-100px, -100px) scale(1) translate(100px, 100px);\r\n}\r\n</style>","import mod from \"-!../../node_modules/cache-loader/dist/cjs.js??ref--12-0!../../node_modules/thread-loader/dist/cjs.js!../../node_modules/babel-loader/lib/index.js!../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Loader.vue?vue&type=script&lang=js&\"; export default mod; export * from \"-!../../node_modules/cache-loader/dist/cjs.js??ref--12-0!../../node_modules/thread-loader/dist/cjs.js!../../node_modules/babel-loader/lib/index.js!../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Loader.vue?vue&type=script&lang=js&\"","import { render, staticRenderFns } from \"./Loader.vue?vue&type=template&id=d36962c8&\"\nimport script from \"./Loader.vue?vue&type=script&lang=js&\"\nexport * from \"./Loader.vue?vue&type=script&lang=js&\"\nimport style0 from \"./Loader.vue?vue&type=style&index=0&lang=scss&\"\n\n\n/* normalize component */\nimport normalizer from \"!../../node_modules/vue-loader/lib/runtime/componentNormalizer.js\"\nvar component = normalizer(\n  script,\n  render,\n  staticRenderFns,\n  false,\n  null,\n  null,\n  null\n  \n)\n\ncomponent.options.__file = \"Loader.vue\"\nexport default component.exports","var render = function () {var _vm=this;var _h=_vm.$createElement;var _c=_vm._self._c||_h;return _c('div',{directives:[{name:\"show\",rawName:\"v-show\",value:(_vm.showModel),expression:\"showModel\"}],staticClass:\"cookies-overlay\",on:{\"showCookieModal\":function($event){_vm.howModal($event)}}},[_c('div',{ref:\"cookies\",staticClass:\"cookies-content\"},[_c('p',{staticClass:\"cookies-text\"},[_vm._v(_vm._s(_vm.$t('meta_content.cookies.1'))+\" \\n\\t\\t\\t\"),_c('a',{staticClass:\"cookie-policy\",attrs:{\"href\":\"\"}},[_c('span',[_vm._v(_vm._s(_vm.$t('meta_content.cookies.2')))])])]),_c('div',{staticClass:\"cookies-buttons-container\"},[_c('a',{staticClass:\"btn-no\",attrs:{\"href\":\"#\",\"tabindex\":\"0\"},on:{\"keyup\":function($event){if(!('button' in $event)&&_vm._k($event.keyCode,\"enter\",13,$event.key,\"Enter\")){ return null; }_vm.createCookie(false)},\"click\":function($event){_vm.createCookie(false)}}},[_c('div',[_vm._v(_vm._s(_vm.$t('meta_content.cookies.3')))])]),_c('a',{staticClass:\"btn-yes\",attrs:{\"href\":\"#\",\"tabindex\":\"0\"},on:{\"keyup\":function($event){if(!('button' in $event)&&_vm._k($event.keyCode,\"enter\",13,$event.key,\"Enter\")){ return null; }_vm.createCookie(true)},\"click\":function($event){_vm.createCookie(true)}}},[_c('div',[_vm._v(_vm._s(_vm.$t('meta_content.cookies.4')))])])])])])}\nvar staticRenderFns = []\n\nexport { render, staticRenderFns }","<template>\r\n  <div v-show=\"showModel\" v-on:showCookieModal=\"howModal($event)\" class=\"cookies-overlay\">\r\n    <div class=\"cookies-content\" ref=\"cookies\">\r\n\t\t<p class=\"cookies-text\">{{ $t('meta_content.cookies.1')}} \r\n\t\t\t<a class=\"cookie-policy\" href=\"\"><span>{{ $t('meta_content.cookies.2')}}</span></a>\r\n        </p>  \r\n        <div class=\"cookies-buttons-container\">\r\n            <a href=\"#\" v-on:keyup.enter=\"createCookie(false)\" v-on:click=\"createCookie(false)\" tabindex=\"0\" class=\"btn-no\">\r\n                <div>{{ $t('meta_content.cookies.3')}}</div>\r\n            </a>\r\n            <a href=\"#\" v-on:keyup.enter=\"createCookie(true)\"  v-on:click=\"createCookie(true)\" tabindex=\"0\" class=\"btn-yes\">\r\n                <div>{{ $t('meta_content.cookies.4')}}</div>\r\n            </a>\r\n        </div>\r\n    </div>\r\n  </div>\r\n</template>\r\n\r\n<script> \r\n  export default {\r\n    name: 'cookies',\r\n    data: function(){\r\n        return {\r\n\t\t\tisVisible: false,\r\n\t\t\tallowAnalytics: false,\r\n\t\t}\r\n\t},\r\n    computed: {\r\n        showModel: {\r\n            get(){\r\n\t\t\t\treturn this.isVisible;\r\n\t\t\t},\r\n\t\t\tset(show){\r\n\t\t\t\tthis.isVisible = show;\r\n\t\t\t}\r\n\t\t},\r\n\t\tenableAnalytics: {\r\n\t\t\tget(){\r\n\t\t\t\treturn this.allowAnalytics;\r\n\t\t\t},\r\n\t\t\tset(value){\r\n\t\t\t\tthis.allowAnalytics = value;\r\n\t\t\t}\r\n\t\t}\r\n    },\r\n\tmethods: {\r\n        getCookie(cookieName){\r\n           let allCookies = document.cookie;\r\n           let cookieArray = allCookies.split(';');\r\n           \r\n           for (var i=0; i<cookieArray.length; i++){\r\n                if (cookieArray[i].split('=')[0] == cookieName){\r\n                    return cookieArray[i];\r\n                }\r\n            }\r\n        },\r\n        getCookieValue(cookie){\r\n\t\t\tlet content = cookie.split(\"=\");\r\n\t\t\treturn content[1];\r\n\t\t},\r\n        createCookie(value){\r\n            const date = new Date();\r\n\t\t\t// expires in one year\r\n            date.setTime(date.getTime() + 365*24*60*60*1000);\r\n            const expires = 'expires=' + date.toUTCString();\r\n            document.cookie = 'stat.si.stedy.analytics=' + value + ';' + expires + ';SameSite=Strict';\r\n            this.showModel = false;\r\n\t\r\n\t\t\tif (value == false){\r\n\t\t\t\tthis.deleteScriptTag(\"StedyAnalyticsScript\");\r\n\t\t\t}\t\t\r\n\t\t\tlocation.reload();\r\n\t\t},\r\n\t\tdeleteCookies(cookieName){\r\n\t\t\tlet allCookies = document.cookie;\r\n\t\t\tlet cookieArray = allCookies.split(';');\r\n           \r\n\t\t\tconst date = new Date();\r\n\t\t\tdate.setTime(date.getTime() - 365*24*60*60*1000);\r\n\t\t\tlet expires = \"expires=\" + date.toUTCString();\r\n\t\t\tfor (var i=0; i<cookieArray.length; i++){\r\n\t\t\t\tif (cookieArray[i].split('=')[0] != cookieName){\r\n\t\t\t\t\r\n\t\t\t\t\tlet cname = cookieArray[i].split('=')[0];\t\t\t\t\t\t\r\n\t\t\t\t\tdocument.cookie = cname + \"=;\" + expires + \";\";\r\n\t\t\t\t}\r\n\t\t\t}\r\n\t\t},\r\n\t\tshowModal(value){\r\n\t\t\tthis.showModel = value;\r\n\t\t},\r\n\t\tdeleteScriptTag(tagId){\r\n\t\t\t// find script element and delete\r\n\t\t\tlet element = document.getElementById(tagId);\r\n\t\t\tif (element != null){\r\n\t\t\t\telement.remove();\t\t\t\t\t\r\n\t\t\t}\t\r\n\t\t}\r\n\t},\r\n\tmounted(){\r\n\t\tthis.$root.$on('showCookieModal', () => {\r\n\t\t\tthis.showModal(true);\r\n\t\t});\r\n\t},\r\n\tcreated(){\t\r\n        if (this.getCookie('stat.si.stedy.analytics') != null){\r\n            let cookie = this.getCookie('stat.si.stedy.analytics');\r\n            this.enableAnalytics = this.getCookieValue(cookie);\r\n\t\t\t\r\n\t\t\tif (this.enableAnalytics == 'true'){\r\n\t\t\t\t// add Analytics script\r\n\t\t\t\tlet analyiticScriptElement = document.createElement('script');\r\n\t\t\t\tanalyiticScriptElement.setAttribute(\"id\",\"StedyAnalyticsScript\");\r\n\t\t\t\t// piwik code\r\n\t\t\t\tlet inlineCode = document.createTextNode('(function(window, document, dataLayerName, id) {window[dataLayerName]=window[dataLayerName]||[],window[dataLayerName].push({start:(new Date).getTime(),event:\"stg.start\"});var scripts=document.getElementsByTagName(\"script\")[0],tags=document.createElement(\"script\");function stgCreateCookie(a,b,c){var d=\"\";if(c){var e=new Date;e.setTime(e.getTime()+24*c*60*60*1e3),d=\"; expires=\"+e.toUTCString()}document.cookie=a+\"=\"+b+d+\"; path=/\"}var isStgDebug=(window.location.href.match(\"stg_debug\")||document.cookie.match(\"stg_debug\"))&&!window.location.href.match(\"stg_disable_debug\");stgCreateCookie(\"stg_debug\",isStgDebug?1:\"\",isStgDebug?14:-1);var qP=[];dataLayerName!==\"dataLayer\"&&qP.push(\"data_layer_name=\"+dataLayerName),isStgDebug&&qP.push(\"stg_debug\");var qPString=qP.length>0?(\"?\"+qP.join(\"&\")):\"\";tags.async=!0,tags.src=\"https://surs.containers.piwik.pro/\"+id+\".js\"+qPString,scripts.parentNode.insertBefore(tags,scripts);!function(a,n,i){a[n]=a[n]||{};for(var c=0;c<i.length;c++)!function(i){a[n][i]=a[n][i]||{},a[n][i].api=a[n][i].api||function(){var a=[].slice.call(arguments,0);\"string\"==typeof a[0]&&window[dataLayerName].push({event:n+\".\"+i+\":\"+a[0],parameters:[].slice.call(arguments,1)})}}(i[c])}(window,\"ppms\",[\"tm\",\"cm\"]);})(window, document, \"dataLayer\", \"2e6be837-9c18-4e36-8acd-7281b4f7e76d\");');\r\n\t\t\t\tanalyiticScriptElement.appendChild(inlineCode);\r\n\t\t\t\tdocument.head.appendChild(analyiticScriptElement);\r\n\t\t\t}\r\n\t\t\telse {\t\r\n\t\t\t\t// delete cookies except the one for decision about cookies (\"stat.si.stedy.analytics\")\r\n\t\t\t\tthis.deleteCookies(\"stat.si.stedy.analytics\");\r\n\t\t\t}\r\n        }\r\n        else{\r\n            // prikazemo popup za piskotke\r\n            this.showModel = true;\r\n\t\t\t//this.$refs.cookies.$el.focus();\r\n\t\t}\r\n\t}\r\n  }\r\n</script>\r\n\r\n<style>\r\n.cookies-overlay {\r\n  position: fixed;\r\n  top: 0;\r\n  left: 0;\r\n  z-index: 100;\r\n  background: #eee;\r\n  width: 100%;\r\n  height: 100%;\r\n  /*ozadje, ki prekrije page*/\r\n  background-color: rgba(48, 48, 48, 0.9);\r\n  display: flex;\r\n  justify-content: center;\r\n  align-items: center;\r\n}\r\n\r\n.cookies-content {\r\n\tmargin: 0 auto;\r\n\twidth: 900px;\r\n}\r\n\r\np.cookies-text {\r\n  box-sizing: border-box;\r\n  color: #fff;\r\n  font-family: Raleway, sans-serif;\r\n  font-size: 1.2rem;\r\n  line-height: 33px;\r\n  margin: 2rem;\r\n  text-align: left;\r\n}\r\n\r\n.cookie-policy:link,\r\n.cookie-policy:visited {\r\n  color: #fff;\r\n  margin-left: 1px;\r\n  padding: 4px;\r\n  text-decoration: underline;\r\n\r\n  &:hover {\r\n    color: #f47;\r\n  }\r\n\r\n  &:focus {\r\n    border: 2px solid #fff;\r\n    outline: none;\r\n    color: #f47;\r\n  }\r\n}\r\n\r\n@media (min-width: 991px) {\r\n  p.cookies-text span {\r\n    display: inline;\r\n  }\r\n}\r\n\r\n.cookies-buttons-container {\r\n  display: flex;\r\n  flex-wrap: wrap;\r\n  justify-content: center;\r\n  align-items: flex-start;\r\n}\r\n\r\n.cookies-buttons-container a {\r\n\tmargin-bottom: 10px;\r\n}\r\n\r\n.btn-no {\r\n  align-items: center;\r\n  background-color: #fff;\r\n  border: 2px solid #fff;\r\n  border-radius: 32px;\r\n  box-sizing: border-box;\r\n  color: #1f1f1f;\r\n  cursor: pointer;\r\n  display: flex;\r\n  font-family: Raleway, sans-serif;\r\n  font-size: 1rem;\r\n  font-weight: 700;\r\n  justify-content: center;\r\n  letter-spacing: 0.125rem;\r\n  line-height: 1.15;\r\n  margin: 0;\r\n  overflow: hidden;\r\n  padding: 0.75rem 1.5rem;\r\n  position: relative;\r\n  text-align: center;\r\n  text-decoration: none;\r\n  transition: all 0.2s;\r\n  margin-right: 1rem;\r\n}\r\n\r\n.btn-no:hover {\r\n    background-color: #9d2d47;\r\n    border-color: #9d2d47;\r\n    color: #fff;\r\n  }\r\n\r\n.btn-no:focus {\r\n    background-color: #9d2d47;\r\n    border-color: #9d2d47;\r\n    color: #fff;\r\n  }\r\n\r\n.btn-yes {\r\n  align-items: center;\r\n  background-color: #f47;\r\n  border: 2px solid #f47;\r\n  border-radius: 32px;\r\n  box-sizing: border-box;\r\n  color: #fff;\r\n  cursor: pointer;\r\n  display: flex;\r\n  font-family: Raleway, sans-serif;\r\n  font-size: 1rem;\r\n  font-weight: 700;\r\n  justify-content: center;\r\n  letter-spacing: 0.125rem;\r\n  line-height: 1.15;\r\n  margin: 0;\r\n  overflow: hidden;\r\n  padding: 0.75rem 1.5rem;\r\n  position: relative;\r\n  text-align: center;\r\n  text-decoration: none;\r\n  transition: all 0.2s;\r\n}\r\n\r\n.btn-yes:hover {\r\n    background-color: #9d2d47;\r\n    border-color: #9d2d47;\r\n    color: #fff;\r\n  }\r\n\r\n.btn-yes:focus {\r\n    background-color: #9d2d47;\r\n    border-color: #9d2d47;\r\n    color: #fff;\r\n  }\r\n  \r\n@media (max-width: 768px) {\r\n .cookies-buttons-container {\r\n\tdisplay: flex;\r\n\tflex-direction: column;\r\n\tjustify-content: center;\r\n\talign-items:center;\r\n }\r\n \r\n .btn-no {\r\n\tmargin-right: 0;\r\n }\r\n}\r\n\r\n</style>","import mod from \"-!../../node_modules/cache-loader/dist/cjs.js??ref--12-0!../../node_modules/thread-loader/dist/cjs.js!../../node_modules/babel-loader/lib/index.js!../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Cookies.vue?vue&type=script&lang=js&\"; export default mod; export * from \"-!../../node_modules/cache-loader/dist/cjs.js??ref--12-0!../../node_modules/thread-loader/dist/cjs.js!../../node_modules/babel-loader/lib/index.js!../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Cookies.vue?vue&type=script&lang=js&\"","import { render, staticRenderFns } from \"./Cookies.vue?vue&type=template&id=5ee26665&\"\nimport script from \"./Cookies.vue?vue&type=script&lang=js&\"\nexport * from \"./Cookies.vue?vue&type=script&lang=js&\"\nimport style0 from \"./Cookies.vue?vue&type=style&index=0&lang=css&\"\n\n\n/* normalize component */\nimport normalizer from \"!../../node_modules/vue-loader/lib/runtime/componentNormalizer.js\"\nvar component = normalizer(\n  script,\n  render,\n  staticRenderFns,\n  false,\n  null,\n  null,\n  null\n  \n)\n\ncomponent.options.__file = \"Cookies.vue\"\nexport default component.exports","<template>\r\n  <div id=\"app\">\r\n    <cookies />\r\n    <loader :class=\"{ 'active': isLoading }\" />\r\n\r\n    <transition name=\"fade\">\r\n      <router-view/>\r\n    </transition>\r\n\r\n  </div>\r\n</template>\r\n\r\n<script>\r\n\r\n  import Loader from '@/components/Loader'\r\n  import Cookies from '@/components/Cookies'\r\n\r\n  export default {\r\n    name: 'App',\r\n    components: {\r\n      Loader,\r\n      Cookies\r\n    },\r\n    data() {\r\n      return {\r\n        imagesUrls: [\r\n          require('@/images/Poglavlje1/green_background_and_illustration@2x.svg'),\r\n          require('@/images/Poglavlje2/purple_background_with_illustration@2x.svg'),\r\n          require('@/images/Poglavlje3/orange_background_with_illustration@2x.svg'),\r\n          require('@/images/Poglavlje4/pink_background_with_illustration@2x.svg'),\r\n          require('@/images/Poglavlje5/blue_background_with_illustration@2x.svg'),\r\n        ]\r\n      }\r\n    },\r\n    computed: {\r\n      isLoading() {\r\n        return this.$store.state.isLoading\r\n      }\r\n    },\r\n    beforeMount() {\r\n      if(!window.localStorage.getItem('lang')) {\r\n        this.$i18n.locale = 'sl'\r\n        window.localStorage.setItem('lang', 'sl')\r\n      }\r\n\r\n      const lessonsProgress = [\r\n        { isOpened: [false, false, false, false, false, false, false, false, false, false] },\r\n        { isOpened: [false, false] },\r\n        { isOpened: [false, false, false, false, false, false] },\r\n     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\"./App.vue?vue&type=style&index=0&lang=css&\"\n\n\n/* normalize component */\nimport normalizer from \"!../node_modules/vue-loader/lib/runtime/componentNormalizer.js\"\nvar component = normalizer(\n  script,\n  render,\n  staticRenderFns,\n  false,\n  null,\n  null,\n  null\n  \n)\n\ncomponent.options.__file = \"App.vue\"\nexport default component.exports","const messages = {\r\n  hr: {\r\n    validation_messages: {\r\n      must_be_number: 'Mora biti broj',\r\n      must_be_positive_number: 'Mora biti pozitivni broj',\r\n      new_start: 'Za novi izračun unesite novi unos za broj bacanja.',\r\n      must_not_be_empty: 'mora biti unesen.'\r\n    },\r\n    chaptersTitle: 'Poglavlja',\r\n    literatureTitle: 'Literatura',\r\n    about: 'O projektu',\r\n    contact: 'Kontakt',\r\n    nextChapterParagraph: 'Sljedeće poglavlje',\r\n    go_button: 'Kreni!',\r\n    chapters_button: 'Poglavlja',\r\n    task_button: 'Zadatak',\r\n    example: 'Primjer',\r\n    task: 'Zadatak',\r\n    chapter1Title: 'Opisivanje podataka',\r\n    chapter2Title: 'Osnove vjerojatnosti',\r\n    chapter3Title: 'Slučajna varijabla',\r\n    chapter4Title: 'Distribucija',\r\n    chapter5Title: 'Statističko zaključivanje',\r\n    buttonText: 'Kreni u poglavlje',\r\n    showTaskSolution: 'Prikaži rješenje',\r\n    hideTaskSolution: 'Sakrij rješenje',\r\n    for_those_who_want_more: 'Za one koji žele znati više',\r\n    show_interaction: 'Prikaži interakciju',\r\n    show_data: 'Prikaži podatke',\r\n    show_table: 'Prikaži tablicu',\r\n    show: 'Prikaži',\r\n    show_interaction_1_9_1: 'Prikaži interakciju',\r\n    show_interaction_1_9_2: 'Prikaži interakciju',\r\n    sidebar: {\r\n      lesson1: {\r\n        1: 'Podaci',\r\n        2: 'Frekvencije i relativne frekvencije',\r\n        3: 'Stupčasti dijagram i histogram',\r\n        4: 'Prosjek',\r\n        5: 'Medijan',\r\n        6: 'Minimum, maksimum i raspon',\r\n        7: 'Kvartili i interkvartilni raspon',\r\n        8: 'Varijanca i standardna devijacija',\r\n        9: 'Kutijasti dijagram',\r\n        10: 'Dijagram raspršenosti'\r\n      },\r\n      lesson2: {\r\n        1: 'Vjerojatnost',\r\n        2: 'Uvjetna vjerojatnost'\r\n      },\r\n      lesson3: {\r\n        1: 'Slučajna varijabla',\r\n        2: 'Diskretna slučajna varijabla',\r\n        3: 'Neprekidna slučajna varijabla',\r\n        4: 'Funkcija distribucije',\r\n        5: 'Očekivanje',\r\n        6: 'Varijanca i standardna devijacija'\r\n      },\r\n      lesson4: {\r\n        1: 'Bernoullijeva distribucija',\r\n        2: 'Binomna distribucija',\r\n        3: 'Normalna distribucija'\r\n      },\r\n      lesson5: {\r\n        1: 'Populacija i uzorak',\r\n        2: 'Procjena proporcije/vjerojatnosti',\r\n        3: 'Procjena očekivanja i varijance',\r\n        4: 'Pouzdani interval za očekivanje',\r\n        5: 'Pouzdani interval za proporciju/vjerojatnost',\r\n        6: 'Testiranje statističkih hipoteza',\r\n        7: 'Jednostavna linearna regresija'\r\n      }\r\n    },\r\n    literature: {\r\n      1: 'Bain, L.E., Engelhardt, M. (2008). Introduction to Probability and Mathematical Statistics. \tBROOKS/COLE Cengage Learning.',\r\n      2: 'Benšić, M., Šuvak, N. (2013). Primijenjena statistika. Sveučilište J.J. Strossmayera u Osijeku, Odjel za matematiku.',\r\n      3: 'Bhattacharyya, G.K., Johnson, R.A. (1977). Statistical Concepts and Methods. John Wiley and Sons.',\r\n      4: 'Benšić, M., Šuvak, N. (2014). Uvod u vjerojatnost i statistiku. Sveučilište J.J. Strossmayera u Osijeku, Odjel za matematiku.',\r\n      5: 'Elezović, N. (2007). Diskretna vjerojatnost. Element.',\r\n      6: 'Elezović, N. (2007). Slučajne varijable. Element.',\r\n      7: 'Elezović, N. (2007). Statistika i procesi. Element.',\r\n      8: 'Ross, S.M. (2017). Introductory statistics. Academic Press.',\r\n      9: 'Sarapa, N. (1987). Teorija vjerojatnosti. Školska knjiga.',\r\n      10: 'Tintle, N., Chance, B.L., Cobb, G.W., Rossman, A.J., Roy, S., Swanson, T., VanderStoep, J. \t(2015). Introduction to Statistical Investigations: High School Binding. John Wiley.'\r\n    },\r\n    title_tag: {\r\n      homepage: 'Stedy - Asistent u vašim statističkim izazovima',\r\n      chapter_literature: 'Popis poglavlja - Stedy',\r\n      privacy_policy: 'Pravila privatnosti - Stedy',\r\n      opisivanje_podataka: 'Opisivanje podataka - Stedy',\r\n      osnove_vjerojatnosti: 'Osnove vjerojatnosti - Stedy',\r\n      slucajna_varijabla: 'Slučajna varijabla - Stedy',\r\n      distribucije: 'Distribucije - Stedy',\r\n      statisticko_zakljucivanje: 'Statisticko zakljucivanje - Stedy',\r\n      chapter1: {\r\n        1: 'Podaci - Opisivanje podataka - Stedy',\r\n        2: 'Frekvencije i relativne frekvencije - Opisivanje podataka - Stedy',\r\n        3: 'Stupčasti dijagram i histogram - Opisivanje podataka - Stedy',\r\n        4: 'Prosjek - Opisivanje podataka - Stedy',\r\n        5: 'Medijan - Opisivanje podataka - Stedy',\r\n        6: 'Minimum, maksimum i raspon - Opisivanje podataka - Stedy',\r\n        7: 'Kvartili i interkvartilni raspon - Opisivanje podataka - Stedy',\r\n        8: 'Varijanca i standardna devijacija - Opisivanje podataka - Stedy',\r\n        9: 'Kutijasti dijagram - Opisivanje podataka - Stedy',\r\n        10: 'Dijagram raspršenosti - Opisivanje podataka - Stedy',\r\n      },\r\n      chapter2: {\r\n        1: 'Vjerojatnost - Osnove vjerojatnosti - Stedy',\r\n        2: 'Uvjetna vjerojatnost - Osnove vjerojatnosti - Stedy'\r\n      },\r\n      chapter3: {\r\n        1: 'Slučajna varijabla - Slučajna varijabla - Stedy',\r\n        2: 'Diskretna slučajna varijabla - Slučajna varijabla - Stedy',\r\n        3: 'Neprekidna slučajna varijabla - Slučajna varijabla - Stedy',\r\n        4: 'Funkcija distribucije - Slučajna varijabla - Stedy',\r\n        5: 'Očekivanje - Slučajna varijabla - Stedy',\r\n        6: 'Varijanca i standardna devijacija - Slučajna varijabla - Stedy'\r\n      },\r\n      chapter4: {\r\n        1: 'Bernoullijeva distribucija - Distribucija - Stedy',\r\n        2: 'Binomna distribucija - Distribucija - Stedy',\r\n        3: 'Normalna distribucija - Distribucija - Stedy',\r\n      },\r\n      chapter5: {\r\n        1: 'Populacija i uzorak - Statističko zaključivanje - Stedy',\r\n        2: 'Procjena proporcije/vjerojatnosti - Statističko zaključivanje - Stedy',\r\n        3: 'Procjena očekivanja i varijance - Statističko zaključivanje - Stedy',\r\n        4: 'Pouzdani interval za očekivanje - Statističko zaključivanje - Stedy',\r\n        5: 'Pouzdani interval za proporciju/vjerojatnost - Statističko zaključivanje - Stedy',\r\n        6: 'Testiranje statističkih hipoteza - Statističko zaključivanje - Stedy',\r\n        7: 'Jednostavna linearna regresija - Statističko zaključivanje - Stedy',\r\n      },\r\n    },\r\n    meta_content: {\r\n      homepage: 'Stedy je interaktivni portal namijenjen educiranju i promicanju statističke pismenosti putem e-učenja.',\r\n      chapter_literature: 'Abecedni popis literature korištene za izradu interaktivnog edukacijskog portala Stedy.',\r\n      privacy_policy: 'Državni zavod za statistiku upravlja interaktivnim edukacijskim portalom Stedy. Zavod posvećuje veliku pažnju zaštiti osobnih podataka korisnika Stedy portala.',\r\n      opisivanje_podataka: 'Stedy - Opisivanje podataka',\r\n      osnove_vjerojatnosti: 'Stedy - Osnove vjerojatnosti',\r\n      slucajna_varijabla: 'Stedy - Slučajna varijabla',\r\n      distribucije: 'Stedy - Distribucije',\r\n      statisticko_zakljucivanje: 'Stedy - Statističko zaključivanje',\r\n      chapter1: {\r\n        1: 'Podatke prikupljamo na objektima (npr. na ljudima, životinjama, biljkama, državama, gradovima, poduzećima itd.) koji se zovu jedinke ili slučajevi.',\r\n        2: 'Frekvencija jedne kategorije jest broj zabilježenih vrijednosti varijable koje pripadaju toj kategoriji. Relativna frekvencija jedne kategorije jest frekvencija podijeljena s ukupnim brojem podataka za tu varijablu.',\r\n        3: 'Stupčasti dijagram jest prikaz frekvencija ili relativnih frekvencija kategorija odabrane varijable. Histogram služi za prikazivanje numeričkih podataka.',\r\n        4: 'Prosjek ili aritmetička sredina podataka jest zbroj svih podataka podijeljen s ukupnim brojem podataka. Prosjek je jedna mjera centra niza numeričkih podataka.',\r\n        5: 'Smisao medijana jest istaknuti broj koji dijeli uređeni niz podataka na dva dijela tako da svaki dio sadržava isti broj podataka i da svi podaci iz prvog dijela nisu veći od podataka iz drugog dijela.',\r\n        6: 'Minimum je najmanji podatak u nizu dok je maksimum najveći podatak u nizu. Raspon je gruba mjera raspršenosti podataka, odnosno razlika između minimuma i maksimuma.',\r\n        7: 'Interkvartilni raspon jest jedna mjera raspršenosti podataka. Definira se s pomoću kvartila. Razlikujemo donji i gornji kvartil.',\r\n        8: 'Varijanca i standardna devijacija jesu mjere raspršenosti podataka koje karakteriziraju raspršenost podataka oko prosjeka.',\r\n        9: 'Kutijasti dijagram (engl. box plot ili box-and-whisker plot) prikazuje odnos minimuma, maksimuma, donjega i gornjega kvartila te medijana podataka.',\r\n        10: 'Ako se za jedinke prikupljaju podaci o dvjema numeričkim veličinama, korisno je parove podataka prikazati dijagramom raspršenosti.',\r\n      },\r\n      chapter1_tasks: {\r\n        1: 'Oblikujte svoju bazu podataka koja ima najmanje jednu kvalitativnu ordinalnu, jednu kvalitativnu nominalnu i jednu numeričku varijablu.',\r\n        2: 'Za tablicu iz primjera grupirajte podatke varijable tako da svaki interval ima duljinu 30. Odredite pripadajuću tablicu frekvencija i relativnih frekvencija.',\r\n        3: 'Za koju je varijablu primjeren prikaz stupčastim dijagramom? Odaberite tu varijablu da biste vidjeli prikaz podataka u stupčastom dijagramu.',\r\n        4: 'Zadana su dva skupa podataka. Odredite prosjek svakog skupa. Po čemu su ti skupovi slični? Iskazuje li se prosjekom dovoljno informacija o skupu podataka?',\r\n        5: 'Razrednik jednog razreda nastoji pratiti koliko učenici njegova razreda igraju računalne igrice. Za tu je svrhu zamolio učenike da vode evidenciju…',\r\n        6: 'Razrednik jednog razreda nastoji pratiti koliko učenici njegova razreda igraju računalne igrice. Za tu je svrhu zamolio učenike da vode evidenciju…',\r\n        7: 'Razrednik jednog razreda nastoji pratiti koliko učenici njegova razreda igraju računalne igrice. Za tu je svrhu zamolio učenike da vode evidenciju…',\r\n        8: 'Zadana su dva skupa podataka. Odredite prosjek i standardnu devijaciju svakog skupa. Po čemu su ti skupovi slični?',\r\n        9: 'Na slici su prikazana tri kutijasta dijagrama. Možemo li identificirati jedan od dijagrama za koji vrijede sljedeće tvrdnje…',\r\n        10: 'Na slici je prikazan dijagram raspršenosti vremena igranja igrica nedjeljom i ponedjeljkom. Uočavate li neku pravilnost?'\r\n      },\r\n      chapter2: {\r\n        1: 'Vjerojatnost događaja jest broj kojim izražavamo stupanj uvjerenja u realizaciju tog događaja.',\r\n        2: 'Uz dodatnu informaciju o ishodu pokusa vjerojatnost nekog događaja može se razlikovati od vjerojatnosti istog događaja bez te informacije.'\r\n      },\r\n      chapter2_tasks: {\r\n        1: 'Dva brata kockara potpuno su različita – jedan je pošten, dok drugi pokušava varati. Pošteni kockar igra pravilnom igraćom kockicom. Kolika je vjerojatnost…',\r\n        2: 'Upotrebom interaktivnog alata odredite vjerojatnost realizacije šestice pri bacanju igraće kockice koja ne mora biti pravilna uz dodatnu informaciju…'\r\n      },\r\n      chapter3: {\r\n        1: 'Slučajna varijabla jest funkcija koja ishodima pokusa (elementima skupa Ω) pridružuje realne brojeve. Obično se označuje velikim tiskanim slovom, primjerice s 𝑋.',\r\n        2: 'Diskretna slučajna varijabla karakterizirana je konačnim ili prebrojivim skupom vrijednosti.',\r\n        3: 'Neprekidna slučajna varijabla karakterizirana je slikom 𝓡(𝑋) koja nije diskretan skup. Primjerice, 𝓡(𝑋) može biti neki interval ili čak cijeli skup realnih brojeva.',\r\n        4: 'Funkcija distribucije 𝐹 slučajne varijable 𝑋 svakome realnom broju 𝑥 pridružuje vjerojatnost događaja (𝑋 ≤ 𝑥): F(x)=P(X≤x),x∈R.',\r\n        5: 'Očekivanje slučajne varijable 𝑋 jest broj koji upućuje na poziciju centra distribucije te slučajne varijable. Označujemo ga s 𝐸[𝑋] ili 𝜇.',\r\n        6: 'Varijanca slučajne varijable 𝑋 pozitivan je broj koji opisuje raspršenost distribucije slučajne varijable 𝑋 u odnosu na njezino očekivanje 𝐸[𝑋].'\r\n      },\r\n      chapter3_tasks: {\r\n        1: 'Pokus se sastoji od bacanja igraće kockice dva puta zaredom. Definirajte slučajnu varijablu koja ishodima tog pokusa pridružuje zbroj brojeva koji su se okrenuli.',\r\n        2: 'Pokus se sastoji od bacanja igraće kockice koja ne mora biti pravilna dva puta zaredom. Odredite distribuciju slučajne varijable X koja ishodima tog pokusa…',\r\n        3: 'Upotrebom interaktivnog alata za λ=1 odredite vjerojatnost da između dvaju uzastopnih dolazaka tramvaja na stanicu prođe…',\r\n        4: '',\r\n        5: 'Ako se zapitamo postoji li realan broj koji je na neki način \"najbliži\" slučajnoj varijabli, onda je to u jednom načinu mjerenja udaljenosti upravo očekivanje. ',\r\n        6: 'Upotrebom interaktivnog alata ispitajte kako se ovisno o vrijednosti parametra λ>0 ponašaju očekivanje i varijanca slučajne varijable X…'\r\n      },\r\n      chapter4: {\r\n        1: 'Slučajna varijabla 𝑋 koja opisuje pokus sa samo dva moguća ishoda: neuspjeh (oznaka 0) i uspjeh (oznaka 1), ima Bernoullijevu distribuciju s parametrom 𝑝 ∈ (0, 1)…',\r\n        2: 'Binomna distribucija pokazuje vjerojatnost događanja međusobno isključivih događaja za svaki broj događaja posebno.',\r\n        3: 'Normalna distribucija je dvoparametarska funkcija kojoj su parametri aritmetička sredina i standardna devijacija.',\r\n      },\r\n      chapter4_tasks: {\r\n        1: 'U igri \"Čovječe, ne ljuti se\" bacamo pravilnu igraću kockicu i uspjehom smatramo okretanje šestice. Ako se okrene bilo koji od brojeva 1, 2, 3, 4, 5, to smatramo…',\r\n        2: 'Upotrebom interaktivnog alata odredite vjerojatnost da će se u 50 bacanja igraće kockice šestica okrenuti više od 5 puta. Je li vjerojatnije da se šestica…',\r\n        3: 'Standardizirani test inteligencije baždaren je s obzirom na pretpostavku da je kvocijent inteligencije u populaciji normalno distribuirano obilježje…',\r\n      },\r\n      chapter5: {\r\n        1: 'Pri statističkom zaključivanju podatke kojima raspolažemo shvaćamo kao vrijednosti zabilježene na jednom dijelu populacije koji se zove uzorak. ',\r\n        2: 'Neka je x1, 𝑥2, ... , 𝑥n uzorak iz varijable 𝑋 koja može imati samo dva ishoda. Ishode možemo označiti s 0 i 1, pa je riječ o uzorku iz Bernoullijeve distribucije…',\r\n        3: 'Ako je 𝑥1, 𝑥2, ... , 𝑥𝑛 uzorak iz varijable 𝑋 koja ima nepoznato očekivanje 𝜇 = 𝐸[𝑋] , onda parametar 𝜇 procjenjujemo aritmetičkom sredinom (prosjekom) uzorka…',\r\n        4: 'Umjesto da procijenimo parametar jednim brojem, možemo procijeniti interval u kojem je taj parametar sadržan s nekom vjerojatnošću, obično 0.95 ili 0.99. Takav interval zove se pouzdani interval.',\r\n        5: 'Umjesto procjene jednim brojem, nepoznatu proporciju nekog obilježja u populaciji možemo procijeniti pouzdanim intervalom za proporciju.',\r\n        6: 'Pretpostavimo da igramo igru u kojoj osvajamo dobitak ako se bacanjem novčića okrene pismo. Nakon 10 igara, 2 puta je palo pismo, a 8 puta glava…',\r\n        7: 'Regresijskim metodama moguće je opisati vezu među varijablama X i Y. Ako točke prikazane dijagramom raspršenosti izgledaju kao da su raspršene…',\r\n      },\r\n      chapter5_tasks: {\r\n        1: 'U pokusu koji se sastoji od bacanja novčića dva puta bilježi se broj pisama u ta dva bacanja. Pokus je ponovljen 200 puta.',\r\n        2: 'Prema istraživanju Državnog zavoda za statistiku, od 2029 anketiranih kućanstava u Republici Hrvatskoj, 1635 kućanstava živi u stanu ili kući…',\r\n        3: '',\r\n        4: 'Prema istraživanju Državnog zavoda za statistiku, kućanstva u Republici Hrvatskoj godišnje prosječno troše 5494 kuna na odjeću i obuću…',\r\n        5: 'Pretpostavimo da na nekim izborima sudjeluju samo dva kandidata, A i B. Anketom se želi prognozirati pobjednik.',\r\n        6: 'Na uzorku od 50 osoba testirano je može li se prepoznati razlika između skupoga i jeftinog vina.',\r\n        7: '',\r\n      }\r\n    },\r\n    table_head: {\r\n      1: 'REDNI BROJ UČENIKA',\r\n      2: 'VRIJEME IGRE (min)',\r\n      3: 'SPOL',\r\n      4: 'OCJENA'\r\n    },\r\n    student_table: {\r\n      table_head: {\r\n        student_number: 'REDNI BROJ UČENIKA',\r\n        play_time: 'VRIJEME IGRE (min)',\r\n        sex: 'SPOL',\r\n        grade: 'OCJENA'\r\n      },\r\n      table_body: {\r\n        1: '1.',\r\n        2: '2.',\r\n        3: '3.',\r\n        4: '4.',\r\n        5: '5.',\r\n        6: '6.',\r\n        7: '7.',\r\n        8: '8.',\r\n        9: '9.',\r\n        10: '10.',\r\n        11: '11.',\r\n        12: '12.',\r\n        13: '13.',\r\n        14: '14.',\r\n        15: '15.',\r\n        16: '16.',\r\n        17: '17.',\r\n        18: '18.',\r\n        19: '19.',\r\n        20: '20.',\r\n        21: '21.',\r\n        22: '22.',\r\n        23: '23.',\r\n        24: '24.',\r\n        47: '47',\r\n        177: '177',\r\n        124: '124',\r\n        135: '135',\r\n        69: '69',\r\n        88: '88',\r\n        0: '0',\r\n        120: '120',\r\n        63: '63',\r\n        57: '57',\r\n        79: '79',\r\n        244: '244',\r\n        99: '99',\r\n        76: '76',\r\n        166: '166',\r\n        193: '193',\r\n        74: '74',\r\n        51: '51',\r\n        data20: '20',\r\n        data19: '19',\r\n        189: '189',\r\n        zene: 'ž',\r\n        muskarci: 'm',\r\n        nedovoljan: 'nedovoljan',\r\n        dovoljan: 'dovoljan',\r\n        dobar: 'dobar',\r\n        vrlo_dobar: 'vrlo dobar',\r\n        odlican: 'izvrstan'\r\n      }\r\n    },\r\n    frequency_table_big: {\r\n      table_head: {\r\n        play_time: 'VRIJEME IGRE (min)',\r\n        frequency: 'FREKVENCIJA',\r\n        relative_frequency: 'RELATIVNA FREKVENCIJA (%)'\r\n      },\r\n      table_body: {\r\n        1: '0',\r\n        2: '19',\r\n        3: '20',\r\n        4: '47',\r\n        5: '51',\r\n        6: '57',\r\n        7: '63',\r\n        8: '69',\r\n        9: '74',\r\n        10: '76',\r\n        11: '79',\r\n        12: '88',\r\n        13: '99',\r\n        14: '120',\r\n        15: '124',\r\n        16: '135',\r\n        17: '166',\r\n        18: '177',\r\n        19: '189',\r\n        20: '193',\r\n        21: '244',\r\n        22: '3',\r\n        23: '1',\r\n        24: '0.12',\r\n        25: '0.04',\r\n        26: '2',\r\n        27: '0.08'\r\n      }\r\n    },\r\n    frequency_table_small: {\r\n      table_head: {\r\n        play_time: 'VRIJEME IGRE (min)',\r\n        frequency: 'FREKVENCIJA',\r\n        relative_frequency: 'RELATIVNA FREKVENCIJA (%)'\r\n      },\r\n      table_body: {\r\n        1: '0',\r\n        2: '<0, 60]',\r\n        3: '<60, 120]',\r\n        4: '> 120',\r\n        5: 'ukupno'\r\n      }\r\n    },\r\n    socials: {\r\n      facebook: 'https://www.facebook.com/statcroatia',\r\n      instagram: 'https://www.instagram.com/drzavni.zavod.za.statistiku/',\r\n      youtube: 'https://www.youtube.com/channel/UCi9ifCO-fuKM71pE0cu6Kiw',\r\n      linkedin: 'https://www.linkedin.com/company/croatian-bureau-of-statistics-dr-avni-zavod-za-statistiku-republike-hrvatske-',\r\n      github: 'https://www.github.com'\r\n    },\r\n    homepage: {\r\n      intro: '<span>Stedy - Asistent</span> u vašim statističkim izazovima',\r\n      about_section: {\r\n        1: 'Mislili ste da je statistika komplicirana i jednostavno nije za vas ili vi za nju?',\r\n        2: 'Svjesni smo činjenice da ste postotke naučili još u osnovnoj školi, ali i da istodobno postoji šansa da su intervali, kvartili ili vrste distribucija za vas bili i ostali zona sumraka. Nadamo se ne zadugo.',\r\n        3: 'Odsad je tu za vas <strong>STEDy</strong> – statistički edukacijski portal koji će vam u nekoliko koraka pojasniti statističke pojmove koji se katkad čine tako komplicirani. S druge strane, ako ste oduvijek bili simpatizeri statistike, ovo je pravo mjesto da proširite, obnovite ili testirate svoje znanje!',\r\n        4: 'Svjesni važnosti promicanja statističke pismenosti te suradnje s obrazovnom i akademskom zajednicom, Državni zavod za statistiku je, u sklopu Eurostatova projekta Support for Statistical Literacy actions in the area of a competition, gamification and e-learning, odlučio pokrenuti jedinstven statistički edukacijski portal.',\r\n        5: 'Uz pomoć profesora sa Sveučilišta J. J. Strossmayera u Osijeku, <strong>prof. dr. sc. Mirte Benšić</strong>, <strong>doc. dr. sc. Danijela Grahovca</strong> i <strong>izv. prof. dr. sc. Nenada Šuvaka</strong>, koji su zaslužni za sadržaj ovog portala, nadamo se da smo pronašli poticajan način da široj javnosti, učiteljima i profesorima, učenicima i studentima te svim zaljubljenicima u statistiku približimo statistiku na drugačiji i zanimljiviji način.',\r\n        6: 'Trudili smo se odmaknuti od klasičnog pristupa, pa se STEDy ne zadržava samo na teorijskoj podlozi, nego vam donosi i praktične primjere, interaktivne vizualizacije te zadatke u kojima odmah možete provjeriti svoje razumijevanje i primjenu statistike.',\r\n        7: 'Bilo da je statistika dio vaše svakodnevnice i pametna podloga za donošenje odluka na temelju činjenica ili tek prepreka koju treba savladati, nadamo se da će STEDy biti odličan asistent u vašim statističkim avanturama. ',\r\n        8: 'Vežite pojaseve, ujurite u čaroban svijet brojeva i poigrajte se s podacima!'\r\n      },\r\n      contact: {\r\n        1: 'Imate li pitanja? Kontaktirajte nas!',\r\n        2: 'Svoje upite, poruke i komentare možete poslati na <a href=\"mailto: gp.surs@gov.si\">gp.surs@gov.si</a>',\r\n        3: 'Kontaktirajte nas'\r\n      },\r\n      footer: {\r\n        1: 'Pravila privatnosti',\r\n        2: 'Državni zavod za statistiku',\r\n        3: 'Izradu internetske stranice sufinancirao je Eurostat - statistički ured Europske unije.',\r\n        4: 'Open Source Projekt'\r\n      }\r\n    },\r\n    privacy_policy: {\r\n      title: 'Politika zaštite privatnosti',\r\n      1: 'Državni zavod za statistiku (u daljnjem tekstu: Zavod) upravlja internetskom stranicom <a href=\"www.stedy.hr\" class=\"link\" target=\"_blank\" rel=\"noopener noreferrer\">www.stedy.hr</a>. Zavod posvećuje veliku pažnju zaštiti osobnih podataka korisnika navedene internetske stranice.',\r\n      2: 'Ova Politika zaštite privatnosti (u daljnjem tekstu: Politika) uređuje način postupanja s podacima koje Zavod obrađuje, odnosno prikuplja prilikom posjeta ovoj internetskoj stranici. Zavod prikuplja vaše osobne podatke samo kad nam ih izričito učinite dostupnima i pristanete na njihovo korištenje.',\r\n      3: 'Tijekom različitih oblika interakcije na internetskoj stranici <a href=\"www.stedy.hr\" class=\"link\" target=\"_blank\" rel=\"noopener noreferrer\">www.stedy.hr</a> Zavod prikuplja vaše osobne podatke, i to adresu elektroničke pošte, kao i druge podatke kao što su npr. kolačići (cookies) i podaci o korištenju.',\r\n      4: 'Kolačići (cookies)',\r\n      5: 'Kolačiće i slične tehnologije za praćenje koristimo kako bismo pratili aktivnost povezanu s ovom internetskom stranicom i prikupili određene informacije. Kolačići su datoteke s malom količinom podataka koje mogu sadržavati anonimni jedinstveni identifikator te se šalju na vaš preglednik s internetske stranice koju koristite i pohranjuju se na vaš uređaj. Tehnologije za praćenje koje se također koriste jesu odašiljači (beacons), oznake (tags) i skripte (scripts), a služe za     prikupljanje i praćenje podataka te za poboljšanje i analizu navika korištenja navedene internetske stranice.',\r\n      6: 'U postavkama svojega preglednika možete odrediti da preglednik odbacuje sve kolačiće ili da prikazuje obavijest kada se šalje kolačić. Međutim, ako ne prihvatite kolačiće, možda nećete moći koristiti neke dijelove internetske stranice.',\r\n      7: 'Primjer kolačića koje koristimo:',\r\n      8: '<strong>privremeni kolačići (session cookies)</strong> – koristimo ih za upravljanje internetskom stranicom',\r\n      9: '<strong>preferencijalni kolačići (preference cookies)</strong> – koristimo ih kako bismo zapamtili vaše preferencije i različite postavke',\r\n      10: '<strong>sigurnosni kolačići (security cookies)</strong> – koristimo ih za sigurnosne svrhe.',\r\n      11: 'Podaci o korištenju',\r\n      12: 'Podaci o korištenju mogu uključivati podatke kao što su podaci o uređaju kojim se spajate na internet, adresa internetskog protokola vašeg računala, vrsta preglednika, verzija preglednika, internetske stranice koje posjećujete, vrijeme i datum vašeg posjeta, vrijeme provedeno na tim stranicama, jedinstveni identifikatori uređaja te druge dijagnostičke podatke.',\r\n      13: '<strong>Korištenje podataka</strong>',\r\n      14: 'Zavod koristi prikupljene podatke za sljedeće svrhe:',\r\n      15: 'pružanje i održavanje ove internetske stranice',\r\n      16: 'praćenje korištenja ove internetske stranice',\r\n      17: 'otkrivanje, sprječavanje i rješavanje tehničkih problema u vezi s korištenjem internetske stranice',\r\n      18: 'pružanje pomoći i podrške korisnicima',\r\n      19: 'analizu i pružanje korisnih informacija radi poboljšanja ove internetske stranice',\r\n      20: 'omogućavanje sudjelovanja korisnika u interaktivnim značajkama ove internetske stranice',\r\n      21: 'obavještavanje korisnika o promjenama na ovoj internetskoj stranici.',\r\n      22: '<strong>Prijenos podataka</strong>',\r\n      23: 'Vaši podaci, uključujući i osobne podatke, mogu se prenijeti na računala i održavati na računalima izvan vaše države ili izvan Europske unije odnosno druge državne jurisdikcije gdje se zakoni o zaštiti podataka mogu razlikovati od onih iz Europske unije.',\r\n      24: 'Ako se nalazite izvan Republike Hrvatske i date nam svoje podatke, napominjemo da te podatke, uključujući osobne podatke, prenosimo u Republiku Hrvatsku i obrađujemo ih.',\r\n      25: 'Zavod će poduzeti sve potrebne mjere kako bi osigurao da se s vašim podacima postupa na siguran način i u skladu s ovom Politikom, a vaši osobni podaci prenosit će se samo ako se provedu odgovarajuće kontrole radi zaštite sigurnosti vaših podataka.',\r\n      26: 'Zavod može prenositi vaše osobne podatke trećim stranama isključivo u sljedećim slučajevima: ',\r\n      27: 'ako postoji zakonska obveza ili izričito zakonsko ovlaštenje',\r\n      28: 'ako za obavljanje pojedinih poslova angažiramo izvršitelja obrade, koji djeluje isključivo po nalogu Zavoda, pri čemu Zavod osigurava sve mjere zaštite podataka',\r\n      29: 'ako je podatke potrebno proslijediti trećim stranama radi izvršenja ugovora s ispitanikom.',\r\n      30: 'Prilikom prijenosa podataka ispitanika Zavod strogo poštuje načelo ograničenja obrade uz prijenos minimalne količine podataka koja je potrebna te uz poštivanje svih ostalih relevantnih načela zaštite podataka. Treće strane imaju pristup vašim osobnim podacima samo za obavljanje usluga u ime Zavoda i obvezuju se čuvati povjerljivost vaših osobnih podataka te ih upotrebljavati samo u skladu s određenom namjenom zbog koje su proslijeđeni.',\r\n      31: '<strong>Sigurnost podataka</strong>',\r\n      32: 'Važna nam je sigurnost vaših podataka, ali ne zaboravite da nijedan način prijenosa podataka putem interneta ni način elektroničke pohrane nije 100% siguran. Iako nastojimo koristiti komercijalno prihvatljiva sredstva za zaštitu vaših osobnih podataka, ne možemo jamčiti njihovu apsolutnu sigurnost.',\r\n      33: '<strong>Analitika</strong>',\r\n      34: 'Zavod može angažirati treće strane kao pružatelje usluge za praćenje i analizu korištenja ove internetske stranice.',\r\n      35: '<strong>Google Analytics</strong>',\r\n      36: 'Google Analytics jest internetska usluga analize koju nudi Google, a služi za praćenje i izvještavanje o prometu na nekoj internetskoj stranici. Google koristi prikupljene podatke za praćenje korištenja ove internetske stranice. Ti se podaci dijele s drugim Google uslugama. Google može koristiti prikupljene podatke za kontekstualizaciju i prilagodbu oglasa vlastite oglasne mreže',\r\n      37: 'Možete isključiti mogućnost da podatke o svojoj aktivnosti vezanoj uz korištenje ove internetske stranice stavite na raspolaganje Google Analyticsu instaliranjem dodatka za preglednik za isključivanje usluge Google Analytics. Dodatak sprječava Google Analytics JavaScript (ga.js, analytics.js i dc.js) da dijeli podatke o aktivnosti tijekom posjeta internetskoj stranici s Google Analyticsom.',\r\n      38: 'Za dodatne informacije o Googleovim pravilima zaštite privatnosti, posjetite internetsku stranicu Google Privacy & Terms: <a href=\"https://policies.google.com/privacy?hl=en\" class=\"link\" target=\"_blank\" rel=\"noopener noreferrer\">https://policies.google.com/privacy?hl=en</a>',\r\n      39: '<strong>Poveznice na druge stranice</strong>',\r\n      40: 'Ova internetska stranica može sadržavati poveznice na druge stranice kojima ne upravlja Zavod. Preporučujemo da pročitate politiku zaštite privatnosti svake internetske stranice koju posjećujete. Zavod nema kontrolu nad sadržajem, politikom zaštite privatnosti, niti pravilima internetskih stranica ili usluga trećih strana te ne preuzima odgovornost za navedeno.',\r\n      41: '<strong>Zaštita privatnosti osoba mlađih od 18 godina</strong>',\r\n      42: 'Ovu internetsku stranicu mogu koristiti i osobe mlađe od 18 godina. Zavod ne prikuplja svjesno osobne podatke o osobama mlađim od 18 godina. Ukoliko ste roditelj ili skrbnik i znate da je vaše dijete pružilo osobne podatke, molimo, kontaktirajte Zavod. Ako Zavod dozna da su osobni podaci osoba mlađih od 18 godina prikupljeni bez valjane suglasnosti roditelja ili skrbnika, Zavod će u razumnoj mjeri i u najkraćem mogućem roku poduzeti sljedeće: ',\r\n      43: 'ukloniti te podatke iz evidencija Zavoda',\r\n      44: 'ako brisanje nije moguće, osigurati da se ti osobni podaci ne koriste dalje za bilo koju svrhu',\r\n      45: 'u svakom slučaju neće podatke davati nijednoj trećoj strani.',\r\n      46: '<strong>Izmjene Politike zaštite privatnosti</strong>',\r\n      47: 'Zavod zadržava pravo izmjene ove Politike objavljivanjem nove politike na ovoj internetskoj stranici. Savjetujemo vam da povremeno provjeravate Politiku zbog mogućih izmjena. Izmjene Politike stupaju na snagu danom njihove objave na ovoj internetskoj stranici.',\r\n      48: 'Prava koja vam pripadaju',\r\n      49: 'U vezi s obradom osobnih podataka, imate pravo ostvariti sljedeća prava: ',\r\n      50: 'pravo na pristup osobnim podacima',\r\n      51: 'pravo na ispravak osobnih podataka',\r\n      52: 'pravo na brisanje (\"pravo na zaborav\") ',\r\n      53: 'pravo na ograničenje obrade',\r\n      54: 'pravo na prenosivost podataka ',\r\n      55: 'pravo na podnošenje prigovora.',\r\n      56: 'Kako možete ostvariti svoja prava?',\r\n      57: 'Za sva navedena prava kao i pitanja u vezi sa svojim osobnim podacima možete se obratiti našim službenicima za zaštitu osobnih podataka, i to slanjem e-poruke na e-adresu <a href=\"mailto: zastitapodataka@dzs.hr\" class=\"link\">zastitapodataka@dzs.hr</a> .',\r\n      58: 'Zahtjeve i upite obradit ćemo bez nepotrebnog odgađanja i u skladu sa zakonskim obvezama te ćemo vas u pisanom obliku obavijestiti o mjerama koje smo poduzeli.',\r\n      59: 'Ukoliko smatrate da Zavod postupa na nezakonit način te to ne možete riješiti u suradnji s nama, imate pravo podnijeti pritužbu nadzornom tijelu za zaštitu osobnih podataka u Republici Hrvatskoj ‒ Agenciji za zaštitu osobnih podataka (AZOP).'\r\n    },\r\n    opisivanje_podataka: {\r\n      chapterNumber: '&mdash; Poglavlje 1 &mdash;',\r\n      title: 'Opisivanje podataka',\r\n      table: {\r\n        rank: 'REDNI BROJ UČENIKA',\r\n        time: 'VRIJEME IGRE (min)',\r\n        sex: 'SPOL',\r\n        grade: 'OCJENA',\r\n        freq: 'FREKVENCIJA',\r\n        relFreq: 'RELATIVNA FREKVENCIJA (%)'\r\n      },\r\n      game_time: {\r\n        1: '47',\r\n        2: '177',\r\n        3: '124',\r\n        4: '135',\r\n        5: '69',\r\n        6: '88',\r\n        7: '0',\r\n        8: '120',\r\n        9: '63',\r\n        10: '57',\r\n        11: '79',\r\n        12: '244',\r\n        13: '99',\r\n        14: '76',\r\n        15: '166',\r\n        16: '193',\r\n        17: '19',\r\n        18: '74',\r\n        19: '51',\r\n        20: '20',\r\n        21: '189',\r\n        22: 'ukupno'\r\n      },\r\n      sex: {\r\n        1: 'ž',\r\n        2: 'm',\r\n        3: 'ukupno'\r\n      },\r\n      grade: {\r\n        1: 'nedovoljan',\r\n        2: 'dovoljan',\r\n        3: 'dobar',\r\n        4: 'vrlo dobar',\r\n        5: 'izvrstan',\r\n        6: 'ukupno'\r\n      },\r\n      resultTable: {\r\n        1: 'KATEGORIJA',\r\n        2: 'FREKVENCIJA',\r\n        3: 'RELATIVNA FREKVENCIJA (%)'\r\n      },\r\n      podaci: {\r\n        title: 'Podaci',\r\n        1: 'Podatke prikupljamo na <strong>objektima</strong> (npr. na ljudima, životinjama, biljkama, državama, gradovima, poduzećima itd.) koji se zovu <strong>jedinke</strong> ili <strong>slučajevi</strong>.',\r\n        2: 'Veličine koje nas zanimaju o jedinkama zovu se <strong>varijable</strong>.',\r\n        3: 'Evidenciju o prikupljenim podacima vodimo u <strong>tablicama</strong>. Jedan <strong>redak</strong> odgovara jednoj jedinki, a jedan <strong>stupac</strong> odgovara jednoj varijabli.',\r\n        4: '<strong>Tipovi varijabli:</strong>',\r\n        5: '<strong>numeričke varijable</strong> – vrijednosti tih varijabli su brojevi.',\r\n        6: '<strong>kvalitativne varijable</strong> – vrijednosti tih varijabli po svojim svojstvima nisu brojevi, nego nebrojčane veličine koje se zovu <strong>kategorije</strong>. Kvalitativne varijable dijelimo u dvije skupine:',\r\n        7: '<strong>nominalne varijable</strong> – među kategorijama varijable ne može se uspostaviti prirodan poredak (npr. spol, boja, ime grada, rod  životinje, itd.).',\r\n        8: '<strong>ordinalne varijable</strong> – među kategorijama varijable može se uspostaviti prirodan poredak (npr. stručna sprema osobe, ocjena, itd.). Kategorije ordinalnih varijabli često označujemo brojem.',\r\n        9: '<strong>Primjer 1.1.1.</strong>',\r\n        10: 'Razrednik jednog razreda nastoji pratiti koliko učenici njegova razreda igraju računalne igrice. Za tu je svrhu zamolio učenike da vode evidenciju te je zabilježio koliko su vremena u nedjelju proveli igrajući računalne igrice. Tomu je dodao informacije o spolu učenika te o ocjeni na posljednjem testu iz matematike. Podaci se nalaze u tablici.',\r\n        11: '<strong>Ovdje je:</strong>',\r\n        12: '<strong>vrijeme igre</strong> – numerička varijabla',\r\n        13: '<strong>spol</strong> – kvalitativna nominalna varijabla',\r\n        14: '<strong>ocjena</strong> – kvalitativna ordinalna varijabla.',\r\n        15: 'REDNI BROJ<br>UČENIKA',\r\n        16: 'VRIJEME<br>IGRE (min)',\r\n        17: 'SPOL',\r\n        18: 'OCJENA',\r\n        19: 'ž',\r\n        20: 'dobar',\r\n        21: 'm',\r\n        22: 'dobar',\r\n        23: 'ž',\r\n        24: 'vrlo dobar',\r\n        25: 'm',\r\n        26: 'dobar',\r\n        27: 'm',\r\n        28: 'vrlo dobar',\r\n        29: 'm',\r\n        30: 'nedovoljan',\r\n        31: 'm',\r\n        32: 'dobar',\r\n        33: 'm',\r\n        34: 'dobar',\r\n        35: 'ž',\r\n        36: 'izvrstan',\r\n        37: 'm',\r\n        38: 'dobar',\r\n        39: 'm',\r\n        40: 'vrlo dobar',\r\n        41: 'ž',\r\n        42: 'dobar',\r\n        43: 'ž',\r\n        44: 'dovoljan',\r\n        45: 'm',\r\n        46: 'dobar',\r\n        47: 'm',\r\n        48: 'dobar',\r\n        49: 'ž',\r\n        50: 'vrlo dobar',\r\n        51: 'ž',\r\n        52: 'dobar',\r\n        53: 'm',\r\n        54: 'dovoljan',\r\n        55: 'm',\r\n        56: 'izvrstan',\r\n        57: 'm',\r\n        58: 'vrlo dobar',\r\n        59: 'm',\r\n        60: 'vrlo dobar',\r\n        61: 'ž',\r\n        62: 'nedovoljan',\r\n        63: 'm',\r\n        64: 'vrlo dobar',\r\n        65: 'ž',\r\n        66: 'vrlo dobar',\r\n        67: 'VRIJEME IGRE NEDJELJOM',\r\n        68: 'VRIJEME IGRE PONEDJELJKOM'\r\n      },\r\n      'podaci-tablica-varabli': {\r\n        1: 'Ime i prezime',\r\n        2: 'Ocjena iz matematike',\r\n        3: 'Ocjena iz biologije',\r\n        4: 'Broj sati izostanaka',\r\n        5: 'Petar Petrić',\r\n        6: '5',\r\n        7: '4',\r\n        8: '20',\r\n        9: 'Ivan Ivić',\r\n        10: '4',\r\n        11: '5',\r\n        12: '45',\r\n        13: 'Marko Marković',\r\n        14: '5',\r\n        15: '4',\r\n        16: '130'\r\n      },\r\n      'podaci-zadatak': {\r\n        title: 'Podaci',\r\n        1: '<strong>Zadatak 1.1.1.</strong>',\r\n        2: 'Prikupljaju se podaci o dnevnim navikama skupine osoba u jednom danu kako je navedeno u sljedećem opisu varijabli:',\r\n        3: 'Odredite tip svake navedene varijable.',\r\n        4: '<strong>Varijabla</strong>',\r\n        5: '<strong>Vrijednosti</strong>',\r\n        6: 'spol',\r\n        7: 'M, Z',\r\n        8: 'trenutačno u braku',\r\n        9: 'DA, NE',\r\n        10: 'broj prelistanih dnevnih novina',\r\n        11: '0, 1, 2, itd.',\r\n        12: 'broj gledanih televizijskih vijesti (ne mora biti u potpunosti)',\r\n        13: '0, 1, 2, itd.',\r\n        14: 'broj ispijenih kava',\r\n        15: '0, 1, 2, itd.',\r\n        16: 'troškovi za hranu',\r\n        17: 'broj',\r\n        18: 'osobno raspoloženje',\r\n        19: 'loše, dobro, odlično',\r\n        20: '<strong>Rješenje</strong>',\r\n        21: '<strong>Tip</strong>',\r\n        22: 'kvalitativna nominalna',\r\n        23: 'numerička',\r\n        24: 'kvalitativna ordinalna',\r\n        25: '<strong>Zadatak 1.1.2.</strong>',\r\n        26: '<strong>Oblikujte svoju bazu podataka</strong> koja ima najmanje jednu kvalitativnu ordinalnu, jednu kvalitativnu nominalnu i jednu numeričku varjiablu.'\r\n      },\r\n      'podaci-zadatak-interakcija': {\r\n        title: 'Zadatak',\r\n        1: 'Unesi broj slučajeva (retci tablice): ',\r\n        2: 'Unesi broj varijabli (stupci tablice):',\r\n        3: 'Maksimum je 10',\r\n        4: 'Maksimum je 5',\r\n        5: 'Stvori tablicu',\r\n        6: 'Izvezi tablicu kao CSV datoteku',\r\n        7: 'Naziv atributa',\r\n        8: 'Tip varijable',\r\n        9: 'Numerička varijabla',\r\n        10: 'Kvalitativna nominalna varijabla',\r\n        11: 'Kvalitativna ordinalna varijabla',\r\n        12: 'Unesi podatak',\r\n        13: 'Netočno unesene vrijenosti.',\r\n        14: 'Maksimalan broj slučajeva je 10! Ponovi unos.',\r\n        15: 'Maksimalan broj varijabli je 5! Ponovi unos.',\r\n        16: 'Potreban je unos svih vrijednosti u tablicu.',\r\n        17: 'Minimalni broj varijabli je 3'\r\n\r\n      },\r\n      'frekvencije-i-relativne-frekvencije': {\r\n        title: 'Frekvencije i relativne frekvencije',\r\n        1: 'Tablica frekvencija i relativnih frekvencija jest jedan oblik izvještaja o podacima.',\r\n        2: 'Prikazuje se za odabranu varijablu.',\r\n        3: '<strong>Frekvencija</strong> jedne kategorije jest broj zabilježenih vrijednosti varijable koje pripadaju toj kategoriji.',\r\n        4: '<strong>Relativna frekvencija</strong> jedne kategorije jest frekvencija podijeljena s ukupnim brojem podataka za tu varijablu.',\r\n        5: 'Uobičajene oznake jesu:',\r\n        6: 'frekvencija ⇒ <i>f</i>',\r\n        7: 'broj podataka odabrane varijable ⇒ <i>n</i>',\r\n        8: 'relativna frekvencija ⇒ <div class=\"fraction\" top=\"f\" bottom=\"n\"></div>.',\r\n        9: '<strong>Tablica frekvencija i relativnih frekvencija</strong>',\r\n        10: 'Frekvencije i relativne frekvencije kategorija prikazujemo tablično. Relativne frekvencije najčešće izražavamo u postocima.',\r\n        11: 'KATEGORIJA',\r\n        12: 'FREKVENCIJA',\r\n        13: 'RELATIVNA <br> FREKVENCIJA (%)',\r\n        14: 'ukupno',\r\n        15: '100',\r\n        16: '<strong>Grupiranje podataka u razrede</strong>',\r\n        17: 'Ako varijabla ima puno različitih vrijednosti te ako želimo prikazati podatke tablicom frekvencija i relativnih frekvencija, korisno je vrijednosti grupirati u <strong>razrede.</strong>',\r\n        18: 'Potreba za grupiranjem često se pojavljuje kod numeričkih podataka. Uobičajeno se primjenjuje <strong>grupiranje vrijednosti po intervalima.</strong>',\r\n        19: 'Različiti razredi ne smiju sadržavati iste vrijednosti.',\r\n        20: 'Razredi za grupiranje biraju se pažljivo da bi se istaknula bitna obilježja podataka.',\r\n        21: '<strong>Primjer 1.2.1.</strong>',\r\n        22: 'Razrednik jednog razred nastoji pratiti koliko učenici njegova razreda igraju računalne igrice. Za tu je svrhu zamolio učenike da vode evidenciju te je zabilježio koliko su vremena u nedjelju proveli igrajući računalne igrice. Tomu je dodao informacije o spolu učenika te o ocjeni na posljednjem testu iz matematike. Podaci se nalaze u tablici.',\r\n        23: 'REDNI BROJ <br> UČENIKA',\r\n        24: 'VRIJEME <br> IGRE',\r\n        25: 'SPOL',\r\n        26: 'OCJENA',\r\n        27: 'ž',\r\n        28: 'dobar',\r\n        29: 'm',\r\n        30: 'dobar',\r\n        31: 'ž',\r\n        32: 'vrlo dobar',\r\n        33: 'm',\r\n        34: 'dobar',\r\n        35: 'm',\r\n        36: 'vrlo dobar',\r\n        37: 'm',\r\n        38: 'nedovoljan',\r\n        39: 'm',\r\n        40: 'dobar',\r\n        41: 'm',\r\n        42: 'dobar',\r\n        43: 'ž',\r\n        44: 'izvrstan',\r\n        45: 'm',\r\n        46: 'dobar',\r\n        47: 'm',\r\n        48: 'vrlo dobar',\r\n        49: 'ž',\r\n        50: 'dobar',\r\n        51: 'ž',\r\n        52: 'dovoljan',\r\n        53: 'm',\r\n        54: 'dobar',\r\n        55: 'm',\r\n        56: 'dobar',\r\n        57: 'ž',\r\n        58: 'vrlo dobar',\r\n        59: 'ž',\r\n        60: 'dobar',\r\n        61: 'm',\r\n        62: 'dovoljan',\r\n        64: 'm',\r\n        65: 'izvrstan',\r\n        66: 'm',\r\n        67: 'vrlo dobar',\r\n        68: 'm',\r\n        69: 'vrlo dobar',\r\n        70: 'ž',\r\n        71: 'nedovoljan',\r\n        72: 'm',\r\n        73: 'vrlo dobar',\r\n        74: 'ž',\r\n        75: 'vrlo dobar',\r\n        76: '<strong>Primjer 1.2.2.</strong>',\r\n        77: 'Sljedeće tablice prikazuju frekvencije i relativne frekvencije numeričke varijable <strong>vrijeme igre</strong> za tablicu iz prethodnog primjera. U jednoj tablici podaci nisu grupirani u razrede, a u drugoj tablici vrijednosti su grupirane.',\r\n        78: 'VRIJEME IGRE <br> (min)',\r\n        79: 'FREKVENCIJA',\r\n        80: 'RELATIVNA <br> FREKVENCIJA <br> %',\r\n        81: 'ukupno',\r\n        82: 'Tablica frekvencija i relativnih frekvencija.'\r\n      },\r\n      'frekvencije-i-relativne-frekvencije-primjer': {\r\n        1: 'KATEGORIJA',\r\n        2: 'FREKVENCIJA',\r\n        3: 'RELATIVNA FREKVENCIJA (%)',\r\n        4: 'Odaberite varijablu u tablici za prikaz tablice frekvencija i relativnih frekvencija.',\r\n        5: 'Tablica frekvencija i relativnih frekvencija'\r\n      },\r\n      'frekvencije-i-relativne-frekvencije-zadatak': {\r\n        title: 'Frekvencije i relativne frekvencije',\r\n        1: '<strong>Zadatak 1.2.1.</strong>',\r\n        2: 'Za tablicu iz prethodnog primjera grupirajte podatke varijable <i>vrijeme igre</i> tako da svaki interval ima duljinu 30. Odredite pripadajuću tablicu frekvencija i relativnih frekvencija. Odgovorite na sljedeća pitanja:',\r\n        3: 'Koliki je postotak djece koja su igrala igrice više od tri sata?',\r\n        4: 'Koliki je postotak djece koja su igrala igrice manje od dva sata? Je li tablica frekvencija i relativnih frekvencija tako grupiranih podataka dovoljna da biste odgovorili na ovo pitanje? ',\r\n        5: '<strong>Rješenje</strong>',\r\n        6: 'VRIJEME IGRE (min)',\r\n        7: 'FREKVENCIJA',\r\n        8: 'RELATIVNA FREKVENCIJA (%)',\r\n        9: '[0, 30]',\r\n        10: '<30, 60]',\r\n        11: '<60, 90]',\r\n        12: '<90, 120]',\r\n        13: '<120, 150]',\r\n        14: '<150, 180]',\r\n        15: '<180, 210]',\r\n        16: '<210, 240]',\r\n        17: '<240, 270]',\r\n        18: 'ukupno',\r\n        19: '5',\r\n        20: '3',\r\n        21: '7',\r\n        22: '2',\r\n        23: '0',\r\n        24: '1',\r\n        25: '24',\r\n        26: '20.8',\r\n        27: '12.5',\r\n        28: '29.2',\r\n        29: '8.3',\r\n        30: '0',\r\n        31: '4.2',\r\n        32: 'Više od tri sata igrice je igralo troje djece, što čini 12,5%.',\r\n        33: 'Manje od dva sata igrice je igralo petnaestero djece, što čini 62,5%. Taj podatak ne može se prepoznati samo iz ovako grupiranih podataka. Stoga se moramo služiti i tablicom negrupiranih podataka iz prethodnog primjera.'\r\n      },\r\n      'stupicasti-dijagram-i-histogram': {\r\n        title: 'Stupčasti dijagram i histogram',\r\n        1: '<strong>Stupčasti dijagram</strong> jest prikaz frekvencija ili relativnih frekvencija kategorija odabrane varijable. Sastoji se od stupaca pridruženih kategoriji čija visina odgovara frekvenciji ili relativnoj frekvenciji kategorije. ',\r\n        2: '<strong>Histogram </strong> služi za prikazivanje numeričkih podataka. Prije izrade histograma potrebno je grupirati podatke u intervale te izraditi tablicu frekvencija grupiranih podataka. Histogram se crta u koordinatnom sustavu tako da se stupci postavljaju nad odgovarajućim intervalima. Visina stupca odgovara frekvenciji intervala.',\r\n        3: '<strong>Primjer 1.3.1.</strong>',\r\n        4: 'Razrednik jednog razreda nastoji pratiti koliko učenici njegova razreda igraju računalne igrice. Za tu je svrhu zamolio učenike da vode evidenciju te je zabilježio koliko su vremena u nedjelju proveli igrajući računalne igrice. Tomu je dodao informacije o spolu učenika te o ocjeni na posljednjem testu iz matematike. Podaci se nalaze u tablici.',\r\n        5: 'redni broj<br>učenika',\r\n        6: 'vrijeme<br>igre (u min)',\r\n        7: 'spol',\r\n        8: 'ocjena',\r\n        9: 'ž',\r\n        10: 'dobar',\r\n        11: 'm',\r\n        12: 'dobar',\r\n        13: 'ž',\r\n        14: 'vrlo dobar',\r\n        15: 'm',\r\n        16: 'dobar',\r\n        17: 'm',\r\n        18: 'vrlo dobar',\r\n        19: 'm',\r\n        20: 'nedovoljan',\r\n        21: 'm',\r\n        22: 'dobar',\r\n        23: 'm',\r\n        24: 'dobar',\r\n        25: 'ž',\r\n        26: 'izvrstan',\r\n        27: 'm',\r\n        28: 'dobar',\r\n        29: 'm',\r\n        30: 'vrlo dobar',\r\n        31: 'ž',\r\n        32: 'dobar',\r\n        33: 'ž',\r\n        34: 'dovoljan',\r\n        35: 'm',\r\n        36: 'dobar',\r\n        37: 'm',\r\n        38: 'dobar',\r\n        39: 'ž',\r\n        40: 'vrlo dobar',\r\n        41: 'ž',\r\n        42: 'dobar',\r\n        43: 'm',\r\n        44: 'dovoljan',\r\n        45: 'm',\r\n        46: 'izvrstan',\r\n        47: 'm',\r\n        48: 'vrlo dobar',\r\n        49: 'm',\r\n        50: 'vrlo dobar',\r\n        51: 'ž',\r\n        52: 'nedovoljan',\r\n        53: 'm',\r\n        54: 'vrlo dobar',\r\n        55: 'ž',\r\n        56: 'vrlo dobar',\r\n        57: 'Sljedećim alatom možemo nacrtati stupčaste dijagrame za kvalitativne varijable iz prethodne tablice. Možemo nacrtati stupčasti dijagram frekvencija ili relativnih frekvencija. Uočljivo je da dijagrami imaju isti oblik, a različite su samo vrijednosti visine stupaca.',\r\n        58: '<strong>Primjer 1.3.2.</strong>',\r\n        59: 'Sljedećim alatom možemo nacrtati histogram za varijablu <i>vrijeme igre</i> iz prethodnog primjera. Odaberite minimalnu i maksimalnu vrijednost te broj intervala na koji će biti podijeljen skup za prikaz histograma.'\r\n      },\r\n      'stupcasti-dijagram-i-histogram-primjer': {\r\n        1: 'Jedinstvena ponavljanja',\r\n        2: 'Frekvencija',\r\n        3: 'Relativna frekvencija (%)',\r\n        4: 'Stupčasti dijagram frekvencija',\r\n        5: 'Frekvencija osoba',\r\n        6: 'Žene',\r\n        7: 'Muškarci',\r\n        8: 'Stupčasti dijagram relativnih frekvencija',\r\n        9: 'Relativna frekvencija osoba',\r\n        10: 'Minimalna i maksimalna zabilježena vrijednost vremena igre: ',\r\n        11: 'Donja granica vrijednosti za prikaz histograma: ',\r\n        12: 'Početak niza',\r\n        13: 'Gornja granica vrijednosti za prikaz histograma: ',\r\n        14: 'Kraj niza',\r\n        15: 'Unesi broj segmenata na koje želiš podijeliti niz:',\r\n        16: 'Broj segmenata',\r\n        17: 'Stvori tablicu',\r\n        18: 'VRIJEME IGRE (min)',\r\n        19: 'FREKVENCIJA',\r\n        20: 'RELATIVNA FREKVENCIJA (%)',\r\n        21: 'Histogram frekvencija',\r\n        22: 'Histogram relativnih frekvencija',\r\n        23: 'Stupčasti dijagram frekvencija',\r\n        24: 'Frekvencija ocjena',\r\n        25: 'nedovoljan',\r\n        26: 'dovoljan',\r\n        27: 'dobar',\r\n        28: 'vrlo dobar',\r\n        29: 'izvrstan',\r\n        30: 'Stupčasti dijagram relativnih frekvencija',\r\n        31: 'Relativna frekvencija ocjena',\r\n        32: 'Unesene vrijednosti moraju biti brojevi',\r\n        33: 'ukupno',\r\n        34: 'Za početak odaberite varijablu spol ili varijablu ocjena.',\r\n        35: 'Za početak odaberite varijablu vrijeme igre.',\r\n        36: 'Frekvencija vremena igre',\r\n        37: 'Relativna frekvencija vremena igre',\r\n        38: 'Prazan unos bilo kojeg podatka nije dozvoljen.',\r\n        39: 'Odabrani niz se ne moze podijeliti na odabrani broj elemenata.'\r\n      },\r\n      'stupicasti-dijagram-i-histogram-zadatak': {\r\n        title: 'Stupčasti dijagram i Histogram',\r\n        1: '<strong>Zadatak 1.3.1.</strong>',\r\n        2: 'U tablici se nalaze podaci o anketiranim ispitanicima: varijabla <i>broj pregleda</i> označuje ukupan broj pregleda, varijabla <i>dopunsko zdravstveno</i> označuje ima li ispitanik dopunsko zdravstveno osiguranje (1 – ima; 0 – nema) i varijabla <i>cijena</i> sadržava cijenu najskupljega zdravstvenog pregleda ispitanika (u kunama).',\r\n        3: 'BROJ <br> PREGLEDA',\r\n        4: 'DODATNO <br> ZDRAVSTVENO',\r\n        5: 'CIJENA',\r\n        6: 'Za koju je varijablu primjeren prikaz stupčastim dijagramom? Odaberite tu varijablu da biste vidjeli prikaz podataka u stupčastom dijagramu.',\r\n        7: 'Odaberite varijablu <i>cijena</i> da biste otvorili alat za grupiranje podataka te unesite potrebne parametre kako biste vidjeli pripadajuću tablicu frekvencija i relativnih frekvencija te histogram i utvrdili u kolikom je postotku najskuplji zdravstveni pregled bio skuplji od 200 kuna, a u kolikom postotku veći od 150 kuna. ',\r\n        8: '<strong>Rješenje</strong>',\r\n        9: 'Najskuplji zdravstveni pregled bio je veći od 200 kuna u 30% slučajeva, a veći od 150 kuna u 67,5% slučajeva.'\r\n      },\r\n      'stupcasti-dijagram-i-histogram-zadatak-interakcija': {\r\n        1: 'BROJ PREGLEDA',\r\n        2: 'DOPUNSKO ZDRAVSTVENO',\r\n        3: 'CIJENA',\r\n        4: 'Određeni nizovi',\r\n        5: 'Frekvencija elemenata niza',\r\n        6: 'Relativna frekvencija niza',\r\n        7: 'Minimum i maksimum',\r\n        8: 'Donja granica vrijednosti za prikaz histograma: ',\r\n        9: 'Početak niza',\r\n        10: 'Gornja granica vrijednosti za prikaz histograma: ',\r\n        11: 'Kraj niza',\r\n        12: 'Unesi broj segmenata na koje želiš podijeliti niz:',\r\n        13: 'Broj segmenata',\r\n        14: 'Stvori tablicu',\r\n        15: 'Stupčasti dijagram frekvencija',\r\n        16: 'Frekvencija',\r\n        17: 'Relativna frekvencija',\r\n        18: ' broja pregleda',\r\n        19: ' cijene pregleda',\r\n        20: ' dopunskog zdravstvenog osiguranja',\r\n        21: 'Početni broj niza mora biti manji od krajnjeg broja niza',\r\n        22: 'Krajnji broj niza mora biti unutar odabranog niza',\r\n        23: 'Početni broj niza mora biti untuar odabranog niza',\r\n        24: 'Stupčasti dijagram relativnih frekvencija',\r\n        25: 'Krajnji broj niza mora biti veći od početnog broja niza'\r\n      },\r\n      prosjek: {\r\n        title: 'Prosjek',\r\n        1: `<strong>Prosjek </strong> ili <strong>aritmetička sredina</strong> podataka 𝑥<sub>1</sub> , 𝑥<sub>2</sub> , … , 𝑥<sub>𝑛</sub> jest zbroj svih podataka podijeljen s ukupnim brojem podataka:`,\r\n        2: 'Prosjek je jedna mjera centra niza numeričkih podataka.',\r\n        3: '<strong>Osjetljivost prosjeka na stršeće vrijednosti</strong>',\r\n        4: 'Stršeća vrijednost jest podatak čija je vrijednost puno veća ili manja u odnosu na druge podatke. Ako se podacima dodaje vrijednost koja znatno odstupa od prosjeka postojećih vrijednosti, novi prosjek promijenit će se u velikoj mjeri.',\r\n        5: '<strong>Primjer 1.4.1.</strong>',\r\n        6: 'VRIJEME IGRE <br> (min)',\r\n        7: 'SPOL',\r\n        8: 'Dodamo li postojećem nizu broj 4, prosjek će iznositi 4.181.',\r\n        9: 'Dodamo li postojećem nizu broj 50, prosjek će iznositi 8.36.',\r\n        10: 'Odaberite jedan broj i dodajte ga postojećem nizu. Promatrajte kako se mijenja prosjek.',\r\n        11: 'm',\r\n        12: 'dobar',\r\n        13: 'ž',\r\n        14: 'vrlo dobar',\r\n        15: 'm',\r\n        16: 'dobar',\r\n        17: 'm',\r\n        18: 'vrlo dobar',\r\n        19: 'm',\r\n        20: 'nedovoljan',\r\n        21: 'm',\r\n        22: 'dobar',\r\n        23: 'm',\r\n        24: 'dobar',\r\n        25: 'ž',\r\n        26: 'izvrstan',\r\n        27: 'm',\r\n        28: 'dobar',\r\n        29: 'm',\r\n        30: 'vrlo dobar',\r\n        31: 'ž',\r\n        32: 'dobar',\r\n        33: 'ž',\r\n        34: 'dovoljan',\r\n        35: 'm',\r\n        36: 'dobar',\r\n        37: 'm',\r\n        38: 'dobar',\r\n        39: 'ž',\r\n        40: 'vrlo dobar',\r\n        41: 'ž',\r\n        42: 'dobar',\r\n        43: 'm',\r\n        44: 'dovoljan',\r\n        45: 'm',\r\n        46: 'izvrstan',\r\n        47: 'm',\r\n        48: 'vrlo dobar',\r\n        49: 'm',\r\n        50: 'vrlo dobar',\r\n        51: 'ž',\r\n        52: 'nedovoljan',\r\n        53: 'm',\r\n        54: 'vrlo dobar',\r\n        55: 'ž',\r\n        56: 'vrlo dobar',\r\n        57: 'REDNI BROJ <br> UČENIKA',\r\n        58: 'OCJENA',\r\n        59: 'ž',\r\n        60: 'dobar',\r\n        61: 'Prosječno vrijeme koje su učenici jednog razreda proveli u igranju igrica nedjeljom iznosi 89,96. Dodajte jedan podatak i promatrajte kako se mijenja prosjek i histogram.',\r\n        62: '<strong>Primjer 1.4.2.</strong>',\r\n        63: 'Razrednik jednog razreda nastoji pratiti koliko učenici njegova razreda igraju računalne igrice. Za tu je svrhu zamolio učenike da vode evidenciju te je zabilježio koliko su vremena u nedjelju proveli igrajući računalne igrice. Tomu je dodao informacije o spolu učenika te o ocjeni na posljednjem testu iz matematike. Podaci se nalaze u tablici.',\r\n        64: 'Za podatke 3, 5, 7, 2, 1, 7, 4, 3, 5, 5 prosjek iznosi',\r\n\t65: 'Za početak, odaberite varijablu vrijeme igre.'\r\n      },\r\n      'prosjek-tablica': {\r\n        1: '1.',\r\n        2: '2.',\r\n        3: '3.',\r\n        4: '4.',\r\n        5: '5.',\r\n        6: '6.',\r\n        7: '7.',\r\n        8: '8.',\r\n        9: '9.',\r\n        10: '10.',\r\n        11: '11.',\r\n        12: '12.',\r\n        13: '13.',\r\n        14: '14.',\r\n        15: '15.',\r\n        16: '16.',\r\n        17: '17.',\r\n        18: '18.',\r\n        19: '19.',\r\n        20: '20.',\r\n        21: '21.',\r\n        22: '22.',\r\n        23: '23.',\r\n        24: '24.'\r\n      },\r\n      'prosjek-interakcija': {\r\n        1: 'Početni niz brojeva: ',\r\n        2: 'Unesi novi element niza: ',\r\n        3: 'Unesi broj',\r\n        4: 'Stvori graf',\r\n        5: 'Prosjek početnog niza: ',\r\n        6: 'Prosjek niza s novim elementom: ',\r\n        7: 'Početna raspodjela niza i prosjek',\r\n        8: 'Dodani element i novi prosjek',\r\n        9: 'Sortirana lista vremena igre:',\r\n        10: 'Vrijeme igre',\r\n        11: 'Frekvencija elemenata niza',\r\n        12: 'Relativna frekvencija niza',\r\n        13: 'Graf frekvencija',\r\n        14: 'Novi element niza mora biti broj',\r\n        15: 'Potrebna je vrijednost novog elementa niza.'\r\n      },\r\n      'prosjek-zadatak': {\r\n        title: 'Prosjek',\r\n        1: '<strong>Zadatak 1.4.1.</strong>',\r\n        2: 'Proučavanjem kretanja cijena prehrambenih proizvoda analitičar tržišta uočio je da isti proizvodi nemaju jednaku cijenu u različitim trgovačkim centrima. Promatrajući jedanaest trgovačkih centara, zabilježio je cijene proizvoda kod kojih su razlike bile najizraženije.',\r\n        3: 'OZNAKA <br> TRGOVINE',\r\n        4: 'CIJENA',\r\n        5: 'Sljedećim alatom možete izračunati prosječnu cijenu za niz odabranih trgovačkih centara. Za koliko se smanji prosjek ako iz niza trgovačkih centara izbacimo prvi, a za koliko ako izbacimo jedanaesti?',\r\n        6: '<strong>Zadatak 1.4.2.</strong>',\r\n        7: 'Zadana su dva skupa podataka:',\r\n        8: '0, 1, 2, 3, −1, −2, −3, 0.5, 0.7, 0.25, −1, −0.45',\r\n        9: '−100, 100, 150, −75, −250, 200, −25.',\r\n        10: 'Odredite prosjek svakog skupa. Po čemu su ti skupovi slični? Iskazuje li se prosjekom dovoljno informacija o skupu podataka?',\r\n        11: '<strong>Rješenje</strong>',\r\n        12: 'Prosjek po svim trgovinama jest 52.88. Ako izbacimo prvi trgovački centar, prosjek iznosi 53.62, a ako izbacimo jedanaesti, prosjek iznosi 48.67.',\r\n        13: 'Prosjek je u oba slučaja 0. Skupovi imaju isti prosjek, a znatno se razlikuju. Dakle, prosjekom se ne iskazuje dovoljno informacija o skupu podataka.',\r\n        14: 'Cijene za izračun prosjeka odaberite klikom na pojedinu cijenu.',\r\n        15: 'Klikom na pojedinu cijenu ona ulazi u izračun prosječne cijene.'\r\n      },\r\n      'prosjek-zadatak-interakcija': {\r\n        1: 'OZNAKA TRGOVINE',\r\n        2: 'CIJENA',\r\n        3: 'Prosječna cijena svih trgovina: ',\r\n        4: 'Prosječna cijena odabranih trgovina: '\r\n      },\r\n      medijan: {\r\n        title: 'Medijan',\r\n        1: '<strong>Medijan </strong> je jedna mjera centra niza numeričkih podataka.',\r\n        2: 'Smisao medijana jest istaknuti broj koji dijeli uređeni niz podataka na dva dijela tako da:',\r\n        3: 'svaki dio sadržava isti broj podataka',\r\n        4: 'svi podaci iz prvog dijela nisu veći od podataka iz drugog dijela.',\r\n        5: 'Tako dobijemo broj za koji možemo reći da je barem 50% podataka manje od tog broja ili jednako njemu, a istodobno je barem 50% podataka veće od tog broja ili jednako njemu.',\r\n        6: 'Za definiciju <strong>medijana podataka</strong> potrebno je podatke prvo poredati po veličini.',\r\n        7: '<strong>Slijedi algoritam za izračun medijana:</strong>',\r\n        8: 'Zadan je niz podataka: 𝑥<sub>1</sub> , 𝑥<sub>2</sub> , … , 𝑥<sub>𝑛</sub>.',\r\n        9: 'Poredamo podatke po veličini, od najmanjega prema najvećemu.',\r\n        10: 'Ako <div class=\"fraction\" top=\"𝑛\" bottom=\"2\"></div> nije prirodan broj, onda je medijan podatak na prvoj poziciji većoj od <div class=\"fraction\" top=\"𝑛\" bottom=\"2\"></div>.',\r\n        11: 'Ako je <div class=\"fraction\" top=\"𝑛\" bottom=\"2\"></div> prirodan broj, onda je medijan prosjek podataka na pozicijama <div class=\"fraction\" top=\"𝑛\" bottom=\"2\"></div> i <div class=\"fraction\" top=\"𝑛\" bottom=\"2\"></div> + 1.',\r\n        12: 'U usporedbi s prosjekom, medijan je manje osjetljiv na <strong>stršeću vrijednost</strong> u podacima. Stršeća vrijednost jest podatak čija je vrijednost puno veća ili manja u odnosu na druge podatke.',\r\n        13: '<strong>Primjer 1.5.1.</strong>',\r\n        14: 'Neka su dani podaci: ',\r\n        15: '3, 5, 7, 2, 1, 7, 4, 3, 5, 5, 5',\r\n        16: 'Za izračun medijana taj niz razvrstavamo od najmanjega prema najvećemu:',\r\n        17: '1, 2, 3, 3, 4, 5, 5, 5, 5, 7, 7',\r\n        18: 'U tom nizu ima 11 podataka (neparan broj). Medijan je podatak koji se nalazi na srednjoj (šestoj) poziciji u uređenom nizu podataka, tj. medijan je 5.',\r\n        19: '<strong>Primjer 1.5.2.</strong>',\r\n        20: 'Neka su dani podaci',\r\n        21: '3, 5, 7, 2, 1, 7, 4, 3, 5, 5',\r\n        22: 'Za izračun medijana taj niz razvrstavamo od najmanjega prema najvećemu:',\r\n        23: '1, 2, 3, 3, 4, 5, 5, 5, 7, 7',\r\n        24: 'U tom nizu ima 10 podataka (paran broj). <div class=\"fraction\" top=\"10\" bottom=\"2\"></div> = 5 , pa je medijan prosjek vrijednosti na petoj i šestoj poziciji u uređenom nizu, tj. <div class=\"fraction\" top=\"(4 + 5)\" bottom=\"2\"></div> = 4.5.',\r\n        25: '<strong>Primjer 1.5.3.</strong>',\r\n        26: '3, 5, 7, 2, 1, 7, 4, 3, 5, 5',\r\n        27: 'Prosjek iznosi 4.2, a medijan 4.5.',\r\n        28: 'Dodate li postojećem nizu broj 50, prosjek će iznositi 8.36, a medijan 5.',\r\n        29: 'Sami odaberite broj i dodajte ga ovom nizu te promatrajte kako se mijenja medijan, a kako prosjek.'\r\n      },\r\n      'median-interaction': {\r\n        1: 'Medijan početnog niza: ',\r\n        2: 'Početni niz brojeva: ',\r\n        3: 'Unesi novi element niza: ',\r\n        4: 'Unesi broj',\r\n        5: 'Izračunaj i nacrtaj',\r\n        6: 'Prosjek početnog niza:',\r\n        7: 'Prosjek niza s novim elementom:',\r\n        8: 'Početna raspodjela elemenata niza',\r\n        9: 'Prosjek',\r\n        10: 'Medijan',\r\n        11: 'Nova raspodjela elemenata niza',\r\n        12: 'Novi prosjek',\r\n        13: 'Novi medijan',\r\n        14: 'Sortiraj niz',\r\n        15: 'Izračunaj medijan',\r\n        16: 'Novi element niza mora biti broj',\r\n        17: 'Potrebna je vrijednost novog elementa niza',\r\n        18: 'Medijan niza s novim elementom: ',\r\n      },\r\n      'medijan-zadatak': {\r\n        title: 'Medijan',\r\n        1: '<strong>Zadatak 1.5.1.</strong>',\r\n        2: 'Razrednik jednog razreda nastoji pratiti koliko učenici njegova razreda igraju računalne igrice. Za tu je svrhu zamolio učenike da vode evidenciju te je zabilježio koliko su vremena u nedjelju proveli igrajući računalne igrice. Tomu je dodao informacije o spolu učenika te o ocjeni na posljednjem testu iz matematike. Podaci se nalaze u tablici.',\r\n        3: 'Možemo li reći da je barem 50% učenika igralo igrice manje od prosječnog vremena igranja u razredu?',\r\n        4: '<strong>Rješenje</strong>',\r\n        5: 'Prosjek iznosi 89.96, dok je medijan 75 i manji je od prosjeka. Dakle, tvrdnja je istinita.'\r\n      },\r\n      'minimum-maksimum-i-raspon': {\r\n        title: 'Minimum, maksimum i raspon',\r\n        1: 'Neka su 𝑥<sub>1</sub> , 𝑥<sub>2</sub> , … , 𝑥<sub>𝑛</sub> dani podaci.',\r\n        2: '<strong>Minimum</strong> je najmanji podatak u nizu i označujemo ga 𝑥<sub>𝑚𝑖𝑛</sub>.',\r\n        3: '<strong>Maksimum</strong> je najveći podatak u nizu i označujemo ga 𝑥<sub>𝑚𝑎𝑥</sub>.',\r\n        4: '<strong>Raspon</strong> je razlika između minimuma i maksimuma:',\r\n        5: '𝑟𝑎𝑠𝑝𝑜𝑛 = 𝑥𝑚𝑎𝑥 − 𝑥𝑚𝑖𝑛',\r\n        6: 'Raspon je gruba mjera raspršenosti podataka.',\r\n        7: '<strong>Primjer 1.6.1.</strong>',\r\n        8: 'Za podatke:',\r\n        9: '3, 5, 7, 2, 1, 7, 4, 3, 5, 5',\r\n        10: 'Lako izračunamo:',\r\n        14: 'raspon'\r\n      },\r\n      'minimum-maksimum-i-raspon-interakcija': {\r\n        1: 'Podaci: ',\r\n        2: 'Sortirani niz: ',\r\n        3: 'Minimum: ',\r\n        4: 'Maksimum: ',\r\n        5: 'Raspon: ',\r\n        6: 'Sortiraj niz',\r\n        7: 'Izračunaj min, max i raspon'\r\n      },\r\n      'minimum-maksimum-i-raspon-zadatak': {\r\n        title: 'Minimum, maksimum i raspon',\r\n        1: '<strong>Zadatak 1.6.1.</strong>',\r\n        2: 'Razrednik jednog razreda nastoji pratiti koliko učenici njegova razreda igraju računalne igrice. Za tu je svrhu zamolio učenike da vode evidenciju te je zabilježio koliko su vremena u nedjelju proveli igrajući računalne igrice. Tomu je dodao informacije o spolu učenika te o ocjeni na posljednjem testu iz matematike. Podaci se nalaze u tablici.',\r\n        3: 'Odredite minimum, maksimum i raspon podataka varijable vrijeme igre.',\r\n        4: '<strong>Rješenje</strong>',\r\n        5: 'Minimum je 0, maksimum je 244, pa je raspon 244.'\r\n      },\r\n      'kvartili-i-interkvartilni-raspon': {\r\n        title: 'Kvartili i interkvartilni raspon',\r\n        1: '<strong>Interkvartilni raspon</strong> jest jedna mjera raspršenosti podataka. Definira se s pomoću <strong>kvartila</strong>.',\r\n        2: 'Smisao <strong>kvartila</strong> jest istaknuti broj koji dijeli uređeni niz podataka na dva dijela tako da:',\r\n        3: 'jedan dio sadržava četvrtinu podataka, a drugi dio tri četvrtine podataka',\r\n        4: 'svi podaci iz prvog dijela nisu veći od podataka iz drugog dijela.',\r\n        5: 'Razlikujemo dva kvartila: <strong>donji kvartil</strong>, koji ćemo označiti s 𝑄<sub>1</sub>, i <strong>gornji kvartil</strong>, koji ćemo označiti s 𝑄<sub>3</sub>.',\r\n        6: '<strong>Donji kvartil</strong> dijeli prvu četvrtinu uređenog niza podataka od druge tri četvrtine. Tako dobijemo broj za koji možemo reći da je barem 25% podataka manje od tog broja ili jednako njemu, a istodobno barem 75% podataka veće od tog broja ili jednako njemu.',\r\n        7: '<strong>Gornji kvartil</strong> dijeli prve tri četvrtine uređenog niza podataka od posljednje četvrtine. Tako dobijemo broj za koji možemo reći da je barem 75% podataka manje od tog broja ili jednako njemu, a istodobno barem 25% podataka veće od tog broja ili jednako njemu.',\r\n        8: 'Uočite sličnost ideje upotrebe kvartila s medijanom.',\r\n        9: 'Min',\r\n        10: '𝑄1',\r\n        11: 'Medijan',\r\n        12: '𝑄3',\r\n        13: 'Max',\r\n        14: 'Sortirani <br> podaci',\r\n        15: 'Pozicija u <br> uređenom <br> nizu',\r\n        16: '<strong>Interkvartilni raspon</strong> jest razlika između gornjega i donjega kvartila:',\r\n        18: '<strong>Primjer 1.7.1.</strong>',\r\n        19: 'Zadan je niz od 18 podataka:',\r\n        21: 'Oznaka <br> pozicije',\r\n        22: 'interkvartilni',\r\n        23: 'raspon',\r\n        24: 'pa \\\\thinspace je',\r\n        25: 'Zadan je niz podataka: x<sub>1</sub>,x<sub>2</sub>,…,x<sub>n</sub>.',\r\n        26: 'Podatke poredamo po veličini, od najmanjega prema najvećemu.',\r\n        27: '<strong>Donji kvartil<strong>, Q<sub>1</sub>',\r\n        28: 'Ako <div class=\"fraction\" top=\"𝑛\" bottom=\"4\"></div> nije prirodan broj, onda je podatak na prvoj poziciji većoj od <div class=\"fraction\" top=\"𝑛\" bottom=\"4\"></div> donji kvartil.',\r\n        29: 'Ako je <div class=\"fraction\" top=\"𝑛\" bottom=\"4\"></div> prirodan broj, onda je donji kvartil prosjek podataka na pozicijama <div class=\"fraction\" top=\"𝑛\" bottom=\"4\"></div> i <div class=\"fraction\" top=\"𝑛\" bottom=\"4\"></div> + 1.',\r\n        30: '<strong>Gornji kvartil<strong>, Q<sub>3</sub>',\r\n        31: 'Ako 3<div class=\"fraction\" top=\"𝑛\" bottom=\"4\"></div> nije prirodan broj, onda je podatak na prvoj poziciji većoj od 3<div class=\"fraction\" top=\"𝑛\" bottom=\"4\"></div> gornji kvartil.',\r\n        32: 'Ako je 3<div class=\"fraction\" top=\"𝑛\" bottom=\"4\"></div>prirodan broj, onda je gornji kvartil prosjek podataka na pozicijama 3<div class=\"fraction\" top=\"𝑛\" bottom=\"4\"></div> i 3<div class=\"fraction\" top=\"𝑛\" bottom=\"4\"></div> + 1.',\r\n        33: 'Za one koji žele znati više'\r\n      },\r\n      'kvartili-i-interkvartilni-raspon-interakcija': {\r\n        1: 'Početni niz brojeva: ',\r\n        2: 'Stvori tablicu',\r\n        3: 'Sortirani podaci',\r\n        4: 'Oznaka pozicije',\r\n        5: 'Izračunaj kvartile',\r\n        6: 'pa je Q1: ',\r\n        7: 'pa je Q3: ',\r\n        8: 'Interkvartilni raspon je: ',\r\n        9: 'Medijan je: '\r\n      },\r\n      'kvartili-i-interkvartilni-raspon-zadatak': {\r\n        title: 'Kvartili i interkvartilni raspon',\r\n        1: '<strong>Zadatak 1.7.1.</strong>',\r\n        2: 'Razrednik jednog razreda nastoji pratiti koliko učenici njegova razreda igraju računalne igrice. Za tu je svrhu zamolio učenike da vode evidenciju te je zabilježio koliko su vremena u nedjelju proveli igrajući računalne igrice. Tomu je dodao informacije o spolu učenika te o ocjeni na posljednjem testu iz matematike. Podaci se nalaze u tablici.',\r\n        3: 'Odredite donji i gornji kvartil te interkvartilni raspon podataka varijable <i>vrijeme igre</i> te odgovorite na sljedeća pitanja:',\r\n        4: 'Je li istinita tvrdnja da je više od 75% djece igralo igrice manje od dva sata?',\r\n        5: 'Je li istinita tvrdnja da je manje od 25% djece igralo igrice više od dva sata?',\r\n        6: 'Je li istinita tvrdnja da je više od 25% djece igralo igrice manje od pola sata?',\r\n        7: '<strong>Rješenje</strong>',\r\n        8: 'Odgovori: ',\r\n        9: 'Gornji kvartil jest 129.5 minuta, pa tvrdnja nije istinita.',\r\n        10: 'Gornji kvartil jest 129.5 minuta, pa je tvrdnja istinita.',\r\n        11: 'Donji kvartil jest 49, pa tvrdnja nije istinita.'\r\n      },\r\n      'varijanca-i-standardna-devijacija': {\r\n        title: 'Varijanca i standardna devijacija',\r\n        1: 'Varijanca i standardna devijacija jesu mjere raspršenosti podataka koje karakteriziraju raspršenost podataka oko prosjeka.',\r\n        2: '<strong>Varijanca</strong> je srednje kvadratno odstupanje niza podataka od njihova prosjeka. Ako je <i>n</i> broj podataka, njihovu varijancu označit ćemo sa <i>s</i><sup>2</sup><sub>n</sub>.',\r\n        3: 'Za niz podataka 𝑥<sub>1</sub>, 𝑥<sub>2</sub>, … ,𝑥<sub>𝑛</sub> varijanca je dana izrazom',\r\n        4: 'formula',\r\n        5: '<strong>Standardna devijacija</strong> jest drugi korijen varijance. Oznaka za standardnu devijaciju jest <i>s</i><sub>n</sub>.',\r\n        6: 'formula',\r\n        7: '<strong>Primjer 1.8.1.</strong>',\r\n        8: 'Za podatke:',\r\n        10: 'prosjek iznosi 4.2. Izračun varijance može se ilustrirati tablicom.',\r\n        11: 'PODATAK',\r\n        12: 'ODSTUPANJE OD PROSJEKA',\r\n        13: 'KVADRAT <br> ODSTUPANJA OD PROSJEKA',\r\n        14: 'zbroj',\r\n        15: 'Varijanca iznosi <span class=\"fraction\" top=\"35,6\" bottom=\"9\"></span> = 3.96, a standardna devijacija iznosi 1.99.'\r\n      },\r\n      'varijanca-i-standardna-devijacija-zadatak': {\r\n        title: 'Varijanca i standardna devijacija',\r\n        1: '<strong>Zadatak 1.8.1.</strong>',\r\n        2: 'Zadana su dva skupa podataka:',\r\n        3: '0, 1, 2, 3, -1, -2, -3, 0.5, 0.7, 0.25, -1, -0.45',\r\n        4: '-100, 100, 150, -75, -250, 200, -25.',\r\n        5: 'Odredite prosjek i standardnu devijaciju svakog skupa.',\r\n        6: 'Po čemu su ti skupovi slični? Iskazuje li se prosjekom dovoljno informacija o skupu podataka? Smatrate li standardnu devijaciju važnom informacijom pri izvještavanju o podacima?',\r\n        7: '<strong>Zadatak 1.8.2.</strong>',\r\n        8: 'Razrednik jednog razreda nastoji pratiti koliko učenici njegova razreda igraju računalne igrice. Za tu je svrhu zamolio učenike da vode evidenciju te je zabilježio koliko su vremena u nedjelju proveli igrajući računalne igrice. Tomu je dodao informacije o spolu učenika te o ocjeni na posljednjem testu iz matematike. Podaci se nalaze u tablici.',\r\n        9: 'Koristite se nekim tabličnim kalkulatorom pa izračunajte varijancu i standardnu devijaciju za varijablu <i>vrijeme igre</i>.',\r\n        10: '<strong>Rješenje zadatka 1.8.1.</strong>',\r\n        11: 'Prosjek prvog skupa jest 0, a standardna devijacija iznosi 1.65.',\r\n        12: 'Prosjek drugog skupa jest 0, a standardna devijacija iznosi 158.77.',\r\n        13: 'Prosjeci su isti, a razlike su vidljive u standardnoj devijaciji.',\r\n        14: 'Prosjek iznosi 89.96.',\r\n        15: 'VRIJEME IGRE (min)',\r\n        16: 'ODSTUPANJE OD PROSJEKA',\r\n        17: 'KVADRAT ODSTUPANJA OD PROSJEKA',\r\n        18: '47',\r\n        19: '177',\r\n        20: '124',\r\n        21: '135',\r\n        22: '69',\r\n        23: '88',\r\n        24: '0',\r\n        25: '69',\r\n        26: '120',\r\n        27: '63',\r\n        28: '57',\r\n        29: '79',\r\n        30: '244',\r\n        31: '99',\r\n        32: '76',\r\n        33: '166',\r\n        34: '193',\r\n        35: '19',\r\n        36: '74',\r\n        37: '51',\r\n        38: '20',\r\n        39: '189',\r\n        40: '<strong>zbroj</strong>',\r\n        41: '-42.96',\r\n        42: '87.04',\r\n        43: '34.04',\r\n        44: '45.04',\r\n        45: '-20.96',\r\n        46: '-1.96',\r\n        47: '-89.96',\r\n        48: '-20.96',\r\n        49: '30.04',\r\n        50: '-89.96',\r\n        51: '-26.96',\r\n        52: '-32.96',\r\n        53: '-10.96',\r\n        54: '154.04',\r\n        55: '-89.96',\r\n        56: '9.04',\r\n        57: '-13.96',\r\n        58: '76.04',\r\n        59: '103.04',\r\n        60: '-70.96',\r\n        61: '-15.96',\r\n        62: '-38.96',\r\n        63: '-69.96',\r\n        64: '99.04',\r\n        65: '1845.56',\r\n        66: '7575.96',\r\n        67: '1158.72',\r\n        68: '2028.60',\r\n        69: '439.32',\r\n        70: '3.84',\r\n        71: '8092.80',\r\n        72: '439.32',\r\n        73: '902.40',\r\n        74: '8092.80',\r\n        75: '726.84',\r\n        76: '1086.36',\r\n        77: '120.12',\r\n        78: '23728.32',\r\n        79: '8092.80',\r\n        80: '81.72',\r\n        81: '194.88',\r\n        82: '5782.08',\r\n        83: '10617.24',\r\n        84: '5035.32',\r\n        85: '254.72',\r\n        86: '1517.88',\r\n        87: '4894.40',\r\n        88: '9808.92',\r\n        89: '102520.96',\r\n        90: 'Varijanca iznosi 4457.43, a standardna devijacija iznosi 66.76.',\r\n        91: '<strong>Rješenje zadatka 1.8.2.</strong>',\r\n      },\r\n      'kutijasti-dijagram': {\r\n        title: 'Kutijasti dijagram',\r\n        1: '<strong>Kutijasti dijagram</strong> (engl. box plot ili box-and-whisker plot) prikazuje odnos minimuma, maksimuma, donjega i gornjega kvartila te medijana podataka.',\r\n        2: 'Ako u podacima postoje stršeće vrijednosti (podaci čije su vrijednosti puno veće ili manje u odnosu na druge podatke), one se također označuju na tom tipu dijagrama.',\r\n        3: '<strong>Primjer 1.9.1.</strong>',\r\n        4: 'Zadan je niz od 20 podataka:',\r\n        5: '1, 0, 9, 1.1, 1.1, 0.8, 1.1, 1.2, 0.7, 1, 0.6, 0.9, 1.3, 1.1, 0.7, 1, 1.1, 1, 1.3',\r\n        6: 'Na slici je dan prikaz podataka kutijastim dijagramom te vrijednosti minimuma, maksimuma, donjega i gornjega kvartila te medijana.',\r\n        7: 'Pokrenite interakciju da bi vidjeli kutijasti dijagram koji se dobije dodamo li tom nizu broj 2. Možete uočiti da je 2 izdvojena vrijednost (stršeća vrijednost) te da se prikazuje i maksimum podataka bez te vrijednosti (1.3).',\r\n        8: '<strong>Primjer 1.9.2.</strong>',\r\n      },\r\n      'kutijasti-dijagram-interakcija': {\r\n        1: 'Sortiraj',\r\n        2: 'Nesortirano:',\r\n        3: 'Sortirano:',\r\n        4: 'točno',\r\n        5: 'medijan',\r\n        6: 'netočno'\r\n\r\n      },\r\n      'kutijasti-dijagram-zadatak': {\r\n        title: 'Kutijasti dijagram',\r\n        1: '<strong>Zadatak 1.9.1.</strong>',\r\n        2: 'Na slici su prikazana tri kutijasta dijagrama. Možemo li identificirati jedan od dijagrama za koji vrijede sljedeće tvrdnje:',\r\n        3: 'Barem 25% podataka jednako je minimumu.',\r\n        4: 'Barem 75% podataka manje je ili jednako medijanu.',\r\n        5: 'Barem 25% podataka jednako je maksimumu.',\r\n        6: 'Medijan i gornji kvartil jednaki su.',\r\n        7: '<strong>Rješenje</strong>',\r\n        8: 'Tvrdnja:',\r\n        13: 'odgovara dijagramu 1',\r\n        14: 'odgovara dijagramu 3',\r\n        15: 'odgovara dijagramu 2',\r\n        16: 'odgovara dijagramu 3.'\r\n      },\r\n      'dijagram-rasprsenosti-i-standardna-devijacija': {\r\n        title: 'Dijagram raspršenosti',\r\n        1: 'Ako se za jedinke prikupljaju podaci o dvjema numeričkim veličinama, korisno je parove podataka prikazati dijagramom raspršenosti. Na takvu dijagramu često se može uočiti povezanost varijabli.',\r\n        2: '<strong>Dijagram raspršenosti</strong> sastoji se od točkama označenih parova podataka u koordinatnom sustavu.',\r\n        3: '<strong>Primjer 1.10.1.</strong>',\r\n        4: 'Neka su dani parovi podataka:',\r\n        5: 'Na slici je prikazan njihov dijagram raspršenosti.',\r\n        6: 'SLJEDEĆE POGLAVLJE:',\r\n        7: '2. Osnove vjerojatnosti',\r\n        8: 'Klikom na gumb \"Pao je paran broj\" prikazat će se novi skup svih mogućih ishoda i novi skup povoljnih ishoda uz dodatnu informaciju da se pri bacanju kockice okrenuo paran broj.'\r\n      },\r\n      'dijagram-rasprsenosti-i-standardna-devijacija-zadatak': {\r\n        title: 'Dijagram raspršenosti',\r\n        1: '<strong>Zadatak 1.10.1.</strong>',\r\n        2: 'Razrednik jednog razreda nastoji pratiti koliko učenici njegovog razreda igraju računalne igrice. U tu svrhu zamolio je učenike da vode evidenciju te je zabilježio koliko su vremena učenici proveli igrajući računalne igrice u nedjelju i ponedjeljak. Podaci se nalaze u tablici.',\r\n        3: 'Na slici je prikazan dijagram raspršenosti vremena igranja igrica nedjeljom i ponedjeljkom. Uočavate li neku pravilnost?',\r\n        4: '<strong>Rješenje</strong>',\r\n        5: 'Uočava se rastuća veza. Iz takva dijagrama može se naslutiti da ona djeca koja dugo igraju igrice nedjeljom, u pravilu, dugo igraju igrice i ponedjeljkom.'\r\n      }\r\n    },\r\n    osnove_vjerojatnosti: {\r\n      chapterNumber: '&mdash; Poglavlje 2 &mdash;',\r\n      title: 'Osnove vjerojatnosti',\r\n      'vjerojatnost': {\r\n        title: 'Vjerojatnost',\r\n        1: '<strong>Vjerojatnost događaja</strong> jest broj kojim izražavamo stupanj uvjerenja u realizaciju tog događaja.',\r\n        2: '<strong>Događaj</strong> je podskup skupa svih mogućih ishoda nekog pokusa.',\r\n        3: '<strong>Skup svih mogućih ishoda</strong> nekog pokusa jest cjelina koju označujemo s Ω.',\r\n        4: '<strong>Primjer 2.1.1.</strong>',\r\n        5: 'Pri bacanju novčića mogu se okrenuti ili pismo (oznaka 𝑝) ili glava (oznaka 𝑔). Primjećujemo da je skup svih mogućih ishoda jednog bacanja novčića dvočlani skup',\r\n        6: 'Ω = {𝑝, 𝑔}.',\r\n        7: 'Pokus se sastoji od bacanja jednog novčića dva puta zaredom. Pri svakom se bacanju okreće ili 𝑝 ili 𝑔. Ishod jednog izvođenja takva pokusa pregledno je prikazati uređenim parom u kojem je prva komponenta ishod prvog bacanja, a druga komponenta ishod drugog bacanja. Prema tome, ishodi tog pokusa uređeni su parovi (𝑝, 𝑝), (𝑝, 𝑔), (𝑔, 𝑝) i (𝑔, 𝑔), a skup svih mogućih ishoda jest četveročlani skup ',\r\n        8: 'Ω = {(𝑝, 𝑝), (𝑝, 𝑔), (𝑔, 𝑝), (𝑔, 𝑔)}.',\r\n        9: 'Pri bacanju igraće kockice, čije su strane numerirane brojevima od 1 do 6, kao ishod se može pojaviti bilo koji od tih brojeva. Slijedi da je skup svih mogućih ishoda jednog bacanja igraće kockice šesteročlani skup',\r\n        10: 'Ω = {1, 2, 3, 4, 5, 6}.',\r\n        11: 'Znamo da se pri izvođenju pokusa realizira element cjeline &#937;. U tom kontekstu kažemo da smo sigurni da će se dogoditi &#937;, a još češće kažemo da će se &#937; dogoditi 100%. Tako brojem izražavamo stupanj uvjerenja u realizaciju  &#937;.',\r\n        12: 'Događaj A dio je cjeline &#937;, pa stupanj uvjerenja da će se dogoditi A izražavamo postotkom manjim ili jednakim 100%.',\r\n        13: 'Kako je postotak broj s nazivnikom 100, primjećujemo da stupanj uvjerenja u realizaciju Ω izražavamo brojem 1, a stupanj uvjerenja u realizaciju događaja A izražavamo brojem iz intervala [0, 1].',\r\n        14: '<strong>Vjerojatnost</strong> definiramo kao funkciju P koja događajima pridružuje brojeve iz intervala [0, 1] tako da vrijedi sljedeće: ',\r\n        15: 'Vjerojatnost cjeline &#937; jest 𝑃(Ω) = 1,',\r\n        16: 'Ako su događaji A i B dijelovi cjeline &#937; koji ne sadržavaju iste ishode pokusa, tada je vjerojatnost da se dogode 𝐴 ili 𝐵 (𝐴 ∪ 𝐵) jednaka zbroju njihovih vjerojatnosti',\r\n        17: '',\r\n        18: 'Zahtjev 2. vrijedi i za više od dva događaja koji ne sadržavaju iste ishode pokusa.',\r\n        19: '<strong>Primjer 2.1.2.</strong>',\r\n        20: '<strong>Klasični pristup određivanju vjerojatnosti</strong>',\r\n        21: 'Ako pokus ima konačno mnogo ishoda koji su svi jednako mogući, tada je vjerojatnost događaja A kvocijent broja povoljnih ishoda i broja svih mogućih ishoda tog pokusa. ',\r\n        22: 'Broj povoljnih ishoda jest broj elemenata događaja A i ima oznaku k(A), a broj svih mogućih ishoda jest broj elemenata skupa &#937; i ima oznaku k(&#937;) .',\r\n        23: 'Vjerojatnost događaja A računamo na sljedeći način:',\r\n        25: 'Primjerice, skup svih mogućih ishoda bacanja novčića jest Ω = {𝑝, 𝑔}. Ako je novčić koji bacamo pravilan, nemamo osnove davati prednost okretanju jedne njegove strane, pa je vjerojatnost da se okrene pismo jednaka vjerojatnosti da se okrene glava.',\r\n        27: '<strong>Primjer 2.1.3.</strong>',\r\n        28: '<strong>Statistički pristup određivanju vjerojatnosti</strong>',\r\n        29: 'Skup svih mogućih ishoda Ω ne mora biti konačan niti svi ishodi moraju biti jednako mogući. U tom se slučaju za određivanje vjerojatnosti događaja 𝐴 ⊆ Ω ne možemo koristiti klasičnim pristupom. Jedan od načina na koji možemo doći do vjerojatnosti događaja A temelji se na nezavisnom ponavljanju pokusa mnogo puta.',\r\n        30: 'Nakon svakog ponavljanja pokusa brojimo koliko se puta realizirao događaj A. Taj se broj zove <strong>frekvencija događaja</strong> A.',\r\n        31: 'Osim frekvencije, nakon svakog ponavljanja pokusa računamo kvocijent frekvencije događaja  i broja izvođenja pokusa. Taj se broj zove <strong>relativna frekvencija događaja</strong> A.',\r\n        32: 'Ako se s povećanjem broja izvođenja pokusa relativne frekvencije događaja  grupiraju oko jednog broja, taj broj uzimamo za vjerojatnost P(A).',\r\n        33: 'Primjerice, s povećanjem broja bacanja pravilnog novčića relativne frekvencije okretanja glave grupiraju se oko <div class=\"fraction\" top=\"1\" bottom=\"2\"></div>. Ako novčić bacimo 40 puta, grupiranje tih relativnih frekvencija grafički prikazujemo sljedećim linijskim grafom:',\r\n        34: 'Međutim, novčić ne mora biti pravilan. Što ako bacamo novčić kod kojega se glava okreće dva puta vjerojatnije od pisma? Provedite taj pokus mnogo puta i vizualizirajte kolika je vjerojatnost okretanja glave.',\r\n        35: 'Upute za uspješno korištenje interakcije:',\r\n        36: 'Pitanje br. 1. -  Odaberite “Izračunaj vjerojatnost“ kako bi se prikazalo rješenje.',\r\n        37: 'Pitanja br. 2. i 3. - Odaberite 2 uređena para od ponuđenih te nakon toga odaberite “Izračunaj vjerojatnost“. U slučaju točnog odabira prikazat će se rješenje.',\r\n        38: 'Pitanje br. 4. - Odaberite “Izračunaj vjerojatnost“ kako bi se prikazalo rješenje.'\r\n      },\r\n      'vjerojatnost-interakcija': {\r\n        1: 'Kolika je vjerojatnost da se u prvom bacanju okrene glava?',\r\n        2: 'Izračunaj vjerojatnost',\r\n        3: 'Resetiraj označene događaje',\r\n        4: 'Kolika je vjerojatnost da se u drugom bacanju okrene glava?',\r\n        5: 'Netočno odabrani događaji, pokušaj ponovno.',\r\n        6: 'Kolika je vjerojatnost da se u oba bacanja okrene ista strana novčića?',\r\n        7: 'Provjerite kolike su vjerojatnosti drugih dvočlanih dijelova od Ω. Također, odredite vjerojatnosti nekih tročlanih dijelova od Ω.',\r\n        8: 'Relativne frekvencije okretanje glave',\r\n        9: 'Redni broj bacanja novčića',\r\n        10: 'Ok'\r\n      },\r\n      'vjerojatnost-interakcija-2': {\r\n        1: 'Baci novčić',\r\n        2: 'Broj bacanja mora biti pozitivan cijeli broj veći od 0.',\r\n        3: 'Novčić',\r\n        4: 'Broj bacanja',\r\n        5: 'Broj glava',\r\n        6: 'Broj pisama',\r\n        7: 'Pravilan novčić',\r\n        8: 'Glava se okreće dva puta vjerojatnije od pisma',\r\n        9: 'Pismo se okreće dva puta vjerojatnije od glave',\r\n      },\r\n      'vjerojatnost-zadatak': {\r\n        title: 'Vjerojatnost',\r\n        1: '<strong>Zadatak 2.1.1.</strong>',\r\n        2: 'Dva brata kockara potpuno su različita – jedan je pošten, dok drugi pokušava varati.',\r\n        3: 'Pošteni kockar igra pravilnom igraćom kockicom. Kolika je vjerojatnost da će pri jednom bacanju kockice dobiti paran broj?',\r\n        4: 'Njegov brat odlučio je varati i dao izraditi igraću kockicu kod koje se neki brojevi okreću s većom vjerojatnošću od drugih. Uživite se u njegovu ulogu i sami izaberite brojeve kojima želite dati prednost. Upotrebom interaktivnog alata primijenite statistički pristup kako biste saznali kolika je vjerojatnost okretanja parnog broja pri bacanju takve kockice.',\r\n        5: '<strong>Rješenje</strong>',\r\n        6: 'Skup svih mogućih ishoda bacanja kockice jest ',\r\n        7: 'Događaj \"okrenuo se paran broj\" (oznaka A) sljedeći je dio od Ω:',\r\n        8: 'Kako je kockica pravilna, s pomoću klasičnog pristupa slijedi da je vjerojatnost da će pošteni kockar pri bacanju kockice dobiti paran broj',\r\n        9: 'U sljedeću formu za svaki broj na kockici unesite vjerojatnost njegova okretanja. Pritom pazite da, kao što je navedeno u tekstu zadatka, parnim brojevima pridružite veće vjerojatnosti te da zbroj svih šest vjerojatnosti bude 1. Primjerice:',\r\n        10: 'Ishod',\r\n        11: 'Vjerojatnost'\r\n      },\r\n      'vjerojatnost-zadatak-interakcija': {\r\n        1: 'Ishod',\r\n        2: 'Vjerojatnost',\r\n        3: 'Vjerojatnost da padne parni broj',\r\n        4: 'Vjerojatnost da padne neparni broj',\r\n        5: 'Baci kockicu',\r\n        6: 'Kocka',\r\n        7: 'Nedozvoljen broj!',\r\n        8: 'Vjerojatosti nisu dobro izabrane (zbroj ne iznosi 1)',\r\n        9: 'Unesi broj bacanja kocke:',\r\n        10: 'Broj bacanja',\r\n        11: 'Vjerojatnost realizacije parnog broja (%)',\r\n        12: 'Izračunaj vjerojatnost'\r\n      },\r\n      'uvjetna-vjerojatnost': {\r\n        title: 'Uvjetna vjerojatnost',\r\n        1: 'Uz dodatnu informaciju o ishodu pokusa vjerojatnost nekog događaja može se razlikovati od vjerojatnosti istog događaja bez te informacije.',\r\n        2: 'Neka je A događaj čija nas vjerojatnost zanima. Drugim riječima, A je skup povoljnih ishoda pokusa. Ako znamo da se pri izvođenju pokusa realizirao događaj B za koji je P (B) > 0, mijenja se skup povoljnih ishoda. Točnije, skup povoljnih ishoda više nije cijeli A, nego A ∩ B.',\r\n        3: '<strong>Primjer 2.2.1.</strong>',\r\n        4: 'U igri na sreću cilj je bacanjem igraće kockice dobiti prosti broj.',\r\n        5: 'Skup svih mogućih ishoda bacanja kockice jest &Omega; = {<span class=\"math-symbol\">1</span>, <span class=\"math-symbol\">2</span>, <span class=\"math-symbol\">3</span>, <span class=\"math-symbol\">4</span>, <span class=\"math-symbol\">5</span>, <span class=\"math-symbol\">6</span>}, a skup povoljnih ishoda jest skup svih prostih brojeva iz &Omega;, tj. tročlani skup {<span class=\"math-symbol\">2</span>, <span class=\"math-symbol\">3</span>, <span class=\"math-symbol\">5</span>}.',\r\n        6: 'Međutim, uz dodatnu informaciju da se pri bacanju kockice okrenuo paran broj, mijenja se skup povoljnih ishoda.',\r\n        7: 'Vjerojatnost realizacije događaja A, ako znamo da se realizirao događaj B takav da je P (B > 0), zove se <strong>uvjetna vjerojatnost događaja</strong> A <strong>uz uvjet</strong> B, označujemo ju s P(A | B) i definiramo na sljedeći način:',\r\n        8: '<strong>Primjer 2.2.2.</strong>',\r\n        9: 'U pokusu u kojem jedan pravilan novčić bacamo dva puta zaredom skup svih mogućih ishoda jest &Omega; = {(p,p), (p,g), (g,p), (g,g)} i svi su ishodi jednako mogući.',\r\n        10: 'Vjerojatnost da se u oba bacanja okrenula ista strana novčića, označimo taj događaj s A = {(p,p), (g,g)}, određujemo po klasičnom pristupu i ona iznosi <div class=\"fraction\" top=\"1\" bottom=\"2\"></div>.',\r\n        11: 'Međutim, ako znamo da je rezultat prvoga ili drugog bacanja p, onda znamo da se realizirao događaj',\r\n        12: 'B = {(𝑝, 𝑝), (𝑝, 𝑔), (𝑔, 𝑝)}, 𝑃(𝐵) = 3/4',\r\n        13: 'Uz tu dodatnu informaciju vjerojatnost da se u oba bacanja okrenula ista strana novčića, tj. vjerojatnost događaja A uz uvjet B jest',\r\n        14: '1 𝑃(𝐴 ∩ 𝐵) 4 1 𝑃(𝐴|𝐵) = = = . 𝑃(𝐵) 3 3 4',\r\n        15: 'Također uočavamo da je, uz uvjet B, vjerojatnost pojavljivanja ishoda (g,g) 0.'\r\n      },\r\n      'uvjetna-vjerojatnost-interakcija': {\r\n        1: '(Skup svih ishoda):',\r\n        2: 'Skup povoljnih ishoda:',\r\n        3: 'Pao je paran broj',\r\n        4: 'Realizirani događaj',\r\n        5: 'Novi skup povoljnih ishoda',\r\n        6: '3. Slučajna varijabla'\r\n      },\r\n      'uvjetna-vjerojatnost-zadatak': {\r\n        title: 'Uvjetna vjerojatnost',\r\n        1: '<strong>Zadatak 2.2.1.</strong>',\r\n        2: 'Upotrebom interaktivnog alata odredite vjerojatnost realizacije šestice pri bacanju igraće kockice koja ne mora biti pravilna uz dodatnu informaciju da se realizirao proizvoljno odabrani događaj B. Vjerojatnosti pojavljivanja ishoda bacanja kockice i realizirani događaj B birate sami.',\r\n        3: 'Zbroj svih vjerojatnosti za svaki ishod bacanja kockice mora biti jednak 1.'\r\n      },\r\n      'uvjetna-vjerojatnost-zadatak-interakcija': {\r\n        1: 'Ishod',\r\n        2: 'Vjerojatnost',\r\n        3: 'Unesi broj',\r\n        4: 'Vjerojatnost realizacije šestice uz uvjet B',\r\n        5: 'Suma svih elemenata mora biti jednaka 1. Ponovi unos!',\r\n        6: 'Svi uneseni brojevi moraju biti pozitivni.',\r\n        7: 'Unos teksta nije dozvoljen.',\r\n        8: 'Elementi događaja B biraju se klikom na željene ishode u prvom redu tablice. Potrebno je unijeti i vjerojatnosti događaja za odabrane ishode.',\r\n        9: 'Sva polja za unos su obavezna',\r\n        10: 'Potrebno je odabrati barem jedan ishod iz prvog retka tablice.'\r\n      }\r\n    },\r\n    statisticko_zakljucivanje: {\r\n      chapterNumber: '&mdash; Poglavlje 5 &mdash;',\r\n      title: 'Statističko zaključivanje',\r\n      'populacija_i_uzorak': {\r\n        title: 'Populacija i uzorak',\r\n        1: 'Pri statističkom zaključivanju podatke kojima raspolažemo shvaćamo kao vrijednosti zabilježene na jednom dijelu <strong>populacije</strong> koji se zove <strong>uzorak</strong>. Tipičan takav primjer jesu predizborne ankete kada se bira dio populacije birača i na osnovi njihovih odgovora pokušava zaključiti o rezultatu izbora.',\r\n        2: 'Prikupljanjem <a href=\"../opisivanje-podataka/podaci\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">podataka</a> na uzorku o nekom obilježju populacije – varijabli X dobivamo niz brojeva x<sub>1</sub>, x<sub>2</sub>, ... , x<sub>n</sub>, pri čemu je n <strong>veličina uzorka</strong>.',\r\n        3: 'Statistički zaključci izvedeni iz uzorka sadržavaju određenu nesigurnost iz sljedećih razloga:',\r\n        4: 'Podaci se temelje na nepotpunim podacima (npr. predizborne ankete provode se samo na dijelu populacije radi predviđanja ishoda izbora).',\r\n        5: 'Podaci sadržavaju komponentu slučajnosti (npr. ishode bacanja novčića, u pravilu, ne možemo predvidjeti).',\r\n        6: 'Zato dobiveni uzorak promatramo kao realizacije n <a href=\"../slucajna-varijabla/slucajna-varijabla\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">slučajnih varijabli</a> X<sub>1</sub>, X<sub>2</sub>, ... , X<sub>n</sub> koje se zovu <strong>slučajni uzorak</strong>.',\r\n        7: 'Za slučajni uzorak kažemo da je <strong>jednostavni slučajni uzorak</strong> ako vrijedi da su:',\r\n        8: 'X<sub>1</sub>, X<sub>2</sub>, ... , X<sub>n</sub> sve jednako distribuirane kao slučajna varijabla X (obilježje populacije)',\r\n        9: 'X<sub>1</sub>, X<sub>2</sub>, ... , X<sub>n</sub> međusobno nezavisne.',\r\n        10: 'Često je prikupljanje podataka osmišljeno tako da te dvije pretpostavke budu ispunjene. Primjerice, predizbornu anketu ne možemo provesti samo među umirovljenicima, nego uzorak mora biti <strong>reprezentativan</strong> tako da su u njemu zastupljena tipična obilježja populacije bitna za istraživanje.',\r\n        11: 'Dakle, uzorak predstavljaju realizacije nezavisnih slučajnih varijabli jednako distribuiranih kao obilježje u cijeloj populaciji X. Zato kažemo da je x<sub>1</sub>, x<sub>2</sub>, ... , x<sub>n</sub> <strong>uzorak iz varijable</strong> X ili <strong>distribucije varijable</strong> X.',\r\n        12: 'Na osnovi vrijednosti iz uzorka donose se zaključci o distribuciji <a href=\"../slucajna-varijabla/slucajna-varijabla\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">slučajne varijable</a> X. Distribucija varijable X može biti potpuno nepoznata ili može biti poznat njezin tip, a parametri nepoznati (npr. X ima <a href=\"../distribucije/normalna-distribucija\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">normalnu distribuciju</a> s nepoznatim očekivanjem i varijancom).',\r\n        13: '<strong>Primjer 5.1.1.</strong>',\r\n        14: 'Državni zavod za statistiku provodio je u 2014. istraživanje o izdacima za potrošnju kućanstava te o socioekonomskim i demografskim obilježjima kućanstava. Anketirano je 2029 slučajno odabranih kućanstava, a zabilježene su, između ostalog:',\r\n        15: 'vrijednosti ukupnih godišnjih izdataka, ',\r\n        16: 'vrsta stambene jedinice (kuća ili stan), ',\r\n        17: 'broj članova kućanstva.',\r\n        18: 'U ovom istraživanju populaciju čine sva kućanstva u Republici Hrvatskoj, a uzorak su anketirana kućanstva. Veličina uzorka jest 2029. Spomenute su tri varijable:',\r\n        19: 'Podaci o ukupnim godišnjim izdacima dolaze iz neprekidne distribucije. S obzirom na to da nemamo opravdani razlog pretpostaviti tip distribucije, smatramo je potpuno nepoznatom.',\r\n        20: 'Varijabla koja predstavlja vrstu stambene jedinice može imati samo dva ishoda. Ako ishode označimo s 0 (kuća) i 1 (stan), riječ je o <a href=\"../distribucije/bernoulijeva-distribucija\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">Bernoullijevoj slučajnoj varijabli</a> s nepoznatim parametrom p',\r\n        21: 'Dakle, poznat je tip distribucije obilježja, a nepoznat je samo jedan parametar.',\r\n        22: 'Podaci o broju članova kućanstva dolaze iz neke diskretne distribucije s mogućim vrijednostima 0, 1, 2, .... Vjerojatnosti opažanja tih vrijednosti nisu poznate.'\r\n      },\r\n      'populacija_i_uzorak_zadatak_1': {\r\n        title: 'Populacija i uzorak zadatak',\r\n        1: 'U pokusu koji se sastoji od bacanja novčića dva puta bilježi se broj pisama u ta dva bacanja. Pokus je ponovljen 200 puta. Što je u ovom primjeru populacija, a što uzorak? Koju varijablu promatramo i što možemo reći o njezinoj distribuciji?',\r\n        2: '<strong>Rješenje</strong>',\r\n        3: 'Pokus bacanja novčića možemo ponavljati proizvoljan broj puta pa je populacija u ovom primjeru beskonačna. Uzorak čini 200 ponavljanja. Pokusi su nezavisni, a distribucija mogućih ishoda uvijek je ista jer je riječ o istom novčiću. Dakle, riječ je o <strong>jednostavnome slučajnom uzorku</strong>.',\r\n        4: 'Promatrana varijabla jest broj pisama u dva bacanja. Varijabla može imati tri vrijednosti: 0, 1 i 2. Vjerojatnost pisma 𝑝 u jednom je bacanju nepoznata, ali znamo da distribucija varijable broj pisama ima oblik: ',\r\n        5: '<strong>Zadatak 5.1.1.</strong>'\r\n      },\r\n      'procjena_proporcije_vjerojatnosti': {\r\n        title: 'Procjena proporcije/vjerojatnosti',\r\n        1: 'Neka je x<sub>1</sub>, 𝑥<sub>2</sub>, ... , 𝑥<sub>n</sub> uzorak iz varijable 𝑋 koja može imati samo dva ishoda. Ishode možemo označiti s 0 i 1, pa je riječ o uzorku iz <a href=\"../distribucije/bernoulijeva-distribucija\" class=\"topic-link\" target=\"_blank\" rel=\"noopener noreferrer\">Bernoullijeve distribucije</a>',\r\n        2: 'pri čemu je 𝑝 nepoznat. Parametar predstavlja vjerojatnost realizacije vrijednosti 1 odnosno proporciju vrijednosti 1 u cijeloj populaciji. Nepoznati parametar 𝑝 možemo <strong>procijeniti</strong> <a href=\"../opisivanje-podataka/frekvencije-i-relativne-frekvencije\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">relativnom frekvencijom</a> vrijednosti 1: ',\r\n        3: 'Isti princip može se primijeniti i kada varijabla 𝑋 ima više od dva ishoda. Tada vjerojatnost svake realizacije procjenjujemo relativnom frekvencijom te realizacije u uzorku. Primjerice, ako 𝑋 ima distribuciju',\r\n        4: 'procjena za 𝑝<sub>1</sub> jest relativna frekvencija jedinica u uzorku. Dobivena procjena distribucije od 𝑋 zove se i <strong>empirijska distribucija</strong>.',\r\n        5: '<strong>Primjer 5.2.1.</strong>',\r\n        6: 'Pretpostavimo da bacamo novčić za koji ne znamo je li pravilan. Ako s 1 označimo realizaciju pisma, a s  0 glave, dobit ćemo uzorak iz Bernoullijeve distribucije',\r\n        7: 'gdje je 𝑝 nepoznata vjerojatnost da padne pismo.',\r\n        8: 'Primjećujemo da što je veći broj bacanja, procjena je, u pravilu, sve bliža stvarnoj vrijednosti. Da je zaista tako jamči i <a href=\"../slucajna-varijabla/ocekivanje/dodatni-zadaci\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">zakon velikih brojeva</a>.'\r\n      },\r\n      'procjena_proporcije_vjerojatnosti_interakcija': {\r\n        1: 'Parametar populacije p:',\r\n        2: 'Broj bacanja:',\r\n        3: 'Baci',\r\n        4: 'Procjena',\r\n        5: 'Veličina uzorka n = ',\r\n        6: 'Procjena proporcije/vjerojatnosti',\r\n        7: 'Pismo',\r\n        8: 'Glava',\r\n        9: 'Parametri nisu dobro odabrani.',\r\n        10: 'Vjerojatnost mora biti u intervalu [0, 1]',\r\n        11: 'Unesi sve brojeve',\r\n        12: 'Broj bacanja mora biti veći od 0'\r\n      },\r\n      'procjena_proporcije_vjerojatnosti_zadatak_1': {\r\n        title: 'Procjena proporcije/vjerojatnosti zadatak',\r\n        1: 'Prema istraživanju Državnog zavoda za statistiku, od 2029 anketiranih kućanstava u Republici Hrvatskoj, 1635 kućanstava živi u stanu ili kući u privatnom vlasništvu bez obveze otplate stambenoga kredita, 160 ih živi u privatnom vlasništvu s obvezom otplate stambenoga kredita, 77 ih živi u unajmljenom smještaju i 156 ih živi u besplatno unajmljenom smještaju.',\r\n        2: 'Na osnovi tih podataka procijenite distribuciju varijable kojom se može opisati smještaj u cijeloj populaciji.',\r\n        3: '<strong>Rješenje</strong>',\r\n        4: 'Moguće realizacije varijable 𝑋 koja predstavlja vrstu smještaja mogu biti:',\r\n        5: 'smještaj u privatnom vlasništvu bez obveze otplate stambenoga kredita',\r\n        6: 'smještaj u privatnom vlasništvu s obvezom otplate stambenoga kredita',\r\n        7: 'unajmljeni smještaj',\r\n        8: 'besplatno unajmljeni smještaj.',\r\n        9: 'Procjena distribucije (empirijska distribucija) jest',\r\n        10: '<strong>Zadatak 5.2.1.</strong>'\r\n      },\r\n      'procjena_ocekivanja_i_varijance': {\r\n        title: 'Procjena očekivanja i varijance',\r\n        1: 'Ako je 𝑥<sub>1</sub>, 𝑥<sub>2</sub>, ... , 𝑥<sub>𝑛</sub> uzorak iz varijable 𝑋 koja ima nepoznato očekivanje  𝜇 = 𝐸[𝑋] , onda parametar 𝜇 procjenjujemo <a href=\"../opisivanje-podataka/prosjek\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">aritmetičkom sredinom</a> (prosjekom) uzorka',\r\n        2: 'Nepoznatu varijancu 𝜎<sup>2</sup> = 𝑉𝑎𝑟(𝑋) varijable 𝑋 procjenjujemo <a href=\"../opisivanje-podataka/varijanca-i-standardna-devijacija\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">varijancom</a> uzorka',\r\n        3: 'Procjena za standardnu devijaciju 𝜎 jest <a href=\"../opisivanje-podataka/varijanca-i-standardna-devijacija\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">standardna devijacija</a> uzorka 𝑠<sub>𝑛</sub>.',\r\n        4: '<strong>Primjer 5.3.1.</strong>',\r\n        5: 'Dostupni su podaci o izmjerenim visinama 100 odraslih muškaraca iz neke populacije. Treba procijeniti očekivanje i varijancu visine u toj populaciji.',\r\n        6: 'Na osnovi sljedećeg alata možemo izračunati procjene za uzorke različite veličine slučajno odabrane iz originalnog uzorka veličine 100. Promatrajte što se događa s procjenama očekivanja i varijance na takvim manjim uzorcima.'\r\n      },\r\n      'procjena_ocekivanja_i_varijance_interakcija': {\r\n        1: 'Histogram podataka: ',\r\n        2: 'Veličina poduzorka: ',\r\n        3: 'Procjena očekivanja <span class=\"math-symbol\">𝜇<sup>^</sup></span>= 𝑥̅',\r\n        4: 'Procjena varijance <span class=\"math-symbol\">𝜎<sup>^</sup></span>',\r\n        5: 'Veličina poduzorka mora biti cijeli broj koji je u skupu od 0 do 100!',\r\n        6: 'Uzmi poduzorak',\r\n        7: 'Podaci:',\r\n      },\r\n      'pouzdani_interval_za_ocekivanje': {\r\n        title: 'Pouzdani interval za očekivanje',\r\n        1: 'Umjesto da procijenimo parametar jednim brojem, možemo procijeniti interval u kojem je taj parametar sadržan s nekom vjerojatnošću, obično 0.95 ili 0.99. Takav interval zove se <strong>pouzdani interval</strong>.',\r\n        2: 'Ako uzorak dolazi iz normalne distribucije s nepoznatim očekivanjem 𝜇 i nepoznatom varijancom, tada interval izračunan prema formuli',\r\n        3: 'sadržava stvarnu vrijednost očekivanja 𝜇 u približno 100𝛾% slučajeva.',\r\n        4: 'U gornjoj formuli 𝛾 jest <strong>razina pouzdanosti</strong>, obično 0.95 ili 0.99 . Broj 𝑡<sub>𝑛−1,𝛾</sub> određuje se tako da je',\r\n        5: 'za slučajnu varijablu 𝑇<sub>𝑛−1</sub>, koja ima Studentovu t-distribuciju s 𝑛−1 stupnjeva slobode. Grafički to znači odrediti interval simetričan oko 0 iznad kojeg funkcija gustoće Studentove t-distribucije zatvara površinu 𝛾.',\r\n        6: 'Zbog veze s t-distribucijom takav pouzdani interval često se zove <strong>t-interval</strong>. Opravdano ga je upotrebljavati i kada uzorak nije iz normalne distribucije, ali je dovoljno velik (barem 30 podataka) i distribucija iz koje dolazi uzorak nije jako asimetrična.',\r\n        7: '<strong>Primjer 5.4.1.</strong>',\r\n        8: 'Sljedećim alatom možemo simulirati izračunavanje 100 pouzdanih intervala za uzorke iz normalne distribucije.'\r\n      },\r\n      'pouzdani_interval_za_ocekivanje_interakcija': {\r\n        1: 'Očekivanje 𝜇:',\r\n        2: 'Varijanca 𝜎<sup>2</sup>:',\r\n        3: 'Razina pouzdanosti 𝛾:',\r\n        4: 'Veličina uzorka 𝑛:',\r\n        5: 'Unesi broj',\r\n        6: 'Generiraj 100 uzoraka',\r\n        7: 'Razina pouzdanosti mora biti manja od 1. Ponovi unos!',\r\n        8: 'Unesena vrijednost mora biti broj!',\r\n        9: 'sivo – broj pouzdanih intervala koji sadrže stvarnu vrijednost 𝜇',\r\n        10: 'crveno – broj pouzdanih intervala koji ne sadrže stvarnu vrijednost 𝜇'\r\n      },\r\n      'pouzdani_interval_za_ocekivanje_zadatak_1': {\r\n        title: 'Pouzdani interval za očekivanje zadatak',\r\n        1: 'Prema istraživanju Državnog zavoda za statistiku, kućanstva u Republici Hrvatskoj godišnje prosječno troše 5494 kuna na odjeću i obuću uz standardnu devijaciju od 197.78 kuna. Podaci se temelje na 2029 anketiranih kućanstava.',\r\n        2: 'Koristeći se sljedećim kalkulatorom izračunajte pouzdani interval pouzdanosti 95% za očekivanu potrošnju na odjeću i obuću.',\r\n        3: 'Usporedite dobiveni interval s intervalima koje biste dobili ako je (uz ostale vrijednosti nepromijenjene):',\r\n        4: 'a) standardna devijacija 100',\r\n        5: 'b) veličina uzorka 1000',\r\n        6: 'c) pouzdanost 0.99.',\r\n        7: 'Zaključite kako se pouzdani interval mijenja promjenom standardne devijacije/veličine uzorka/razine pouzdanosti ako su ostale veličine nepromijenjene.',\r\n        8: '<strong>Rješenje</strong>',\r\n        9: 'Za manju standardnu devijaciju interval je uži – ako je raspršenost manja, možemo dati jednako pouzdanu procjenu užim intervalom. Za manju veličinu uzorka interval je širi – ako imamo manje podataka, interval mora biti širi uz jednaku razinu pouzdanosti. Za veću pouzdanost interval je širi – ako želimo veću pouzdanost, onda moramo uzeti širi interval.',\r\n        10: 'Aritmetička sredina <span class=\"math-symbol\"><i>x&#772;</i></span><sub><i>n</i></sub>: ',\r\n        11: 'Standardna devijacija uzorka <span class=\"math-symbol\"><i>s&#772;</i></span><sub><i>n</i></sub>: ',\r\n        12: 'Razina pouzdanosti 𝛾',\r\n        13: 'Veličina uzorka 𝑛',\r\n        14: '<strong>Zadatak 5.4.1.</strong>'\r\n      },\r\n      'pouzdan-interval-za-procjenu-i-vjerojatnost': {\r\n        title: 'Pouzdani interval za proporciju/vjerojatnost',\r\n        1: 'Često se možemo susresti s izjavama tipa \"80% korisnika je primijetilo poboljšanje u ljepoti kose/bjelini zubi/čistoći rublja\". U takvim tvrdnjama može biti skriveno puno nejasnoća. Na primjer, rijetko ćemo čuti koja je veličina uzorka, a 80% može biti i četiri od pet korisnika.',\r\n        2: 'Umjesto procjene jednim brojem, nepoznatu proporciju nekog obilježja u populaciji možemo procijeniti <strong>pouzdanim intervalom za proporciju</strong>',\r\n        3: 'formula',\r\n        4: 'gdje je 𝑝&#770; relativna frekvencija, 𝑛 veličina uzorka i <i>z</i><sub>𝛾</sub> broj koji je određen tako da ',\r\n        5: 'formula',\r\n        6: 'za slučajnu varijablu Z koja ima standardnu <a href=\"../distribucije/normalna-distribucija\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">normalnu distribuciju</a>. Grafički to znači odrediti interval simetričan oko 0 iznad kojeg funkcija gustoće standardne normalne distribucije zatvara površinu 𝛾.',\r\n        7: 'Tako izračunani interval sadržavat će stvarnu vrijednost proporcije 𝑝 u približno 100𝛾% slučajeva. Za primjenu tog intervala treba imati dovoljno velik uzorak.',\r\n        8: '<strong>Primjer 5.5.1.</strong>',\r\n        9: 'U pokusu bacanja novčića želimo pouzdanim intervalom procijeniti vjerojatnost pojavljivanja pisma. Sljedećim alatom možemo uočiti kako se pouzdani intervali, u pravilu, sužavaju s povećanjem veličine uzorka.',\r\n        10: '<strong>Primjer 5.5.2.</strong>',\r\n        11: 'Prema istraživanju Državnog zavoda za statistiku, 26.4% kućanstava u Republici Hrvatskoj vezano je za stan kao stambenu jedinicu. Podaci se temelje na 2029 anketiranih kućanstava. Koristeći se sljedećim kalkulatorom možemo izračunati pouzdani interval pouzdanosti 95% za proporciju kućanstava koja žive u stanovima.'\r\n      },\r\n      'pouzdan-interval-za-procjenu-i-vjerojatnost-interakcija': {\r\n        1: 'Vjerojatnost pisma 𝑝: ',\r\n        2: 'Razina pouzdanosti 𝛾: ',\r\n        3: 'Broj bacanja 𝑛: ',\r\n        4: 'Baci',\r\n        5: 'Razina pouzdanosti mora biti manja od 1. Ponovi unos!',\r\n        6: 'Unesi broj',\r\n        7: 'Unesene vrijednosti moraju biti pozitivne',\r\n        8: 'Unesene vrijednosti moraju biti brojevi',\r\n        9: 'Vjerojatnost mora biti u rasponu [0, 1]'\r\n      },\r\n      'pouzdan-interval-za-procjenu-i-vjerojatnost-interakcija-2': {\r\n        1: 'Relativna frekvencija <i class=\"math-symbol\">p̂</i>:',\r\n        2: 'Razina pouzdanosti ',\r\n        3: 'Veličina uzorka ',\r\n        4: 'Izračunaj',\r\n        5: 'Pouzdani interval',\r\n        6: 'Unesene vrijednosti moraju biti pozitivne',\r\n        7: 'Unesene vrijednosti moraju biti brojevi',\r\n        8: 'Potrebno je unijeti sve vrijednosti',\r\n        9: 'Relativna frekvencija mora biti unutar 0 i 1.',\r\n        10: 'Razina pouzdanosti mora biti unutar 0 i 1.'\r\n      },\r\n      'pouzdan-interval-za-procjenu-i-vjerojatnost-zadatak': {\r\n        title: 'Pouzdani interval za proporciju/vjerojatnost',\r\n        1: '<strong>Zadatak 5.5.1.</strong>',\r\n        2: 'Pretpostavimo da na nekim izborima sudjeluju samo dva kandidata, A i B. Anketom se želi prognozirati pobjednik. Od 1000 anketiranih građana, njih 577 izjasnilo se da će glasati za kandidata A. Koristeći se kalkulatorom pouzdanog intervala izračunajte 95%-tni pouzdani interval za proporciju glasova kandidata A.',\r\n        3: '<strong>Rješenje</strong>',\r\n        4: 'Procjena proporcije glasova za kandidata A jest 0.577 (ili 57.5%), a pouzdani interval jest [0.5464,  0.6076] (ili [54.64%, 60.76%]).',\r\n        5: 'Pouzdani intervali često se prezentiraju i u obliku  0.577±0.0306, odnosno 57.7%±3.06%. Tako ćemo često uz rezultate anketa u medijima čuti napomenu kako, primjerice, \"statistička pogreška iznosi ±3%\". Riječ je o polovici duljine pouzdanog intervala, a obično se prešutno pretpostavlja da je razina pouzdanosti 0.95.'\r\n      },\r\n      'testiranje-statistickih-hipoteza': {\r\n        title: 'Testiranje statističkih hipoteza',\r\n        1: 'Pretpostavimo da igramo igru u kojoj osvajamo dobitak ako se bacanjem novčića okrene pismo. Nakon 10 igara, 2 puta je palo pismo, a 8 puta glava. Ako je novčić pravilan, očekivali bismo idealno 5 pisama i 5 glava. Je li odstupanje koje smo dobili samo slučajnost (loša sreća) ili možemo sumnjati da smo prevareni?',\r\n        2: 'Odgovor možemo dobiti ako dvije tvrdnje postavimo kao <strong>statističke hipoteze</strong> i testiramo njihovu istinitost. Jedna hipoteza zove se <strong>nul hipoteza</strong> i označujemo je s <i>H<sub>0</sub></i>, a suprotna hipoteza zove se <strong>alternativna hipoteza</strong> i označujemo je s <i>H<sub>1</sub></i>. U ovom slučaju hipoteze bi bile:',\r\n        3: '<i>H<sub>0</sub></i>: novčić je pravilan',\r\n        4: '<i>H<sub>1</sub></i>: novčić je nepravilan tako da daje prednost glavi.',\r\n        5: 'Bacanjem novčića dobivamo uzorak iz Bernoullijeve distribucije s parametrom <i>p</i>, koji predstavlja vjerojatnost pojavljivanja pisma. Hipoteze možemo iskazati kao tvrdnje o nepoznatom parametru:',\r\n        6: '<i>H<sub>0</sub></i>: p = 0.5',\r\n        7: '<i>H<sub>1</sub></i>: p < 0.5',\r\n        8: '<strong>Primjer 5.6.1.</strong>',\r\n        9: 'Sljedećim simulatorom možemo ponavljati igru koja se sastoji od 10 bacanja pravilnog novčića. Možemo vidjeti koliko je puta igra završila s 2 ili manje pisama.',\r\n        10: 'Ako je novčić pravilan, kolika je vjerojatnost da smo dobili samo 2 ili manje pisama u 10 bacanja? Tu vjerojatnost možemo točno izračunati. Broj pisama u 10 bacanja pravilnog novčića ima <a href=\"../distribucije/binomna-distribucija\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">binomnu distribuciju</a> s parametrima 10 i 0.5, pa je vjerojatnost da u 10 bacanja padne 2 ili manje pisama jednaka 0.0547. Ta vrijednost zove se p<strong>-vrijednost</strong> – vjerojatnost da smo dobili opaženi ili još ekstremniji uzorak pod uvjetom da je nul hipoteza istinita. Tako p-vrijednost govori koliko je jak dokaz protiv <i>H<sub>0</sub></i>. ',\r\n        11: 'Jesu li dva pisma dovoljan dokaz protiv <i>H<sub>0</sub></i>? Ne možemo biti sigurni u zaključak zato što se tako nešto može dogoditi i pri bacanju pravilnog novčića. Međutim, možemo kontrolirati vjerojatnost da pogriješimo odbacivanjem nul hipoteze, i to tako da unaprijed odredimo koliku vjerojatnost takve pogreške dopuštamo. Taj broj zove se <strong>razina značajnosti</strong> i tipičan izbor jest vrijednost 0.05.',\r\n        12: 'U ovom slučaju p-vrijednost veća je od uobičajene razine značajnosti, 0.0547 > 0.05. Kada je novčić pravilan, ishod igre i nije baš tako nevjerojatan pa onda ne postoji razlog za odbacivanje nul hipoteze.',\r\n        13: 'Koliko bi pisama bio dovoljan dokaz za odbacivanje nul hipoteze? Uzmimo, primjerice, da je palo samo jedno pismo u deset bacanja. Tada je p-vrijednost 0.0107. Samo jedno pismo dogodilo bi se u približno jednoj od 100 igara s pravilnim novčićem. To je tako malo vjerojatno da uz razinu značajnost 0.05 možemo tvrditi da novčić nije pravilan i da daje prednost glavi.',\r\n        14: 'Taj primjer ilustrira samo jedan od brojnih statističkih testova koji se mogu primijeniti na različite probleme i vrste hipoteza.'\r\n      },\r\n      'testiranje-statistickih-hipoteza-interakcija': {\r\n        1: 'Broj ponavljanja N: ',\r\n        2: 'Ponovi 10 bacanja N puta',\r\n        3: 'Dosad pokrenuti broj igara od 10 bacanja: ',\r\n        4: 'Broj igara u kojima je bilo 2 ili manje pisama: ',\r\n        5: 'Relativna frekvencija: ',\r\n        6: 'Vrijednosti',\r\n        7: 'Unesene vrijednosti moraju biti pozitivni brojevi i veći od 0',\r\n        8: 'Unesene vrijednosti moraju biti brojevi',\r\n        9: 'Očekivanje mora biti pozitivan broj',\r\n        10: 'Potrebno je unijeti sve vrijednosti'\r\n      },\r\n      'testiranje-statistickih-hipoteza-zadatak': {\r\n        title: 'Testiranje statističkih hipoteza',\r\n        1: '<strong>Zadatak 5.6.1.</strong>',\r\n        2: 'Na uzorku od 50 osoba testirano je može li se prepoznati razlika između skupoga i jeftinog vina. Svaki ispitanik dobio je neoznačene čaše skupoga i jeftinog vina te nakon kušanja pogađao vrstu vina. Njih 34 točno je odredilo vrstu vina nakon kušanja. Možemo li na razini značajnosti 0.05 tvrditi da ljudi prepoznaju razliku u okusu vina?',\r\n        3: '<strong>Rješenje</strong>',\r\n        4: 'Riječ je o uzorku iz Bernoullijeve distribucije u kojem vrijednost 1 označuje da je osoba točno klasificirala vina. Hipoteze možemo postaviti na sljedeći način: ',\r\n        5: '<i>H<sub>0</sub></i>: p=0.5 (slučajno pogađaju vrstu vina)',\r\n        6: '<i>H<sub>1</sub></i>: p>0.5 (mogu prepoznati vrstu vina),',\r\n        7: 'gdje p-vrijednost iznosi 0.0078 pa na razini značajnosti 0.05 možemo odbaciti nul hipotezu. Dakle, ljudi prepoznaju razliku u vrsti vina.'\r\n      },\r\n      'jednostavna-linearna-regresija': {\r\n        title: 'Jednostavna linearna regresija',\r\n        1: 'Kada proučavamo vezu između dviju neprekidnih varijabli X i Y, onda uzimamo uzorak parova podataka:',\r\n        2: 'formula',\r\n        3: 'Takve parove možemo nacrtati u koordinatnom sustavu, čime dobijemo <a href=\"../opisivanje-podataka/dijagram-rasprsenosti-i-standardna-devijacija\" class=\"topic-link\" target=\"_blank\" rel=\"noopener noreferrer\">dijagram raspršenosti</a>.',\r\n        4: '<strong>Regresijskim metodama</strong> moguće je opisati vezu među varijablama X i Y. Ako točke prikazane dijagramom raspršenosti izgledaju kao da su raspršene oko nekog pravca, onda ima smisla promatrati linearnu vezu između X i Y te govorimo o <strong>linearnoj regresiji</strong>. To znači da treba pronaći pravac oblika',\r\n        5: 'y = ax + b',\r\n        6: 'za neke parametre <strong><i>a</i></strong> i <strong><i>b</i></strong> tako da taj pravac dobro opisuje vezu između dviju varijabli. Parametar <strong><i>a</i></strong> jest <strong>koeficijent smjera</strong> pravca i <strong><i>a</i></strong> > 0 govori da je veza između X i Y rastuća, a <strong><i>a</i></strong> < 0 da je veza padajuća.',\r\n        7: 'Parametri <strong><i>a</i></strong> i <strong><i>b</i></strong> nepoznati su i trebamo ih procijeniti na osnovi podataka. Odrediti parametre <strong><i>a</i></strong> i <strong><i>b</i></strong> znači odrediti pravac koji u nekom smislu najbolje opisuje vezu između varijabli. To možemo napraviti <strong>metodom najmanjih kvadrata</strong> tako da minimiziramo zbroj kvadrata vertikalnih odstupanja svih točaka od pravca. Vertikalne udaljenosti točaka od pravca prikazane su na sljedećoj slici.',\r\n        8: '<strong>Primjer 5.7.1.</strong>',\r\n        9: 'Sljedećim alatom možemo izabrati jedan od ponuđenih skupova parova podataka te pokušati postaviti pravac koji najbolje opisuje podatke.'\r\n      },\r\n      'jednostavna-linearna-regresija-interakcija': {\r\n        1: 'Podaci 1',\r\n        2: 'Podaci 2',\r\n        3: 'Podaci 3',\r\n        4: 'Prikaži procjenu regresijskog pravca',\r\n        5: '<strong>Opis: </strong>Varijabla X sadržava mjesečne izvorne indekse obujma industrijske proizvodnje u razdoblju od 2011. do 2013., dok varijabla Y sadržava mjesečne podatke o broju zaposlenih osoba u istom razdoblju.',\r\n        6: '<strong>Opis: </strong>Proizvođač je uveo novi proizvod i distribuirao ga u trgovine po različitim cijenama. Nakon nekog vremena prikupljeni su podaci o broju prodanih proizvoda ovisno o cijeni. Uočavamo da veća cijena sugerira manje prodanih primjeraka, odnosno veza između varijabli je padajuća.',\r\n        7: '<strong>Opis: </strong>Simulirani podaci raspršeni su oko pravca uz jednu stršeću vrijednost. Uočavamo kako samo jedna stršeća vrijednost znatno utječe na položaj regresijskog pravca.'\r\n      }\r\n    },\r\n    slucajna_varijabla: {\r\n      chapterNumber: '&mdash; Poglavlje 3 &mdash;',\r\n      title: 'Slučajna varijabla',\r\n      slucajna_varijabla: {\r\n        title: 'Slučajna varijabla',\r\n        1: '<strong>Slučajna varijabla</strong> jest funkcija koja ishodima pokusa (elementima skupa Ω) pridružuje realne brojeve. Obično se označuje velikim tiskanim slovom, primjerice s 𝑋.',\r\n        2: 'Skup svih vrijednosti koje slučajna varijabla 𝑋 može poprimiti zove se <strong>slika slučajne varijable</strong> i označujemo je s 𝓡(𝑋).',\r\n        3: 'Često nas zanima vjerojatnost da se slučajna varijabla 𝑋 realizira vrijednostima iz nekog skupa 𝐴 ⊆ 𝑅. Događaj koji je pritom od interesa je {𝜔 ∈ Ω: 𝑋(𝜔) ∈ 𝐴} ⊆ Ω, koji kraće označujemo s (𝑋 ∈ 𝐴).',\r\n        4: '<strong>Primjer 3.1.1.</strong>',\r\n        5: 'Pri bacanju novčića dva puta zaredom zanima nas broj realiziranih pisama. Definiramo funkciju 𝑋 koja svakom ishodu iz skupa',\r\n        6: 'pridružuje broj pisama u uređenom paru koji predstavlja taj ishod:',\r\n        7: 'Ishod pokusa',\r\n        8: 'Vrijednost od <i>X</i>',\r\n        9: '2',\r\n        10: '1',\r\n        11: '1',\r\n        12: '0',\r\n        13: 'Slika te slučajne varijable jest skup',\r\n        14: 'Na analogan način definirali bismo drugu slučajnu varijablu, označimo ju s <i>Y</i>, koja svakom ishodu tog pokusa pridružuje broj realiziranih glava. Slika te slučajne varijable jest skup 𝓡(𝑌) = {0, 1, 2}.',\r\n        15: 'Primjećujemo da na istom Ω možemo definirati više slučajnih varijabli.'\r\n      },\r\n      slucajna_varijabla_zadatak_1: {\r\n        title: 'Slučajna varijabla zadatak',\r\n        1: 'Pokus se sastoji od bacanja igraće kockice dva puta zaredom. Definirajte slučajnu varijablu koja ishodima tog pokusa pridružuje zbroj brojeva koji su se okrenuli.',\r\n        2: '<strong>Rješenje</strong>',\r\n        3: 'Pri bacanju igraće kockice dva puta zaredom mogu se realizirati sljedeći ishodi:',\r\n        4: 'Na prethodnoj slici prikazan je skup svih mogućih ishoda ovog pokusa. U skupovnim oznakama možemo ga zapisati na sljedeći način:',\r\n        5: 'pri čemu svaki ishod reprezentiramo uređenim parom brojeva koji su se okrenuli.',\r\n        6: 'Slučajnu varijablu koja ishodima tog pokusa pridružuje zbroj brojeva koji su se okrenuli definiramo na sljedeći način:',\r\n        7: 'Slika slučajne varijable 𝑋 jest skup 𝓡(𝑋) = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.',\r\n        8: '<strong>Zadatak 3.1.1.</strong>',\r\n        9: '<strong>Zadatak 3.2.1.</strong>'\r\n      },\r\n      diskretna_slucajna_varijabla: {\r\n        title: 'Diskretna slučajna varijabla',\r\n        1: '<strong>Diskretna slučajna varijabla</strong> 𝑋 karakterizirana je: ',\r\n        2: 'konačnim {𝑥<sub>1</sub>, 𝑥<sub>2</sub>, ... , 𝑥<sub>𝑛</sub>} ili',\r\n        3: 'prebrojivim {𝑥<sub>1</sub>, 𝑥<sub>2</sub>, ... , 𝑥<sub>𝑛</sub>, ... }',\r\n        4: 'skupom vrijednosti 𝓡(𝑋).',\r\n        5: 'Ako su za sve moguće vrijednosti 𝑥<sub>𝑖</sub> iz 𝓡(𝑋) poznate vjerojatnosti 𝑃(𝑋 = 𝑥<sub>𝑖</sub>), kažemo da je poznata <strong>distribucija diskretne slučajne varijable</strong> 𝑋, koju pregledno zapisujemo <strong>tablicom distribucije</strong>:',\r\n        6: 'gdje 𝑝<sub>𝑖</sub> označuje 𝑃(𝑋 = 𝑥<sub>𝑖</sub>), 𝑖 = 1,2,...',\r\n        7: 'Upotrebom tablice distribucije računamo vjerojatnost da se 𝑋 realizira iz nekog skupa 𝐴 ⊆ 𝓡(𝑋). ',\r\n        8: 'Ta je vjerojatnost jednaka zbroju vjerojatnosti 𝑝<sub>𝑖</sub> za sve 𝑥<sub>𝑖</sub> iz 𝐴:',\r\n        9: '<strong>Primjer 3.2.1.</strong>',\r\n        10: 'Pri bacanju pravilnog novčića dva puta zaredom skup svih mogućih ishoda jest Ω = {(𝑝, 𝑝), (𝑝, 𝑔), (𝑔, 𝑝), (𝑔, 𝑔)} i svi su ishodi jednako vjerojatni:',\r\n        11: 'Slučajna varijabla 𝑋, koja svakom ishodu tog pokusa pridružuje broj realiziranih pisama, diskretna je i ima sliku:',\r\n        12: 'Vjerojatnosti realizacije elemenata slike 𝓡(𝑋) jesu',\r\n        13: 'Prema tome, distribucija te slučajne varijable dana je tablicom',\r\n        14: 'Primjerice, vjerojatnost da se realizira barem jedno pismo jest',\r\n        15: 'Osim tablicom, distribuciju možemo prikazati i grafički:',\r\n        16: 'Međutim, novčić koji bacamo ne mora biti pravilan - primjerice neka se glava okreće dva puta vjerojatnije nego pismo. To znači da ishodi dvaju uzastopnih bacanja nisu jednako vjerojatni:',\r\n        17: 'Tada distribuciju slučajne varijable koja ishodima ovog pokusa pridružuje broj realiziranih pisama zadajemo tablicom: ',\r\n        18: 'Sada je vjerojatnost da se realizira barem jedno pismo',\r\n        19: 'a grafički prikaz distribucije dan je na sljedećoj slici:',\r\n        20: 'Upotrebom interaktivnog dijela proučimo kako se distribucija od 𝑋 i 𝑃(𝑋 ≥ 1) mijenja s promjenom vjerojatnosti realizacije pisma pri bacanju novčića.'\r\n      },\r\n      diskretna_slucajna_varijabla_interakcija: {\r\n        1: 'Vjerojatnost realizacije pisma: ',\r\n        2: 'Vjerojatnost nije dobro zadana',\r\n        3: 'Izračunaj vjerojatnost P(X>=1)',\r\n        4: 'Izračunaj vjerojatnost',\r\n        5: 'Vjerojatnosti',\r\n        6: '0 pisama',\r\n        7: '1 pismo',\r\n        8: 'Vjerojatnost realizacije pisma mora biti broj',\r\n        9: '2 pisma',\r\n        10: 'Vjerojatnost',\r\n        11: 'Potrebno je unijeti vrijednost vjerojatnosti'\r\n      },\r\n      diskretna_slucajna_varijabla_zadatak_1: {\r\n        title: 'Diskretna slučajna varijabla zadatak',\r\n        1: 'Pokus se sastoji od bacanja igraće kockice koja ne mora biti pravilna dva puta zaredom. Odredite distribuciju slučajne varijable X koja ishodima tog pokusa pridružuje zbroj brojeva koji su se okrenuli. S pomoću interaktivnog alata odredite vjerojatnost da se okrenu brojevi čiji je zbroj element proizvoljnog podskupa slike slučajne varijable X.',\r\n        2: '<strong>Rješenje</strong>',\r\n        3: 'Kockica ne mora biti pravilna. Slučajnu varijablu koja ishodima tog pokusa pridružuje zbroj brojeva koji su se okrenuli označimo s 𝑋. Vjerojatnost da se okrenu brojevi čiji je zbroj manji od pet jest ',\r\n        4: 'gdje su 𝑝<sub>2</sub>, 𝑝<sub>3</sub>, 𝑝<sub>4</sub>, 𝑝<sub>5</sub> vjerojatnosti iz tablice distribucije slučajne varijable 𝑋.'\r\n      },\r\n      diskretna_slucajna_varijabla_zadatak_interakcija: {\r\n        1: 'Ishod bacanja kockice',\r\n        2: 'Vjerojatnost ishoda',\r\n        3: 'Vjerojatnosti nisu dobro zadane (zbroj ne iznosi 1)',\r\n        4: 'Distribucija od X',\r\n        5: 'Izračunaj vjerojatnost',\r\n        6: 'Vjerojatnosti',\r\n        7: 'Izračunaj vjerojatnost',\r\n        8: 'U sljedeću tablicu unesite vjerojatnosti realizacije brojeva ispisanih na stranama kockice. Klikom na gumb \"Distribucija od X\" ispisuje se tablica distribucije slučajne varijable čija je vrijednost zbroj brojeva koji su se okrenuli pri dva uzastopna bacanja te kockice, dok se klikom na gumb \"Izračunaj vjerojatnost\" ispisuje vjerojatnost da je zbroj brojeva koji su se okrenuli element proizvoljnog podskupa slike slučajne varijable X, pri čemu je p<sub>i</sub> oznaka za P(X=i).',\r\n        9: 'Označite vjerojatnosti u drugom retku tablice za formiranje podskupa na temelju kojeg se izračunava vjerojatnost.',\r\n        10: 'Potrebno je označiti vjerojatnosti u tablici!'\r\n      },\r\n      neprekidna_slucajna_varijabla: {\r\n        title: 'Neprekidna slučajna varijabla',\r\n        1: '<strong>Neprekidna slučajna varijabla</strong> karakterizirana je slikom 𝓡(𝑋) koja nije diskretan skup.',\r\n        2: 'Primjerice, 𝓡(𝑋) može biti neki interval ili čak cijeli skup realnih brojeva.',\r\n        3: '<strong>Distribuciju</strong> neprekidne slučajne varijable 𝑋 zadajemo nenegativnom funkcijom 𝑓, <strong> funkcijom gustoće</strong>, za koju je površina između grafa te funkcije i osi-𝑥 jednaka 1.',\r\n        4: 'Vjerojatnost da se neprekidna slučajna varijabla 𝑋 realizira vrijednostima iz nekog skupa 𝐴 ⊆ <i>R</i> jednaka je površini ispod grafa funkcije gustoće 𝑓 nad skupom 𝐴, kao što je prikazano na sljedećoj slici:',\r\n        5: '<strong>Primjer 3.3.1.</strong>',\r\n        6: 'Slučajnu varijablu 𝑋 čija je slika interval (𝑎, 𝑏), − <span class=\"infinity\">∞</span> < 𝑎 < 𝑏 < <span class=\"infinity\">∞</span>, a svi su jednako dugi podintervali od (𝑎, 𝑏) jednako vjerojatni zadajemo funkcijom gustoće',\r\n        7: 'Primjerice, za 𝑎 = −1 i 𝑏 = 1 ta se slučajna varijabla može primijeniti za opisivanje pogreške u rezultatu mjerenja nekoga preciznog uređaja, pri čemu se pogreške iz jednako dugih podintervala od (−1,1) realiziraju s jednakim vjerojatnostima. Graf funkcije gustoće za 𝑎 = −1 i 𝑏 = 1 i prikazan je na sljedećoj slici:',\r\n        8: 'Primjerice za 𝑎 = −1, 𝑏 = 1, 𝑐 = −1, 𝑑 = 0 je 𝑃(𝑋 ∈ (−1, 0)) jednaka površini pravokutnika sa stranicama duljina 1 i <div class=\"fraction\" top=\"1\" bottom=\"2\"></div> :',\r\n        9: 'Analogno, za 𝑎 = −1, 𝑏 = 1, 𝑐 = 1/2 , 𝑑 = 1 jest',\r\n        10: 'S pomoću interaktivnog alata isprobajte izračunavanje vjerojatnosti P(<i>c < X < d</i>) za gore navedenu distribuciju za različite vrijednosti 𝑎 i 𝑏.'\r\n      },\r\n      neprekidna_slucajna_varijabla_interakcija: {\r\n        1: 'Početna vrijednost',\r\n        2: 'Krajnja vrijednost',\r\n        3: 'Nacrtaj graf funkcije gustoće',\r\n        4: 'Odredi vjerojatnost P(c < X < d)',\r\n        5: 'Parametri nisu dobro odabrani. Broj a mora biti manji od b!',\r\n        6: 'Početak intervala 2',\r\n        7: 'Kraj intervala 2',\r\n        8: 'Parametri nisu dobro odabrani. Broj c mora biti manji od d!',\r\n        9: 'Unesene vrijednosti moraju biti brojevi',\r\n        10: 'Početna i krajnja vrijednost podintervala mora biti unutar granica intervala.',\r\n        11: 'Potrebno je unijeti sve vrijednosti'\r\n      },\r\n      neprekidna_slucajna_varijabla_zadatak_1: {\r\n        title: 'Neprekidna slučajna varijabla zadatak',\r\n        1: 'Slučajna varijabla zadana funkcijom gustoće',\r\n        2: 'može se upotrebljavati za opisivanje vremena koje protekne između dviju uzastopnih realizacija promatranog događaja, primjerice dolaska tramvaja na stanicu. Broj <i>λ</i> zove se parametar te distribucije. Upotrebom interaktivnog alata za <i>λ</i>=1 odredite vjerojatnost da između dvaju uzastopnih dolazaka tramvaja na stanicu prođe:',\r\n        3: '<strong>Rješenje</strong>',\r\n        4: 'Za graf funkcije gustoće prikazan je na sljedećoj slici:',\r\n        5: 'Tražene vjerojatnosti jesu',\r\n        6: 'a) 𝑃(0<𝑋<1)=0.6321',\r\n        7: 'Vjerojatnost da će između dvaju uzastopnih dolazaka tramvaja na stanicu proći manje od 1 minute jest 0.6321.',\r\n        8: 'b) 𝑃(1<𝑋<2)=0.2325',\r\n        9: 'Vjerojatnost da će između dvaju uzastopnih dolazaka tramvaja na stanicu proći između 1 i 2 minute jest 0.2325.',\r\n        10: 'c) 𝑃(𝑋 > 2) = 0.1353',\r\n        11: 'Vjerojatnost da će između dvaju uzastopnih dolazaka tramvaja na stanicu proći više od 2 minute jest 0.1353.',\r\n        12: 'Grafički prikazi funkcije gustoće i traženih vjerojatnosti:',\r\n        13: 'manje od 1 minute',\r\n        14: 'između 1 i 2 minute',\r\n        15: 'više od 2 minute.',\r\n        16: 'Mijenjajte vrijednost parametra <i>λ</i> i analizirajte dobivene rezultate.',\r\n        17: '<strong>Zadatak 3.3.1.</strong>',\r\n        18: 'Vjerojatnost za element između 0 i 1',\r\n        19: 'Vjerojatnost za element između 1 i 2',\r\n        20: 'Vjerojatnost za element veći od 2'\r\n      },\r\n      neprekidna_slucajna_varijabla_zadatak_interakcija: {\r\n        1: 'Unesi vrijednost',\r\n        2: 'Nacrtaj graf funkcije gustoće',\r\n        3: 'Odredi vjerojatnost P(c < X < d)',\r\n        4: 'Graf funkcije gustoće',\r\n        5: 'Vrijednosti moraju biti brojevi.',\r\n        6: 'Vrijednosti c i d ne smiju biti jednake.',\r\n        7: 'Vrijednost d mora biti veća od c.',\r\n        8: 'Potrebno je unijeti sve vrijednosti.'\r\n      },\r\n      funkcija_distribucije: {\r\n        title: 'Funkcija distribucije',\r\n        1: '<strong>Funkcija distribucije</strong> 𝐹 slučajne varijable 𝑋 svakome realnom broju 𝑥 pridružuje vjerojatnost događaja (𝑋 ≤ 𝑥): ',\r\n        2: 'Za diskretnu slučajnu varijablu 𝑋 vrijednost funkcije distribucije izračunavamo s pomoću <a href=\"../slucajna-varijabla/diskretna-slucajna-varijabla\" class=\"topic-link\" target=\"_blank\" rel=\"noopener noreferrer\">tablice distribucije</a>. Za proizvoljan 𝑥, vrijednost 𝐹(𝑥) jest zbroj vjerojatnosti 𝑝<sub>𝑖</sub> za one 𝑥<sub>𝑖</sub> ∈ 𝓡(𝑋) koji su manji ili jednaki 𝑥: ',\r\n        3: '<strong>Primjer 3.4.1.</strong>',\r\n        4: 'Distribucija diskretne slučajne varijable 𝑋 koja pri bacanju pravilnog novčića dva puta zaredom broji realizirana pisma zadana je tablicom',\r\n        5: 'Vrijednosti funkcije distribucije od 𝑋 u točkama njezine slike jesu',\r\n        6: 'Funkcija distribucije od 𝑋 dana je izrazom',\r\n        7: 'a njezin graf prikazan je na sljedećoj slici: ',\r\n        8: 'Primjećujemo da funkcija distribucije diskretne slučajne varijable u svakom x<sub>i</sub>∈𝓡 (X) ima skok vrijednosti p<sub>i</sub>=P (X=x<sub>i</sub>) te da je monotono rastuća i ograničena (pravcem y=0 odozdo i pravcem y=1 odozgo).',\r\n        9: '<strong>Primjer 3.4.2.</strong>',\r\n        10: 'Neprekidnu slučajnu varijablu 𝑋 čija je slika interval (-1, 1), a svi su jednako dugi podintervali od (-1, 1) jednako vjerojatni zadajemo funkcijom gustoće',\r\n        11: 'Prikažimo vrijednost funkcije distribucije 𝑋 u točki 𝑥 = <div class=\"fraction\" top=\"1\" bottom=\"2\"></div> na grafičkim prikazima funkcije gustoće i funkcije distribucije te slučajne varijable:',\r\n        12: 'Gornja funkcija primjer je funkcije gustoće zadane izrazom',\r\n        13: 'Za neke druge 𝑎 i 𝑏 te proizvoljan 𝑥 promotrimo graf funkcije gustoće, graf funkcije distribucije i vjerojatnost 𝑃(𝑋 ≤ 𝑥) na tim grafovima.',\r\n        14: 'Što ako novčić koji se baca nije pravilan? Pogledajmo kako se funkcija distribucije od X mijenja s promjenom vjerojatnosti realizacije pisma pri bacanju novčića.',\r\n        15: 'Za neprekidnu slučajnu varijablu 𝑋 vrijednost funkcije distribucije izračunavamo s pomoću <a href=\"../slucajna-varijabla/neprekidna-slucajna-varijabla\" class=\"topic-link\" target=\"_blank\" rel=\"noopener noreferrer\">funkcije gustoće</a>. Za proizvoljan 𝑥 vrijednost <i>F(</i>𝑥<i>)</i> jednaka je površini ispod grafa njezine funkcije gustoće nad intervalom (-∞, 𝑥].'\r\n      },\r\n      funkcija_distribucije_dodatni_zadaci: {\r\n        title: 'Za one koji žele znati više: Kako računati vjerojatnost P(X∈A)?',\r\n        1: 'Vjerojatnost da se slučajna varijabla X realizirala iz intervala (a, b) možemo odrediti s pomoću vrijednosti funkcije distribucije u točkama a i b:',\r\n        2: 'P X∈(a, b)=P a<X≤b=P X≤b-P X≤a=F b-F (a).',\r\n        3: 'Na sličan se način određuju i vjerojatnosti da se X realizirala iz intervala [a, b], [a, b] i(a, b)',\r\n        4: 'Kod diskretne slučajne varijable (poveznica na temu) s tablicom distribucije',\r\n        5: 'X~(x1 x2 ... p1 p2 ... xn…  pn…)',\r\n        6: 'svaka od tih vjerojatnosti jest zbroj vjerojatnosti pi=P(X = xi) za sve xi iz promatranog intervala.',\r\n        7: 'Kod neprekidne slučajne varijable (poveznica na temu) svaka je od tih vjerojatnosti jednaka površini ispod grafa funkcije gustoće nad intervalom a, b- vjerojatnosti P(a<X≤b),',\r\n        8: 'P (a≤X<b), P (a≤X≤b) i P (a<X≤b) jednake su jer je za neprekidnu slučajnu varijablu P X=x = 0 za svaki broj x.'\r\n      },\r\n      funkcija_distribucije_interakcija: {\r\n        1: 'Vjerojatnost realizacije pisma:',\r\n        2: 'Distribucija od X',\r\n        3: 'Funkcija distribucije od X',\r\n        4: 'Graf funkcije distribucije',\r\n        5: 'Graf diskretne distribucije',\r\n        6: 'Vjerojatnost mora biti broj',\r\n        7: 'Vjerojatnost mora biti unutar intervala [0, 1]',\r\n        8: 'Prazan unos vjerojatnosti nije dozvoljen.'\r\n      },\r\n      funkcija_distribucije_interakcija_2: {\r\n        1: 'Graf funkcije gustoće',\r\n        2: 'Graf funkcije distribucije',\r\n        3: 'Vrijednost x nije u intervalu između a i b',\r\n        4: 'Unesene vrijednosti moraju biti brojevi',\r\n        5: 'Vjerojatnost P(X ≤ ',\r\n        6: 'Potrebno je unijeti sve vrijednosti',\r\n      },\r\n      ocekivanje: {\r\n        title: 'Očekivanje',\r\n        1: '<strong>Očekivanje</strong> slučajne varijable 𝑋 jest broj koji upućuje na poziciju centra distribucije te slučajne varijable. Označujemo ga s 𝐸[𝑋] ili 𝜇.',\r\n        2: 'Očekivanje slučajne varijable ne mora postojati, no ako postoji, računamo ga na sljedeći način:',\r\n        3: 'Za <a href=\"../slucajna-varijabla/diskretna-slucajna-varijabla\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">diskretnu slučajnu varijablu</a> 𝑋 s tablicom distribucije',\r\n        4: 'očekivanje je zbroj umnožaka svake vrijednosti 𝑥<sub>𝑖</sub> s pripadajućom vjerojatnošću 𝑝<sub>𝑖</sub>',\r\n        5: 'Za <a href=\"../slucajna-varijabla/neprekidna-slucajna-varijabla\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">neprekidnu slučajnu varijablu</a> 𝑋 s funkcijom gustoće 𝑓 očekivanje računamo s pomoću površine između 𝑥-osi i grafa funkcije 𝑥𝑓(𝑥) tako da od površine između 𝑥-osi i grafa pozitivnog dijela funkcije 𝑥𝑓(𝑥) oduzmemo površinu između grafa negativnog dijela funkcije 𝑥𝑓(𝑥) i osi 𝑥.',\r\n        6: '<strong>Primjer 3.5.1.</strong>',\r\n        7: 'Distribucija slučajne varijable koja ishodima bacanja pravilne igraće kockice pridružuje brojeve kojima su numerirane strane kockice dana je tablicom',\r\n        8: 'Očekivanje te slučajne varijable jest broj',\r\n        9: 'Na sljedećoj slici prikazan je graf distribucije i pozicija očekivanja te slučajne varijable:',\r\n        10: 'Možemo uočiti da je u ovom slučaju očekivanje aritmetička sredina vrijednosti kojima se ta slučajna varijabla može realizirati.',\r\n        11: 'No to ne mora biti tako. Ako kockica koju bacamo nije pravilna, onda zbog promjene u distribuciji slučajne varijable 𝑋 očekivanje neće biti aritmetička sredina brojeva iz njezine slike. Pogledajmo kako se zbog promjene distribucije mijenja pozicija očekivanja.',\r\n        12: '<strong>Primjer 3.5.2.</strong>',\r\n        13: 'Neprekidnu slučajnu varijablu 𝑋 čija je slika interval (−1, 1), a svi su jednako dugi podintervali od (−1, 1) jednako vjerojatni zadajemo funkcijom gustoće',\r\n        14: 'Kako je funkcija 𝑥𝑓(𝑥) s pomoću koje računamo očekivanje neparna, očekivanje jest 0.',\r\n        15: 'Na sljedećim slikama prikazana je površina između 𝑥-osi  i grafa funkcije 𝑥𝑓(𝑥) s pomoću koje računamo očekivanje te graf funkcije gustoće 𝑓 s istaknutim očekivanjem na 𝑥-osi:',\r\n        16: 'Upotrebom interaktivnog alata promotrimo površinu između 𝑥-osi i grafa funkcije 𝑥𝑓(𝑥) te graf općenitije funkcije gustoće ',\r\n        17: 's istaknutim očekivanjem na 𝑥-osi.',\r\n        18: '<strong>Primjer 3.5.3.</strong>',\r\n        19: 'Neka je (𝑋𝑛, 𝑛 ∈ 𝑁) niz slučajnih varijabli kojim opisujemo ishode uzastopnog bacanja pravilne igraće kockice. Slučajna varijabla 𝑋𝑛 prima vrijednost 1 ako se u 𝑛-tom bacanju na kockici okrene broj 6, a inače prima vrijednost 0. Distribucija od 𝑋𝑛 dana je tablicom ',\r\n        20: 'Možemo uočiti da se aritmetička sredina 𝑋𝑛 podudara s relativnom frekvencijom jedinica. Osim toga, možemo uočiti da je očekivanje relativne frekvencije jedinica upravo 1/6. ',\r\n        21: 'Prema slabom zakonu velikih brojeva, s povećanjem broja bacanja kockice vjerojatnost odstupanja relativne frekvencija jedinica od 1/6 možemo učiniti proizvoljno malom.'\r\n      },\r\n      ocekivanje_interakcija: {\r\n        1: 'Nacrtaj grafove',\r\n        2: 'Graf funkcije xf(x)',\r\n        3: 'Graf funkcije f(x)',\r\n        4: 'Potrebno je unijeti sve vrijednosti.',\r\n        5: 'Unesene vrijednosti moraju biti brojevi.',\r\n        6: 'Broj a mora biti manji od broja b.'\r\n      },\r\n      ocekivanje_interakcija_2: {\r\n        1: 'Nacrtaj distribuciju i označi očekivanje',\r\n        2: 'Očekivanje',\r\n        3: 'Vjerojatnosti nisu dobro zadane (zbroj ne iznosi 1)'\r\n      },\r\n      ocekivanje_dodatni_zadaci: {\r\n        title: 'Za one koji žele znati više',\r\n        1: 'Neka je (𝑋<sub>𝑛</sub>, 𝑛 ∈ 𝑁) niz nezavisnih jednako distribuiranih slučajnih varijabli s očekivanjem 𝜇 koji opisuje ishode ponavljanja nekog pokusa.',\r\n        2: 'Slabi zakon velikih brojeva govori o graničnom ponašanju pripadnog niza aritmetičkih sredina (<span class=\"overline\">X</span><sub>n</sub>, 𝑛 ∈ 𝑁), gdje je',\r\n        3: 'Prema slabom zakonu velikih brojeva, vjerojatnost odstupanja aritmetičke sredine <span class=\"overline\">X</span><sub>n</sub> od očekivanja 𝜇 može se učiniti proizvoljno malom odabirom dovoljno velikog broja ponavljanja pokusa, tj. broja 𝑛.',\r\n        4: '<strong>Za one koji žele znati više - primjer 1</strong>',\r\n        5: 'Neka je (𝑋<sub>𝑛</sub>, 𝑛 ∈ 𝑁) niz slučajnih varijabli kojim opisujemo ishode uzastopnog bacanja pravilne igraće kockice. Slučajna varijabla 𝑋<sub>𝑛</sub> prima vrijednost 1 ako se u 𝑛-tom bacanju na kockici okrene broj 6, a inače prima vrijednost 0. Distribucija od 𝑋<sub>𝑛</sub> dana je tablicom',\r\n        6: 'Možemo uočiti da se aritmetička sredina <span class=\"overline\">X</span><sub>n</sub> podudara s relativnom frekvencijom jedinica. Osim toga, uočimo da je očekivanje relativne frekvencije jedinica upravo <div class=\"fraction\" top=\"1\" bottom=\"6\"></div>.',\r\n        7: 'Prema slabom zakonu velikih brojeva, s povećanjem broja bacanja novčića vjerojatnost odstupanja relativne frekvencije jedinica od <div class=\"fraction\" top=\"1\" bottom=\"6\"></div> možemo učiniti proizvoljno malom.',\r\n        8: '<strong>Za one koji žele znati više - primjer 2</strong>',\r\n        9: 'Neka je (𝑋<sub>𝑛</sub>, 𝑛 ∈ 𝑁) niz slučajnih varijabli kojim opisujemo ishode uzastopnog bacanja novčića. Slučajna varijabla 𝑋<sub>𝑛</sub> prima vrijednost 1 ako se u 𝑛-tom bacanju okrenula glava, a ako se okrenulo pismo prima vrijednost 0. Uz oznaku 𝑝 za vjerojatnost uspjeha (1) slijedi da je distribucija od 𝑋<sub>𝑛</sub> dana tablicom',\r\n        10: 'Možemo uočiti da se aritmetička sredina <span class=\"overline\">X</span><sub>n</sub> podudara s relativnom frekvencijom jedinica. Osim toga, uočimo da je očekivanje relativne frekvencije jedinica upravo 𝑝, 𝐸[<span class=\"overline\">x</span><sub>n</sub>] = 𝑝.',\r\n        11: 'Prema slabom zakonu velikih brojeva, s povećanjem broja bacanja novčića vjerojatnost odstupanja relativne frekvencije jedinica od očekivanja 𝑝 možemo učiniti proizvoljno malom.',\r\n        12: '<strong>Pozicija očekivanja</strong>',\r\n        13: 'Ako se zapitamo postoji li realan broj koji je na neki način \"najbliži\" slučajnoj varijabli, onda je to u jednom načinu mjerenja udaljenosti upravo očekivanje. Pritom udaljenost između slučajne varijable X i broja <i>a</i> mjerimo kao očekivano kvadratno odstupanje.',\r\n        14: 'Promotrimo li to kao funkciju s nezavisnom varijablom <i>a</i>,',\r\n        15: 'pokazuje se da ona svoj minimum postiže upravo u <i>a = E[X]</i>. Dakle, <i>E[X]</i> minimizira očekivano kvadratno odstupanje od slučajne varijable <i>X</i>.',\r\n        16: '<strong>Slabi zakon velikih brojeva</strong>',\r\n        17: 'Za one koji žele znati više',\r\n        18: 'Za one koji žele znati više - primjer '\r\n      },\r\n      ocekivanje_dodatni_zadaci_interakcije: {\r\n        1: 'Broj bacanja: ',\r\n        2: 'Unesi broj bacanja',\r\n        3: 'Baci kockicu',\r\n        4: 'Broj bacanja mora biti veći od 1!',\r\n        5: 'Vjerojatnost glave',\r\n        6: 'Broj bacanja',\r\n        7: 'Baci novčić',\r\n        8: 'Vjerojatnost mora biti između 0 i 1.',\r\n        9: 'Broj bacanja ne moze biti tekst!',\r\n        10: 'Broj bacanja mora biti cijeli broj.',\r\n        11: 'Potreban je unos broja bacanja.',\r\n        12: 'Unos svih vrijednosti je potreban.'\r\n      },\r\n      varijanca_i_standardna_devijacija: {\r\n        title: 'Varijanca i standardna devijacija',\r\n        1: '<strong>Varijanca</strong> slučajne varijable 𝑋 pozitivan je broj koji opisuje <strong>raspršenost</strong> distribucije slučajne varijable 𝑋 u odnosu na njezino očekivanje 𝐸[𝑋].',\r\n        2: 'Označujemo je s 𝑉𝑎𝑟(𝑋) ili 𝜎<sup> 2</sup>.',\r\n        3: 'Točnije, 𝑉𝑎𝑟(𝑋) je očekivano kvadratno odstupanje slučajne varijable 𝑋 od njezina očekivanja:',\r\n        4: 'Kvadratni korijen iz 𝑉𝑎𝑟(𝑋) zove se <strong>standardna devijacija</strong> slučajne varijable 𝑋 i označujemo ju sa 𝜎.',\r\n        5: '<strong>Primjer 3.6.1.</strong>',\r\n        6: 'Neprekidnu slučajnu varijablu 𝑋 čija je slika interval (𝑎, 𝑏), a svi su jednako dugi podintervali od (𝑎, 𝑏) jednako vjerojatni zadajemo funkcijom gustoće',\r\n        7: 'Upotrebom interaktivnog alata uočavamo kako se ponašaju očekivanje i varijanca te slučajne varijable za različite vrijednosti parametara 𝑎 i 𝑏:',\r\n        8: 'Slučajne varijable s distribucijom na jednako dugim intervalima imaju jednake varijance.',\r\n        9: 'Ako uspoređujemo varijancu slučajne varijable s distribucijom na užemu i slučajne varijable s distribucijom na širem intervalu, varijanca slučajne varijable s distribucijom na širem intervalu bit će veća.'\r\n      },\r\n      varijanca_i_standardna_devijacija_interakcija: {\r\n        1: 'Izračunaj očekivanje i varijancu',\r\n        2: 'Nacrtaj graf funkcije gustoće',\r\n        3: 'Očekivanje: ',\r\n        4: 'Varijanca: ',\r\n        5: 'Originalni graf gustoće',\r\n        6: 'Očekivanje',\r\n        7: 'Očekivanje minus standardna devijacija',\r\n        8: 'Broj b mora biti veći od broja a',\r\n        9: 'Očekivanje plus standardna devijacija',\r\n        10: '4. Distribucije',\r\n        11: 'Potrebno je unijeti sve vrijednosti.'\r\n      },\r\n      varijanca_i_standardna_devijacija_zadatak: {\r\n        1: 'Upotrebom interaktivnog alata ispitajte kako se ovisno o vrijednosti parametra λ>0 ponašaju očekivanje i varijanca slučajne varijable X s funkcijom gustoće',\r\n        2: '<strong>Rješenje</strong>:',\r\n        3: 'S povećanjem vrijednosti parametra λ smanjuju se očekivanje i varijanca.',\r\n        4: '<strong>Zadatak 3.6.1.</strong>'\r\n      },\r\n      varijanca_i_standardna_devijacija_zadatak_interakcija: {\r\n        1: 'Izračunaj očekivanje i varijancu',\r\n        2: 'Nacrtaj graf funkcije gustoće',\r\n        3: 'Očekivanje: ',\r\n        4: 'Varijanca: ',\r\n        5: 'Originalni graf gustoće',\r\n        6: 'Očekivanje minus standardna devijacija',\r\n        7: 'Očekivanje plus standardna devijacija',\r\n        8: 'Očekivanje'\r\n      }\r\n    },\r\n    distribucije: {\r\n      chapterNumber: '&mdash; Poglavlje 4 &mdash;',\r\n      title: 'Distribucije',\r\n      bernoulijeva_distribucija: {\r\n        title: 'Bernoullijeva distribucija',\r\n        1: 'Slučajna varijabla 𝑋 koja opisuje pokus sa samo <strong>dva moguća ishoda</strong>:',\r\n        2: '<strong>neuspjeh</strong> (oznaka 0), koji se realizira s vjerojatnošću (1 − 𝑝)',\r\n        3: '<strong>uspjeh</strong> (oznaka 1), koji se realizira s vjerojatnošću 𝑝',\r\n        4: 'ima <strong>Bernoullijevu distribuciju</strong> s parametrom 𝑝 ∈ (0, 1) i tablicom distribucije',\r\n        5: '<strong>Očekivanje</strong> i <strong>varijanca</strong> Bernoullijeve distribucije s parametrom 𝑝 jesu',\r\n        6: '<strong>Primjer 4.1.1.</strong>',\r\n        7: 'Novčić se pri bacanju može okrenuti ili na pismo ili na glavu. Ako je novčić koji bacamo pravilan, ti su ishodi jednako vjerojatni. Ako ishod &#39;&#39;okrenula se glava&#39;&#39; proglasimo uspjehom i označimo ga s 1, a ishod &#39;&#39;okrenulo se pismo&#39;&#39; proglasimo neuspjehom i označimo ga s 0, primjećujemo da ishod njegova bacanja opisujemo slučajnom varijablom 𝑋 s Bernoullijevom distribucijom s parametrom 𝑝 = <div class=\"fraction\" top=\"1\" bottom=\"2\"></div> i tablicom distribucije',\r\n        8: 'Očekivanje i varijanca jesu',\r\n        9: 'Na sljedećoj slici prikazan je graf te Bernoullijeve distribucije s istaknutim očekivanjem:',\r\n        10: 'Ako bacamo novčić koji nije pravilan, ishodi &#39;&#39;okrenulo se pismo&#39;&#39; (neuspjeh) i &#39;&#39;okrenula se glava&#39;&#39; (uspjeh) nisu jednako vjerojatni.',\r\n        11: 'Upotrebom interaktivnog alata promotrite kako se s promjenom vjerojatnosti uspjeha 𝑝 mijenja Bernoullijeva distribucija kojom opisujemo ishod bacanja takva novčića te kako se mijenja njezino očekivanje.'\r\n      },\r\n      bernoulijeva_distribucija_interakcija: {\r\n        1: 'Vjerojatnost',\r\n        2: 'Graf distribucije',\r\n        3: 'Očekivanje',\r\n        4: 'Varijanca',\r\n        5: 'Vjerojatnost mora biti unutar intervala [0, 1]!',\r\n        6: 'Vjerojatnost mora biti broj!'\r\n      },\r\n      bernoulijeva_distribucija_zadatak_1: {\r\n        title: 'Bernoullijeva distribucija zadatak',\r\n        1: 'a) U igri &#39;&#39;Čovječe, ne ljuti se&#39;&#39; bacamo pravilnu igraću kockicu i uspjehom smatramo okretanje šestice. Ako se okrene bilo koji od brojeva 1, 2, 3, 4, 5, to smatramo neuspjehom. Odredite distribuciju, očekivanje i varijancu slučajne varijable kojom u ovom kontekstu opisujemo bacanje pravilne igraće kockice. Distribuciju i poziciju očekivanja prikažite grafički upotrebom interaktivnog alata.',\r\n        2: 'b) S pomoću interaktivnog alata proučite kako se distribucija i očekivanje mijenjaju ako kockica koju bacamo nije pravilna, primjerice zbog promjene vjerojatnosti realizacije šestice.',\r\n        3: '<strong>Rješenje</strong>',\r\n        4: 'a) Kako je kockica pravilna, vjerojatnost realizacije uspjeha (šestice) u jednome njezinu bacanju jest <div class=\"fraction\" top=\"1\" bottom=\"6\"></div> , pa u ovom kontekstu ishod bacanja kockice opisujemo Bernoullijevom slučajnom varijablom 𝑋 s parametrom 𝑝 = <div class=\"fraction\" top=\"1\" bottom=\"6\"></div> i tablicom distribucije',\r\n        5: 'Očekivanje i varijanca jesu',\r\n        6: 'b) Korisnik s pomoću interaktivnog alata crta grafove distribucija s istaknutim očekivanjima za različite odabire vrijednosti parametra 𝑝.',\r\n        7: '<strong>Zadatak 4.1.1.</strong>'\r\n      },\r\n      bernoulijeva_distribucija_zadatak_interakcija: {\r\n        1: 'Vjerojatnost',\r\n        2: 'Graf distribucije',\r\n        3: 'Očekivanje',\r\n        4: 'Varijanca',\r\n        5: 'Vjerojatnost mora biti unutar intervala [0, 1]!'\r\n      },\r\n      binomna_distribucija: {\r\n        title: 'Binomna distribucija',\r\n        1: 'Slučajna varijabla 𝑋 koja broji uspjehe u 𝑛 nezavisnih izvođenja istog pokusa sa samo dva moguća ishoda (uspjeh i neuspjeh), pri čemu se u svakom izvođenju uspjeh realizira s vjerojatnošću 𝑝, ima <strong>binomnu distribuciju</strong> s parametrima 𝑛 ∈ 𝑁 i 𝑝 ∈ (0, 1) te oznaku 𝑋~ℬ(𝑛, 𝑝).',\r\n        2: 'Slika ℬ(𝑛, 𝑝) distribucije jest , 𝓡(𝑋) = {0, 1, 2, ... , 𝑛}, a vjerojatnosti realizacije elemenata slike jesu: ',\r\n        3: '<strong>Očekivanje</strong> i <strong>varijanca</strong> ℬ(𝑛, 𝑝) distribucije jesu',\r\n        4: '<strong>Primjer 4.2.1.</strong>',\r\n        5: 'Pretpostavimo da smo novčić nezavisno bacili 20 puta. Ako je novčić koji bacamo pravilan, broj pojavljivanja ishoda \"okrenula se glava\" u tih 20 bacanja opisujemo slučajnom varijablom X s binomnom distribucijom s parametrima n = 20 i p = <div class=\"fraction\" top=\"1\" bottom=\"2\"></div>. Očekivanje i varijanca te distribucije jesu: ',\r\n        6: 'Grafički je distribucija s istaknutim očekivanjem prikazana na sljedećoj slici: ',\r\n        7: 'Upotrebom interaktivnog alata možemo izračunati neke zanimljive vjerojatnosti, primjerice:',\r\n        8: 'Vjerojatnost da se glava okrene točno 10 puta jest P(X=10) = 0.1762.',\r\n        9: 'Vjerojatnost da se glava okrene manje od  10 puta jest P(X<10) = 0.4119.',\r\n        10: 'Vjerojatnost da se glava okrene barem 10 puta jest P(X≥10) = 0.5881.'\r\n      },\r\n      binomna_distribucija_interakcija: {\r\n        1: 'Graf distribucije',\r\n        2: 'Očekivanje',\r\n        3: 'Varijanca',\r\n        4: 'Izračunajte tražene vjerojatnosti',\r\n        5: 'Unesene vrijednosti moraju biti brojevi',\r\n        6: 'Vjerojatnost mora biti u rasponu [0, 1]',\r\n        7: 'Broj bacanja mora biti pozitivan broj',\r\n        8: 'Za odabrane parametre n i p binomne distribucije te vrijednost x iz njezine slike odredimo vjerojatnosti P(X=x), P(X<=x) i P(X>x).',\r\n        9: 'P(X<=x)',\r\n        10: 'P(X>x)',\r\n        11: 'Potrebno je unijeti vrijednost vjerojatnosti.',\r\n        12: 'Potrebno je unijeti sve vrijednosti.',\r\n        13: 'Molimo, unesite vrijednost između 0 i '\r\n      },\r\n      binomna_distribucija_zadatak_1: {\r\n        title: 'Binomna distribucija zadatak',\r\n        1: 'Upotrebom interaktivnog alata odredite vjerojatnost da će se u 50 bacanja igraće kockice šestica okrenuti više od 5 puta. Je li vjerojatnije da se šestica okrene barem 5 puta ili najviše 10 puta?',\r\n        2: '<strong>Rješenje</strong>',\r\n        3: 'Slijedi primjer rješenja za slučaj pravilne kockice:',\r\n        4: '𝑋 opisuje broj šestica koje se okrenu u 50 ponavljanja bacanja pravilne igraće kockice:',\r\n        5: 'Tražene vjerojatnosti jesu',\r\n        6: 'Dakle, vjerojatnije je da se šestica okrene barem 5 puta nego najviše 10 puta.',\r\n        7: '<strong>Task 4.2.1.</strong>',\r\n        8: 'Za odabrane parametre n (broj bacanja kockice) i p (vjerojatnost realizacije šestice) binomne distribucije odredimo vjerojatnosti P(X>5), P(X>=5) i P(X<=10).'\r\n      },\r\n      uniformna_distribucija: {\r\n        title: 'Uniformna distribucija',\r\n        1: 'Slučajna varijabla s 𝑋 funkcijom gustoće',\r\n        2: 'ima <strong>uniformnu distribuciju</strong> na intervalu (𝑎, 𝑏) i oznaku <strong>𝑿~𝓤(𝒂, 𝒃)</strong>. Realni brojevi 𝑎 i 𝑏, −∞ < 𝑎 < 𝑏 < ∞, parametri su te distribucije.',\r\n        3: 'Funkcija gustoće uniformne distribucije odražava činjenicu da su jednako dugi podintervali od (𝑎,𝑏) jednako vjerojatni.',\r\n        4: 'Vjerojatnost da se slučajna varijabla 𝑋~𝒰(𝑎, 𝑏) realizira iz intervala (𝑐, 𝑑), 𝑎 ≤ 𝑐 < 𝑑 ≤ 𝑏, jednaka je površini ispod grafa funkcije gustoće nad intervalom (𝑐, 𝑑):',\r\n        5: 'Očekivanje i varijanca 𝒰(𝑎, 𝑏) distribucije jesu',\r\n        6: 'O toj smo distribuciji dosta govorili kod neprekidnih slučajnih varijabli (poveznica na temu).',\r\n        7: '<strong>Primjer 4.3.1.</strong>',\r\n        8: 'Promotrimo grafove funkcija gustoća uniformnih distribucija na različitim intervalima, s istaknutim očekivanjima.',\r\n        9: 'Primjerice, 𝒰(5, 10) distribucija zadana je funkcijom gustoće',\r\n        10: 'Nadalje, 𝒰(−1,1) distribucija zadana je funkcijom gustoće'\r\n      },\r\n      uniformna_distribucija_zadatak_1: {\r\n        title: 'Uniformna distribucija zadatak',\r\n        1: 'U specifikacijama preciznoga mjernog uređaja za masu navedeno je kako izmjerena masa odstupa od stvarne za manje od 1 𝜇𝑔 te da je distribucija pogreške uniformna. S pomoću interaktivnog alata odredite:',\r\n        2: 'a) vjerojatnost da je izmjerena masa manja od stvarne',\r\n        3: 'b) vjerojatnost da je izmjerena masa veća od stvarne.',\r\n        4: '<strong>Rješenje</strong>',\r\n        5: 'Pogrešku pri mjerenju mase opisujemo slučajnom varijablom 𝑋 s uniformnom distribucijom na intervalu (−1, 1). Funkcija gustoće 𝒰(−1, 1) distribucije jest',\r\n        6: 'a grafički je prikazana u prethodnom primjeru.',\r\n        7: 'a) Ako su stvarna i izmjerena masa jednake, pogreška je nula. Dakle, vjerojatnost da je izmjerena masa manja od stvarne, 𝑃(𝑋 < 0), jednaka je površini ispod grafa funkcije gustoće 𝒰(−1, 1) distribucije nad intervalom (−1, 0).',\r\n        8: 'Primjećujemo da je ovdje riječ o površini pravokutnika sa stranicama duljina 1 i 1/2 , pa je tražena vjerojatnost 𝑃(𝑋 < 0) = 1/2',\r\n        9: 'b) Vjerojatnost da je izmjerena masa veća od stvarne jednaka je površini ispod grafa funkcije gustoće 𝒰(−1, 1) distribucije nad intervalom (0, 1) i iznosi 𝑃(𝑋 > 0) = 1/2'\r\n      },\r\n      normalna_distribucija: {\r\n        title: 'Normalna distribucija',\r\n        1: 'Slučajna varijabla 𝑍 s funkcijom gustoće',\r\n        2: 'ima <strong>normalnu distribuciju</strong> s parametrima  𝜇 ∈ 𝑅 i 𝜎 > 0 i oznaku 𝑍~𝒩(𝜇, 𝜎).',\r\n        3: '<strong>Očekivanje</strong> i <strong>varijanca</strong> 𝒩(𝜇, 𝜎) distribucije jesu',\r\n        4: 'Dakle, 𝜎 > 0 jest standardna devijacija 𝒩(𝜇, 𝜎) distribucije.',\r\n        5: 'Normalna distribucija s očekivanjem 𝜇 = 0 i standardnom devijacijom 𝜎 = 1 zove se <strong>standardna normalna distribucija</strong>.',\r\n        6: '<strong>Primjer 4.3.1.</strong>',\r\n        7: 'Promotrimo grafove funkcije gustoće normalnih distribucija s različitim parametrima 𝜇 i 𝜎.',\r\n        8: 'Fiksirajmo standardnu devijaciju 𝜎 = 1, a za očekivanje 𝜇 uzmimo redom vrijednosti −1, 0, 1, 2. Uočavamo da funkcija gustoće postiže svoj maksimum u očekivanju 𝜇.',\r\n        9: 'Fiksirajmo očekivanje 𝜇 = 0, a za standardnu devijaciju 𝜎 uzmimo redom vrijednosti 0.1, 0.5, 1, 5. Uočavamo da se, uz fiksno očekivanje 𝜇, s povećanjem standardne devijacije maksimum funkcije gustoće normalne distribucije smanjuje, a graf postaje sve &#39;&#39;spljošteniji&#39;&#39;.',\r\n        10: 'Na grafu funkcije gustoće 𝒩(𝜇,𝜎) distribucije istaknimo očekivanje 𝜇 te granice intervala (𝜇−𝜎, 𝜇+𝜎), (𝜇−2𝜎, 𝜇+2𝜎), (𝜇−3𝜎, 𝜇+3𝜎).',\r\n        11: 'S pomoću interaktivnog alata dobivamo da je za proizvoljne 𝜇 ∈ 𝑅 i 𝜎 > 0',\r\n        12: 'Slijedi da slučajna varijabla 𝑍~𝒩(𝜇, 𝜎) odstupa od očekivanja za više od jedne standardne devijacije s vjerojatnošću 31.73%, vjerojatnost da od očekivanja odstupa za više od dvije standardne devijacije jest 4.55%, a vjerojatnost da od očekivanja odstupa za više od tri standardne devijacije jest 0.27%.'\r\n      },\r\n      normalna_distribucija_interakcija: {\r\n        1: 'Očekivanje',\r\n        2: 'Početna vrijednost',\r\n        3: 'Standardna devijacija',\r\n        4: 'Krajnja vrijednost',\r\n        5: 'Graf funkcije gustoće',\r\n        6: 'P(c < Z < d)',\r\n        7: 'Granice intervala c i d nisu dobro odabrane!',\r\n        8: 'Očekivanje',\r\n        9: 'Varijanca',\r\n        10: 'Vrijednosti moraju biti brojevi',\r\n        11: 'Pogrešan unos devijacije',\r\n        12: '5. Statističko zaključivanje',\r\n        13: 'Potrebno je unijeti sve vrijednosti.',\r\n        14: 'Vrijednosti c i d moraju biti unutar intervala',\r\n        15: ' uz uvjet da je c < d.'\r\n      },\r\n      normalna_distribucija_zadatak_1: {\r\n        title: 'Normalna distribucija zadatak',\r\n        1: 'Standardizirani test inteligencije baždaren je s obzirom na pretpostavku da je kvocijent inteligencije u populaciji normalno distribuirano obilježje s očekivanjem 𝜇 = 100 i standardnom devijacijom 𝜎 = 15. Upotrebom interaktivnog alata odredite:',\r\n        2: 'a) vjerojatnost da slučajno odabrana osoba iz populacije ima kvocijent inteligencije veći od očekivanoga,',\r\n        3: 'b) vjerojatnost da slučajno odabrana osoba iz populacije ima kvocijent inteligencije između 85 i 115.',\r\n        4: '<strong>Rješenje</strong>',\r\n        5: 'Kvocijent inteligencije u populaciji opisujemo slučajnom varijablom 𝑍~𝒩(100, 15).',\r\n        6: 'a) Kako je  𝐸[𝑍] = 100, tražimo vjerojatnost 𝑃 (𝑍 > 100). Ta je vjerojatnost jednaka površini ispod grafa funkcije gustoće 𝒩 (100, 15) distribucije nad intervalom (100, ∞) i iznosi <div class=\"fraction\" top=\"1\" bottom=\"2\"></div>.',\r\n        7: 'b) Tražena vjerojatnost 𝑃 (85 < 𝑍 < 115) jednaka je površini ispod grafa funkcije gustoće 𝒩 (100, 15) distribucije nad intervalom (85, 115) i iznosi 0.6827.',\r\n        8: '<strong>Zadatak 4.3.1.</strong>'\r\n      },\r\n      normalna_distribucija_zadatak_interakcija: {\r\n        1: 'Očekivanje',\r\n        2: 'Početna vrijednost',\r\n        3: 'Standardna devijacija',\r\n        4: 'Krajnja vrijednost',\r\n        5: 'Graf funkcije gustoće',\r\n        6: 'P(c < Z < d)',\r\n        7: 'Granice intervala c i d nisu dobro odabrane!',\r\n        8: 'Parametri nisu dobro odabrani. Devijacija mora biti veća od 1!'\r\n      },\r\n      distribucija: {\r\n        title: '𝝌𝟐 distribucija ',\r\n        1: 'Ako su 𝑍1, ... , 𝑍𝑛 nezavisne standardne normalne slučajne varijable, tada je zbroj njihovih kvadrata',\r\n        2: 'slučajna varijabla s <strong>𝝌𝟐 distribucijom</strong> s parametrom 𝑛 ∈ 𝑁 i ima oznaku 𝑌~𝜒2(𝑛).',\r\n        3: 'Parametar zove se <strong>broj stupnjeva slobode</strong> 𝜒2 distribucije.',\r\n        4: '<strong>Očekivanje</strong> i <strong>varijanca</strong> 𝜒2(𝑛) distribucije jesu',\r\n        5: '<strong>Primjer 4.5.1.</strong>',\r\n        6: 'Grafovi funkcija gustoća 𝜒2(3), 𝜒2(5) i 𝜒2(7) distribucije s istaknutim očekivanjem prikazani su na sljedećim slikama:',\r\n        7: 'Upotrebom interaktivnog alata proučite 𝜒2(𝑛) distribucije za druge vrijednosti parametra . '\r\n      },\r\n      studentova_t_distribucija: {\r\n        title: 'Studentova t-distribucija',\r\n        1: 'Ako je  𝑍~𝒩(0, 1) i 𝑌~𝜒2(𝑛), tada slučajna varijabla',\r\n        2: 'ima <strong>Studentovu t-distribuciju</strong> s 𝑛 stupnjeva slobode i oznaku 𝑇 ~𝑡(𝑛).',\r\n        3: '<strong>Očekivanje</strong> i <strong>varijanca</strong> 𝑡(𝑛) distribucije jesu',\r\n        4: '<strong>Primjer 4.6.1.</strong>',\r\n        5: 'Grafovi funkcija gustoća 𝑡(3), 𝑡(5) i 𝑡(7) distribucije s istaknutim očekivanjem prikazani su na sljedećoj slici:',\r\n        6: 'Upotrebom interaktivnog alata proučite 𝑡(𝑛) distribucije za druge vrijednosti parametra .'\r\n      }\r\n    }\r\n  },\r\n  en: {\r\n    validation_messages: {\r\n      must_be_number: 'Must be a number',\r\n      must_be_positive_number: 'Must be a positive number',\r\n      new_start: 'For the new calculation insert a new input for the number of throws.',\r\n      must_not_be_empty: 'must be inserted'\r\n    },\r\n    chaptersTitle: 'Chapters',\r\n    literatureTitle: 'Literature',\r\n    about: 'About project',\r\n    contact: 'Contact',\r\n    nextChapterParagraph: 'Next chapter',\r\n    go_button: 'Go!',\r\n    chapters_button: 'Chapters',\r\n    task_button: 'Task',\r\n    example: 'Example',\r\n    task: 'Task',\r\n    chapter1Title: 'Data description',\r\n    chapter2Title: 'Basic concepts of probability',\r\n    chapter3Title: 'Random variable',\r\n    chapter4Title: 'Distributions',\r\n    chapter5Title: 'Statistical inference',\r\n    buttonText: 'Go to chapter',\r\n    showTaskSolution: 'Show solution',\r\n    hideTaskSolution: 'Hide solution',\r\n    for_those_who_want_more: 'For those who want to learn more',\r\n    show_interaction: 'Show interaction',\r\n    show_data: 'Show data',\r\n    show_table: 'Show table',\r\n    show: 'Show',\r\n    show_interaction_1_9_1: 'Show interaction',\r\n    show_interaction_1_9_2: 'Show interaction',\r\n    sidebar: {\r\n      lesson1: {\r\n        1: 'Data',\r\n        2: 'Frequencies and relative frequencies',\r\n        3: 'Bar graph and histogram',\r\n        4: 'Mean',\r\n        5: 'Median and mode',\r\n        6: 'Minimum, maximum and range',\r\n        7: 'Quartiles and interquartile range',\r\n        8: 'Variance and standard deviation',\r\n        9: 'Box plot',\r\n        10: 'Scatter plot'\r\n      },\r\n      lesson2: {\r\n        1: 'Probability',\r\n        2: 'Conditional probability'\r\n      },\r\n      lesson3: {\r\n        1: 'Random variable',\r\n        2: 'Discrete random variable',\r\n        3: 'Continuous random variable',\r\n        4: 'Distribution function',\r\n        5: 'Expectation',\r\n        6: 'Variance and standard deviation'\r\n      },\r\n      lesson4: {\r\n        1: 'Bernoulli distribution',\r\n        2: 'Binomial distribution',\r\n        3: 'Normal distribution'\r\n      },\r\n      lesson5: {\r\n        1: 'Population and sample',\r\n        2: 'Proportion/probability estimate',\r\n        3: 'Expectation and variance estimate',\r\n        4: 'Confidence interval for expectation',\r\n        5: 'Confidence interval for proportion/probability',\r\n        6: 'Testing statistical hypotheses',\r\n        7: 'Simple linear regression'\r\n      }\r\n    },\r\n    literature: {\r\n      1: 'Bain, L.E., Engelhardt, M. (2008). Introduction to Probability and Mathematical Statistics. \tBROOKS/COLE Cengage Learning.',\r\n      2: 'Benšić, M., Šuvak, N. (2013). Primijenjena statistika. Sveučilište J.J. Strossmayera u Osijeku, Odjel za matematiku.',\r\n      3: 'Bhattacharyya, G.K., Johnson, R.A. (1977). Statistical Concepts and Methods. John Wiley and Sons.',\r\n      4: 'Benšić, M., Šuvak, N. (2014). Uvod u vjerojatnost i statistiku. Sveučilište J.J. Strossmayera u Osijeku, Odjel za matematiku.',\r\n      5: 'Elezović, N. (2007). Diskretna vjerojatnost. Element.',\r\n      6: 'Elezović, N. (2007). Slučajne varijable. Element.',\r\n      7: 'Elezović, N. (2007). Statistika i procesi. Element.',\r\n      8: 'Ross, S.M. (2017). Introductory statistics. Academic Press.',\r\n      9: 'Sarapa, N. (1987). Teorija vjerojatnosti. Školska knjiga.',\r\n      10: 'Tintle, N., Chance, B.L., Cobb, G.W., Rossman, A.J., Roy, S., Swanson, T., VanderStoep, J. \t(2015). Introduction to Statistical Investigations: High School Binding. John Wiley.'\r\n    },\r\n    title_tag: {\r\n      homepage: 'STEDy - Assistant in your statistical challenges',\r\n      chapter_literature: 'Chapter list - STEDy',\r\n      privacy_policy: 'Privacy policy - STEDy',\r\n      opisivanje_podataka: 'Data description - STEDy',\r\n      osnove_vjerojatnosti: 'Basic concepts of probability - STEDy',\r\n      slucajna_varijabla: 'Random variable - STEDy',\r\n      distribucije: 'Distributions - STEDy',\r\n      statisticko_zakljucivanje: 'Statistical inference - STEDy',\r\n      chapter1: {\r\n        1: 'Data - Data description - STEDy',\r\n        2: 'Frequencies and relative frequencies - Data description - STEDy',\r\n        3: 'Bar graph and histogram - Data description - STEDy',\r\n        4: 'Mean - Data description - STEDy',\r\n        5: 'Median and mode - Data description - STEDy',\r\n        6: 'Minimum, maximum and range - Data description - STEDy',\r\n        7: 'Quartiles and interquartile range - Data description - STEDy',\r\n        8: 'Variance and standard deviation - Data description - STEDy',\r\n        9: 'Box plot - Data description - STEDy',\r\n        10: 'Scatter plot - Data description - STEDy',\r\n      },\r\n      chapter2: {\r\n        1: 'Probability - Basic concepts of probability - STEDy',\r\n        2: 'Conditional probability - Basic concepts of probability - STEDy'\r\n      },\r\n      chapter3: {\r\n        1: 'Random variable - Random variable - STEDy',\r\n        2: 'Discrete random variable - Random variable - STEDy',\r\n        3: 'Continuous random variable - Random variable - STEDy',\r\n        4: 'Distribution function - Random variable - STEDy',\r\n        5: 'Expectation - Random variable - STEDy',\r\n        6: 'Variance and standard deviation - Random variable - STEDy'\r\n      },\r\n      chapter4: {\r\n        1: 'Bernoulli distribution - Distributions - STEDy',\r\n        2: 'Binomial distribution - Distributions - STEDy',\r\n        3: 'Normal distribution - Distributions - STEDy',\r\n      },\r\n      chapter5: {\r\n        1: 'Population and sample - Statistical inference - STEDy',\r\n        2: 'Proportion/probability estimate - Statistical inference - STEDy',\r\n        3: 'Expectation and variance estimate - Statistical inference - STEDy',\r\n        4: 'Confidence interval for expectation - Statistical inference - STEDy',\r\n        5: 'Confidence interval for proportion/probability - Statistical inference - STEDy',\r\n        6: 'Testing statistical hypotheses - Statistical inference - STEDy',\r\n        7: 'Simple linear regression - Statistical inference - STEDy',\r\n      },\r\n    },\r\n    meta_content: {\r\n      homepage: 'STEDy is an interactive portal intended for educating and promoting statistical literacy through e-learning.',\r\n      chapter_literature: 'Alphabetical list of literature used to create the interactive educational portal STEDy.',\r\n      privacy_policy: 'Croatian Bureau of Statistics manages the interactive educational portal STEDy. Bureau pays great attention to the protection of personal data of users of Stedy.',\r\n      opisivanje_podataka: 'STEDy - Data description',\r\n      osnove_vjerojatnosti: 'STEDy - Basic concepts of probability',\r\n      slucajna_varijabla: 'STEDy - Random variable',\r\n      distribucije: 'STEDy - Distributions',\r\n      statisticko_zakljucivanje: 'STEDy - Statistical inference',\r\n      chapter1: {\r\n        1: 'Data are collected on subjects (e.g. people, animals, plants, countries, cities, enterprises, etc.), which are called individuals or cases.',\r\n        2: 'Frequency of a category is the number of recorded variable values that belong to that category. Relative frequency of a category is the frequency divided by the total number of data for that variable.',\r\n        3: 'Bar graph is used to present the frequencies or relative frequencies of the selected variable categories. Histogram is used to present numerical data.',\r\n        4: 'Arithmetic mean or average of data is the sum of all data divided by the total number of data. Mean is a measure of central tendency of a numerical data set.',\r\n        5: 'Median is the number that breaks down a sorted data set in 2 parts,  whereby each part contains the same number of data and data from the first part are not bigger than data from the second part.',\r\n        6: 'Minimum is the smallest number in a set, while maximum is the greatest number in a set. Range is a rough measure of dispersion of data, i.e. difference between minimum and maximum.',\r\n        7: 'Interquartile range is a measure of dispersion of data. It is defined by quartiles. We distinguish between the lower and the upper quartile.',\r\n        8: 'Variance and standard deviation are the measures of dispersion of data, which characterise the spread of data around the mean.',\r\n        9: 'Box plot (or box-and-whisker plot) presents the relation between the minimum, the maximum, the lower and the upper quartile and the median of data.',\r\n        10: 'If data on two numerical values are collected for particular individuals, it is useful to present the pairs of data in a scatter plot.'\r\n      },\r\n      chapter1_tasks: {\r\n        1: 'Create your own database having at least one qualitative ordinal, one qualitative nominal and one numerical variable.',\r\n        2: 'For the table from the example, group the variable data so that each interval has a length of 30. Create a corresponding frequency and relative frequency table.',\r\n        3:  'Which variable is appropriate for presentation by a bar graph? Select that variable to see the presentation of data in a bar graph.',\r\n        4: 'The following two data sets are given. Calculate mean of each data set. How are these sets similar? Does mean express sufficient information on data set?',\r\n        5:  'The class master of a particular class is monitoring how much time his students spend playing computer games. For that purpose, he asked the students…',\r\n        6: 'The class master of a particular class is monitoring how much time his students spend playing computer games. For that purpose, he asked students…',\r\n        7: 'The class master of a particular class is monitoring how much time his students spend playing computer games. For that purpose, he asked students…',\r\n        8: 'The following two data sets are given. Calculate the mean and the standard deviation of each data set. How are these sets similar?',\r\n        9: 'The figure shows three box plots. Can we identify which statement applies to which plot…',\r\n        10: 'The figure shows the scatter plot of the variable time spent playing games on Sunday and on Monday. Do you notice any correlation?'\r\n      },\r\n      chapter2: {\r\n        1: 'Probability of an event is a number that expresses the degree of belief in the occurrence of that event.',\r\n        2: 'With additional information on the outcome of experiment, the probability of an event may differ from the probability of the same event without that information.'\r\n      },\r\n      chapter2_tasks: {\r\n        1: 'Two brothers, both gamblers, are completely different – one is honest, the other one is a cheater. The honest gambler is playing with an unbiased die…',\r\n        2: 'Using interactive tool, calculate the probability of rolling a six when rolling a die that is not necessarily unbiased, with additional information…'\r\n      },\r\n      chapter3: {\r\n        1: 'Random variable is a function that assigns real numbers to outcomes of an experiment (elements of the set Ω). It is usually denoted by a capital letter, e.g. 𝑋.',\r\n        2: 'Discrete random variable is characterised by finite or countable set of values.',\r\n        3: 'Continuous random variable is characterised by image 𝓡(𝑋), which is not a discrete set. For example, 𝓡(𝑋) may be an interval or even a whole set of real numbers.',\r\n        4: 'Distribution function 𝐹 of a random variable 𝑋 assigns to each real number 𝑥 the probability of event (𝑋 ≤ 𝑥): F(x)=P(X≤x),x∈R.',\r\n        5: 'Expectation of a random variable 𝑋 is the number that indicates the centre of the probability distribution of that random variable. It is denoted by 𝐸[𝑋] or 𝜇.',\r\n        6: 'Variance of random variable 𝑋 is a positive number indicating the dispersion of distribution of random variable 𝑋 in relation to its expectation 𝐸[𝑋].'\r\n      },\r\n      chapter3_tasks: {\r\n        1: 'An experiment consists of rolling a die twice in a row. Define the random variable which assigns the sum of the numbers rolled to the outcomes of that experiment.',\r\n        2: 'An experiment consists of rolling a die, which does not have to be unbiased, twice in a row. Calculate the distribution of the random variable X, which assigns…',\r\n        3: 'Using the interactive tool for λ=1, calculate the probability that between two consecutive arrivals of a tram…',\r\n        4: '',\r\n        5: 'If we wonder if there is a real number that is somehow “the closest” to the random variable, then in one way of measuring distance, it is precisely the expectation.',\r\n        6: 'Using the interactive tool, examine how the expectation and variance of the random variable X change depending on the value of parameter λ>0…'\r\n      },\r\n      chapter4: {\r\n        1: 'Random variable 𝑋 that describes experiment with only two possible outcomes: failure (denoted by 0) and success (denoted by 1), has a Bernoulli distribution with parameter 𝑝 ∈ (0, 1)…',\r\n        2: 'Binomial distribution shows the probability of occurrence of mutually exclusive events for each number of events separately.',\r\n        3: 'Normal distribution is a two-parameter function, the parameters of which are arithmetic mean and standard deviation.',\r\n      },\r\n      chapter4_tasks: {\r\n        1: 'In the game of Ludo, players roll unbiased die, and when a six is rolled, it is considered success. If any of the numbers 1, 2, 3, 4 or 5 is rolled, it is considered…',\r\n        2: 'Using the interactive tool, calculate the probability of rolling a six more than 5 times in 50 die rolls. Is it more probable that a six…',\r\n        3: 'A standardised intelligence test is calibrated based on the assumption that the intelligence quotient in a population is a normally distributed property…',\r\n      },\r\n     chapter5: {\r\n        1: 'In statistical inference, the data we manage are considered to be the values recorded on one part of the population called the sample.',\r\n        2: 'Let x1, 𝑥2, ... , 𝑥n be the sample from variable 𝑋, which can have only two outcomes. Outcomes can be denoted by 0 and 1, so it is a sample from the Bernoulli…',\r\n        3: 'If  𝑥1, 𝑥2, ... , 𝑥𝑛 is a sample from variable 𝑋 with unknown expectation 𝜇 = 𝐸[𝑋], parameter 𝜇 is estimated by the arithmetic mean (average) of the sample…',\r\n        4: 'Instead of estimating a parameter with one number, we can estimate interval which contains that number with some probability, usually 0.95 or 0.99. Such interval is called confidence interval.',\r\n        5: 'Instead of estimating by one number, an unknown proportion of a characteristic in a population can be estimated by confidence interval for proportion.',\r\n        6: 'Let us assume that we are playing a game in which we win if we toss a coin and it lands tails up. After 10 tosses, the coin landed tails up 2 times and heads up 8 times…',\r\n        7: 'Regression methods can be used to describe the relationship between variables X and Y. If the points shown in the scatter diagram appear to be scattered…',\r\n      },\r\n      chapter5_tasks: {\r\n        1: 'In an experiment where a coin is tossed, the coin lands tails up two times in two tosses. The experiment is repeated 200 times.',\r\n        2: 'According to survey conducted by the Croatian Bureau of Statistics, of 2029 surveyed households in Croatia, 1635 live in a dwelling or house…',\r\n        3: '',\r\n        4: 'According to survey conducted by the Croatian Bureau of Statistics, households in Croatia spend an average of 5494 kuna per year on clothing and…',\r\n        5: 'Let us assume that only two candidates, A and B, are participating in an election. The aim of the poll is to predict the winner.',\r\n        6: 'A test was conducted on a sample of 50 persons on whether they can recognise the difference between expensive and cheap wine.',\r\n        7: '',\r\n      },\r\n      cookies: {\r\n        1: 'The website of the Statistical Office of the Republic of Slovenia uses cookies for analysing visits and for providing web services and functionalities that could not be provided without cookies. Do you accept cookies?',\r\n        2: 'More on cookies.',\r\n        3: 'Do not accept',\r\n        4: 'Accept',\r\n      },\r\n    },\r\n\taccessibility: {\r\n        1: 'Accessibility Statement',\r\n        2: 'The Statistical Office of the Republic of Slovenia (hereinafter SURS) is committed to providing access in line with the <a href=\"http://www.pisrs.si/Pis.web/pregledPredpisa?id=ZAKO7718\">Accessibility of Websites and Mobile Applications Act</a>.',\r\n        3: '<strong>Accessibility statement<strong>',\r\n        4: 'This accessibility statement relates to the STEDy website. The website is partially in line with the Accessibility of Websites and Mobile Applications Act, but only to the extent provided by the Croatian Bureau of Statistics, from which SURS took it over, adapted it, and translated it into Slovene.',\r\n        5: 'SURS did not further adapt the STEDy website to the <a href=\"https://www.w3.org/WAI/standards-guidelines/wcag/\">WCAG 2.0 or WCAG 2.1</a> - Web Content Accessibility Guidelines, as the additional adaptation of the website would represent a disproportionate financial and human burden.',\r\n        6: 'To ensure accessibility requirements, some adjustments have been systemically provided, such as:',\r\n        7: 'Responsive design - the layout of the content adapts to the screen resolution',\r\n        8: 'Partial support for keyboard navigation (customization for users who cannot use the mouse)',\r\n        9: 'Partially appropriate color contrast (between the text and the background)',\r\n       10: '<strong>Feedback and contact information</strong>',\r\n       11: 'SURS appreciates any information on user experience with the website or suggestions for possible additional improvements of the website for vulnerable groups.',\r\n       12: 'You can also inform SURS about potential non-compliance of published content with the provisions of the Accessibility of Websites and Mobile Applications Act. SURS will try to improve it or provide you with alternative sources of access.',\r\n       13: 'You will receive a reply within eight days from the submission of the notification or request. If SURS is unable to send an appropriate reply in this period, you will be informed about when SURS will send a reply and the reasons for the delay.',\r\n       14: 'All information available on SURS’s website and in other SURS’s products can be obtained:',\r\n       15: 'By phone: <a href=\"tel:012416404\">01 241 64 04</a>,',\r\n       16: 'By e-mail: <a href=\"mailto:gp.surs@gov.si\">gp.surs@gov.si</a>,',\r\n       17: 'In person by visiting the Statistical Office of the Republic of Slovenia, Litostrojska cesta 54, 1000 Ljubljana.',\r\n       18: 'Some information on SURS’s operation is also available on its presentation website at <a href=\"https://www.gov.si/en/state-authorities/government-offices/statistical-office/\">gov.si</a>.',\r\n       19: '<strong>Preparation of the accessibility statement</strong>',\r\n       20: 'This statement was prepared on 1 October 2021 based on self-evaluation. The statement was last reviewed on 5 October 2021.',\r\n       21: '<strong>Enforcement</strong>',\r\n       22: 'If you detect any non-compliance with the provisions of the Accessibility of Websites and Mobile Applications Act, you can file a complaint with the information security inspectors by writing a letter or e-mail to:',\r\n       23: 'Information Security Administration of the Republic of Slovenia<br>MINISTRY OF PUBLIC ADMINISTRATION<br>Tržaška cesta 21<br>1000 Ljubljana<br><a href=\"tel:014784778\">01 478 47 78</a><br><a href=\"mailto:gp.uiv@gov.si\">gp.uiv@gov.si</a>',\r\n    },\r\n\tprivacy_cookies: {\r\n       title: 'About STEDy website and Cookies',\r\n       1: 'The STEDy website was developed by the Croatian Bureau of Statistics in cooperation with the J. J. Strossmayer University of Osijek. Its development was co-financed by Eurostat - the Statistical Office of the European Union. It was translated and adapted by the Statistical Office of the Republic of Slovenia (hereinafter SURS). The content of the website was reviewed by the Statistical Society of Slovenia.',\r\n       2: '<strong>Monitoring traffic analytics</strong>',\r\n       3: 'While interacting with the website, SURS collects usage data (traffic analytics). For traffic data collection purposes, security, optimal functioning of the website, and to ensure a good user experience, STEDy can save cookies on a user’s device.',\r\n       4: '<strong>Usage information</strong>',\r\n       5: 'Information on website traffic may include other information such as the device information that users use for accessing the internet, the Internet Protocol address of the device (e.g. IP address), browser type and version, visited websites within STEDy, time and date of visit, time spent on the STEDy website, unique device identifiers, and other diagnostic information.',\r\n       6: 'SURS uses the collected user data to:',\r\n       7: 'Provide and maintain this website',\r\n       8: 'Track the usage of this website',\r\n       9: 'Detect, prevent and address technical issues relating to the use of the website',\r\n      10: 'Provide customer care and support',\r\n      11: 'Provide analysis or valuable information for the improvement of this website.',\t\r\n      12: '<strong>Cookies</strong>',\r\n      13: 'SURS uses cookies to track the activity associated with this website and to collect certain information. Cookies are files with small amount of data, which may include an anonymous unique identifier and are sent to your browser from the website you use and stored on your device.',\r\n      14: 'Examples of cookie usage:',\r\n      15: '<strong>Session cookies</strong> – SURS uses them to operate our website',\r\n      16: '<strong>Preference cookies</strong> – SURS uses them to remember your preferences and various settings',\r\n      17: '<strong>Security cookies</strong> – SURS uses them for security purposes',\r\n      18: 'PROVIDER',\r\n      19: 'EXPIRATON DATE',\r\n      20: 'PURPOSE',\r\n      21: 'COOKIE NAME',\r\n      22: 'Statistical Office',\r\n      23: 'Session (1), daily (1), annual (3).',\r\n      24: 'These are SURS’s cookies that are used for several reasons; to track website traffic of the STEDy website (Piwik tool), to record the user’s decision whether they accept cookies or not, and for security.',\r\n      25: 'pk_id, pk_ref, pk_ses, piwik_agreeme nt, RequestVerifica tionToken, stat.si.STEDy.analytics',\r\n      26: '<strong>Cookie management</strong>',\r\n      27: 'The cookies used by the STEDy website are transferred to your computer or mobile device only if you select \"Accept\". If you select this option, all the cookies listed in the table above will be saved on your computer. If you select the opposite option (\"Do not accept\"), cookies will not be loaded and some functionalities of the website may not work and your visit will not be recorded.',\r\n      28: 'Most web browsers automatically accept cookies. You can change the operation of your web browser in the settings so that the computer automatically rejects cookies or notifies you with a warning before the cookies are saved. You can also completely prevent the installation of cookies in your browser for all the websites you visit. You can delete cookies that are already stored on your computer.',\r\n      29: 'Links to instructions on how to turn off cookies in your web browser:',\r\n      30: '<a href=\"https://support.mozilla.org/en-US/kb/cookies-information-websites-store-on-your-computer?redirectlocale=en-US&redirectslug=Cookies\">Mozilla Firefox</a>',\r\n      31: '<a href=\"https://support.google.com/chrome/answer/95647?hl=en\">Chrome</a>',\r\n      32: '<a href=\"https://support.apple.com/guide/safari/manage-cookies-and-website-data-sfri11471/mac\">Safari</a>',\r\n      33: '<a href=\"https://support.microsoft.com/en-us/microsoft-edge/delete-cookies-in-microsoft-edge-63947406-40ac-c3b8-57b9-2a946a29ae09\">Edge</a>',\r\n      34: 'Information on the use of cookies in browsers of mobile phones and instructions on how to reject or delete them can be found in the manual of your mobile phone.',\r\n      35: '<strong>Your cookie settings</strong>',\r\n      36: 'You can change your decision about cookies on the STEDy website at any time.',\r\n      37: 'Change the decision'\r\n    },\r\n    table_head: {\r\n      1: 'STUDENT NUMBER',\r\n      2: 'TIME SPENT PLAYING (min)',\r\n      3: 'SEX',\r\n      4: 'GRADE'\r\n    },\r\n    student_table: {\r\n      table_head: {\r\n        student_number: 'STUDENT NUMBER',\r\n        play_time: 'TIME SPENT PLAYING (min)',\r\n        sex: 'SEX',\r\n        grade: 'GRADE'\r\n      },\r\n      table_body: {\r\n        1: '1',\r\n        2: '2',\r\n        3: '3',\r\n        4: '4',\r\n        5: '5',\r\n        6: '6',\r\n        7: '7',\r\n        8: '8',\r\n        9: '9',\r\n        10: '10',\r\n        11: '11',\r\n        12: '12',\r\n        13: '13',\r\n        14: '14',\r\n        15: '15',\r\n        16: '16',\r\n        17: '17',\r\n        18: '18',\r\n        19: '19',\r\n        20: '20',\r\n        21: '21',\r\n        22: '22',\r\n        23: '23',\r\n        24: '24',\r\n        47: '47',\r\n        177: '177',\r\n        124: '124',\r\n        135: '135',\r\n        69: '69',\r\n        88: '88',\r\n        0: '0',\r\n        120: '120',\r\n        63: '63',\r\n        57: '57',\r\n        79: '79',\r\n        244: '244',\r\n        99: '99',\r\n        76: '76',\r\n        166: '166',\r\n        193: '193',\r\n        74: '74',\r\n        51: '51',\r\n        data20: '20',\r\n        data19: '19',\r\n        189: '189',\r\n        zene: 'f',\r\n        muskarci: 'm',\r\n        nedovoljan: 'insufficient',\r\n        dovoljan: 'sufficient',\r\n        dobar: 'good',\r\n        vrlo_dobar: 'very good',\r\n        odlican: 'excellent'\r\n      }\r\n    },\r\n    frequency_table_big: {\r\n      table_head: {\r\n        play_time: 'TIME PLAYED (min)',\r\n        frequency: 'FREQUENCY',\r\n        relative_frequency: 'RELATIVE FREQUENCY (%)'\r\n      },\r\n      table_body: {\r\n        1: '0',\r\n        2: '19',\r\n        3: '20',\r\n        4: '47',\r\n        5: '51',\r\n        6: '57',\r\n        7: '63',\r\n        8: '69',\r\n        9: '74',\r\n        10: '76',\r\n        11: '79',\r\n        12: '88',\r\n        13: '99',\r\n        14: '120',\r\n        15: '124',\r\n        16: '135',\r\n        17: '166',\r\n        18: '177',\r\n        19: '189',\r\n        20: '193',\r\n        21: '244',\r\n        22: '3',\r\n        23: '1',\r\n        24: '0.12',\r\n        25: '0.04',\r\n        26: '2',\r\n        27: '0.08'\r\n      }\r\n    },\r\n    frequency_table_small: {\r\n      table_head: {\r\n        play_time: 'TIME PLAYED (min)',\r\n        frequency: 'FREQUENCY',\r\n        relative_frequency: 'RELATIVE FREQUENCY (%)'\r\n      },\r\n      table_body: {\r\n        1: '0',\r\n        2: '<0, 60]',\r\n        3: '<60, 120]',\r\n        4: '> 120',\r\n        5: 'total'\r\n      }\r\n    },\r\n    socials: {\r\n      facebook: 'https://www.facebook.com/StatSlovenija/',\r\n      instagram: 'https://www.instagram.com/statslovenija/',\r\n      youtube: 'https://www.youtube.com/user/StatSlovenia',\r\n      linkedin: '',\r\n      github: ''\r\n    },\r\n    homepage: {\r\n      intro: '<span>STEDy - Assistant</span> for your statistical challenges',\r\n      about_section: {\r\n        1: 'Do you think statistics is complicated and simply not your thing?',\r\n        2: 'We are aware of the fact that you have learned percentages back in elementary school, but there is a chance that intervals, quartiles or types of distribution are still in the twilight zone for you. We hope not for long.',\r\n        3: '<strong>STEDy</strong> is now there for you – a statistical educational portal that will explain in only a few steps the statistical concepts that sometimes seem so complicated. On the other hand, if you have always been a fan of statistics, it is just what you need to expand, renew or test your knowledge! STEDy is intended for everyone – the general public, teachers, professors, pupils and students as well as fans of statistics.',\r\n        4: 'In explaining statistical concepts, we tried to move away from the classic approach, so STEDy is not limited only to the theoretical background, but it also gives you practical examples, interactive visualisations and tasks in which you can immediately check your understanding and application of statistics.',\r\n        5: 'In the world flooded with information and data, statistical literacy is a very useful skill, since it helps us understand and critically evaluate statistical data that we encounter. Whether statistics is part of your everyday life and a smart basis for making fact-based decisions or just an obstacle to overcome, we hope that STEDy will be a great assistant in your statistical challenges.',\r\n        6: 'Fasten you belts, plunge into the magical world of numbers and play with data!',\r\n        7: \"The statistical educational portal was created by the Croatian Bureau of Statistics in cooperation with the J. J. Strossmayer University of Osijek as part of Eurostat's project Support for Statistical Literacy Actions in the Area of a Competition, Gamification and E-learning. Experts cooperating in the project were Full Professor Mirta Benšić, Assistant Professor Danijel Grahovac and Associate Professor Nenad Šuvak.\",\r\n        8: 'The Statistical Office of the Republic of Slovenia translated and adapted the material.'\r\n      },\r\n      contact: {\r\n        1: 'Do you have any questions? Contact us!',\r\n        2: 'You can send your queries, messages and comments at <a href=\"mailto: gp.surs@gov.si\">gp.surs@gov.si</a>',\r\n        3: 'Contact us'\r\n      },\r\n      footer: {\r\n        1: 'About STEDy and Cookies',\r\n        2: 'Croatian Bureau of Statistics',\r\n        3: 'The website was created by the Croatian Bureau of Statistics in cooperation with the J. J. Strossmayer University of Osijek.</br> Its development was co-financed by Eurostat - the Statistical Office of the European Union. It was translated and adapted by the Statistical Office of the Republic of Slovenia.',\r\n        4: 'Open Source Project',\r\n        5: 'Accessibility'\r\n      }\r\n    },\r\n    privacy_policy: {\r\n      title: 'Privacy policy',\r\n      1: 'The Croatian Bureau of Statistics (hereinafter referred to as “the Bureau”) operates the website <a href=\"www.stedy.hr\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"link\">www.stedy.hr</a>. The Bureau pays great attention to the protection of personal data of the users of the above-mentioned website',\r\n      2: 'This Privacy Policy (hereinafter referred to as “the Policy”) regulates the manner of using the data that the Bureau processes or collects when users visit this website. The Bureau collects your personal data only when you explicitly make them available to us and agree to their usage.',\r\n      3: 'During various forms of interaction on the website <a href=\"www.stedy.hr\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"link\">www.stedy.hr</a> the Bureau collects your personal data, such as your e-mail address, as well as other data, for example cookies and usage data.',\r\n      4: 'Cookies',\r\n      5: 'We use cookies and similar tracking technologies to track the activity associated with this website and to collect certain information. Cookies are files with small amount of data, which may include an anonymous unique identifier and are sent to your browser from the website you use and stored on your device. Tracking technologies also used are beacons, tags and scripts, which are used to collect and track information and to improve and analyse the habits of using the above-mentioned website.',\r\n      6: 'You can instruct your browser to refuse all cookies or to indicate when a cookie is being sent. However, if you do not accept cookies, you may not be able to use some parts of the website.',\r\n      7: 'Example of cookies we use:',\r\n      8: '<strong>session cookies</strong> – we use them to operate our website',\r\n      9: '<strong>preference cookies</strong> – we use them to remember your preferences and various settings',\r\n      10: '<strong>security cookies</strong> – we use them for security purposes.',\r\n      11: 'Usage data',\r\n      12: \"Usage data may include information such as the data on the device you are using to connect to the internet, your computer's Internet Protocol address (e.g. IP address), browser type, browser version, websites that you visit, the time and date of your visit, the time spent on those sites, unique device identifiers and other diagnostic data.\",\r\n      13: '<strong>Use of Data</strong>',\r\n      14: 'The Bureau uses the collected data for the following purposes:',\r\n      15: 'to provide and maintain this website',\r\n      16: 'to monitor the usage of this website',\r\n      17: 'to detect, prevent and address technical issues relating to the use of the website',\r\n      18: 'to provide customer care and support',\r\n      19: 'to provide analysis or valuable information for the improvement of this website',\r\n      20: 'to allow users to participate in interactive features of this website',\r\n      21: 'to notify users about changes to this website.',\r\n      22: '<strong>Transfer of Data</strong>',\r\n      23: 'Your data, including personal data, may be transferred to, and maintained on, computers located outside of your state or outside the European Union or other governmental jurisdiction where the data protection laws may differ from those of the European Union.',\r\n      24: 'If you are located outside the Republic of Croatia and choose to provide your data to us, please note that we transfer the data, including personal data, to the Republic of Croatia and process them there.',\r\n      25: 'The Bureau will take all the steps necessary to ensure that your data are treated securely and in accordance with this Policy and no transfer of your personal data will take place unless there are adequate controls in place for the protection of your data.',\r\n      26: 'The Bureau may transfer your personal data to third parties only in the following cases: ',\r\n      27: 'if there is a legal obligation or an explicit legal authorisation',\r\n      28: 'if we hire a processor to provide certain services, who acts exclusively by the order of the Bureau, whereby the Bureau undertakes all measures of data protection',\r\n      29: 'if data are to be transferred to third parties for the performance of the contract with the data subject.',\r\n      30: 'When transferring the data of the data subject, the Bureau strictly respects the principle of the restriction of processing by transferring the minimum amount of data necessary and by respecting all other relevant data protection principles. Third parties have access to your personal data only for performing services on behalf of the Bureau and are committed to preserving the confidentiality of your personal data and to use them only in accordance with the specific purpose for which they are transferred',\r\n      31: '<strong>Security of Data</strong>',\r\n      32: 'The security of your data is important to us, but remember that no method of transmission over the internet or method of electronic storage is 100% secure. While we strive to use commercially acceptable means to protect your personal data, we cannot guarantee their absolute security.',\r\n      33: '<strong>Analytics</strong>',\r\n      34: 'The Bureau may hire third-party service providers to monitor and analyse the use of this website.',\r\n      35: '<strong>Google Analytics</strong>',\r\n      36: 'Google Analytics is a web analytics service offered by Google that tracks and reports website traffic. Google uses the data collected to track and monitor the use of this website. These data are shared with other Google services. Google may use the collected data to contextualise and personalise the ads of its own advertising network',\r\n      37: 'You can opt-out of having made your activity on this website available to Google Analytics by installing the Google Analytics opt-out browser add-on. The add-on prevents the Google Analytics JavaScript (ga.js, analytics.js, and dc.js) from sharing information with Google Analytics about visits activity.',\r\n      38: 'For more information on the privacy practices of Google, please visit the Google Privacy & Terms website: <a href=\"https://policies.google.com/privacy?hl=en\" class=\"link\" target=\"_blank\" rel=\"noopener noreferrer\">https://policies.google.com/privacy?hl=en</a>',\r\n      39: '<strong>Links to Other Sites</strong>',\r\n      40: 'This website may contain links to other sites that are not operated by the Bureau. We strongly advise you to review the Privacy Policy of every site you visit. The Bureau has no control over and assumes no responsibility for the content, privacy policies or practices of any third party sites or services.',\r\n      41: '<strong>Protection of Privacy of Persons under the Age of 18</strong>',\r\n      42: 'This website may be used by persons under the age of 18. The Bureau does not knowingly collect personal data on anyone under the age of 18. If you are a parent or guardian and you are aware that your child has provided us with personal data, please contact the Bureau. If the Bureau becomes aware that they have collected personal data from persons under the age of 18 without a valid consent of the parent or guardian, the Bureau will reasonably and in the shortest possible period take the following steps:',\r\n      43: 'remove those data from the records of the Bureau',\r\n      44: 'in case the erasure is not possible, ensure that personal data are not further used for any purpose',\r\n      45: 'in any case, the Bureau will not give data to any third party.',\r\n      46: '<strong>Changes to the Privacy Policy</strong>',\r\n      47: 'The Bureau reserves the right to change this Policy by publishing the new policy on this website. You are advised to review this Policy periodically for any changes. Changes to this Policy are effective when they are posted on this website.',\r\n      48: 'Your Rights',\r\n      49: 'As regards the processing of personal data, you are entitled to exercise the following rights: ',\r\n      50: 'right to access personal data',\r\n      51: 'right to rectification of personal data',\r\n      52: 'right to erasure of personal data (“right to be forgotten”) ',\r\n      53: 'right to restriction of processing',\r\n      54: 'right to transfer of data ',\r\n      55: 'right to lodge a complaint.',\r\n      56: 'How can you exercise your rights?',\r\n      57: 'For the exercise of the above-mentioned rights and your questions regarding your personal data, you can contact our data protection officers by sending an e-mail to <a href=\"mailto: gp.surs@gov.si\" class=\"link\">gp.surs@gov.si</a> .',\r\n      58: 'We will process the requests and inquiries without undue delay and in accordance with legal obligations and inform you in writing of the measures taken.',\r\n      59: 'If you believe that the Bureau is acting unlawfully and you cannot resolve that matter in cooperation with us, you are entitled to lodge a complaint to the supervisory authority for the protection of personal data in the Republic of Croatia - Croatian Personal Data Protection Agency (AZOP).'\r\n    },\r\n    opisivanje_podataka: {\r\n      chapterNumber: '&mdash; Chapter 1 &mdash;',\r\n      title: 'Data description',\r\n      table: {\r\n        rank: 'STUDENT NUMBER',\r\n        time: 'TIME SPENT PLAYING (min)',\r\n        sex: 'SEX',\r\n        grade: 'GRADE',\r\n        freq: 'FREQUENCY',\r\n        relFreq: 'RELATIVE FREQUENCY (%)'\r\n      },\r\n      game_time: {\r\n        1: '47',\r\n        2: '177',\r\n        3: '124',\r\n        4: '135',\r\n        5: '69',\r\n        6: '88',\r\n        7: '0',\r\n        8: '120',\r\n        9: '63',\r\n        10: '57',\r\n        11: '79',\r\n        12: '244',\r\n        13: '99',\r\n        14: '76',\r\n        15: '166',\r\n        16: '193',\r\n        17: '19',\r\n        18: '74',\r\n        19: '51',\r\n        20: '20',\r\n        21: '189',\r\n        22: 'total'\r\n      },\r\n      sex: {\r\n        1: 'f',\r\n        2: 'm',\r\n        3: 'total'\r\n      },\r\n      grade: {\r\n        1: 'insufficient',\r\n        2: 'sufficient',\r\n        3: 'good',\r\n        4: 'very good',\r\n        5: 'excellent',\r\n        6: 'total'\r\n      },\r\n      resultTable: {\r\n        1: 'CATEGORY',\r\n        2: 'FREQUENCY',\r\n        3: 'RELATIVE FREQUENCY (%)'\r\n      },\r\n      podaci: {\r\n        title: 'Data',\r\n        1: 'Data are collected on <strong>subjects</strong> (e.g. people, animals, plants, countries, cities, enterprises, etc.), which are called <strong>individuals</strong> or <strong>cases</strong>.',\r\n        2: 'The values we are interested in about individuals are called <strong>variables</strong>.',\r\n        3: 'The records on the collected data are kept in <strong>tables</strong>.',\r\n        4: '<strong>Types of variables:</strong>',\r\n        5: '<strong>numerical variables</strong> – values of these variables are numbers.',\r\n        6: '<strong>qualitative variables</strong> – values of these variables, by their characteristics, are not numbers, but non-numerical values called <strong>categories</strong>. Qualitative variables are divided into two groups:',\r\n        7: '<strong>nominal variables</strong> – there is no natural order among the variable categories  (e.g. sex, colour, city name, animal genus, etc.).',\r\n        8: '<strong>ordinal variables</strong> – there is natural order among the variable categories (e.g. professional attainment of a person, grade, etc.). Categories of ordinal variables are usually numbered.',\r\n        9: '<strong>Example 1.1.1.</strong>',\r\n        10: 'The class master of a particular class is monitoring how much time his students spend playing computer games. For that purpose, he asked the students to keep records of the aforementioned and he recorded data on the amount of time they spent playing computer games on Sunday in a table. He added data on the sex of students and the grade they got in the last Mathematics exam. Data are presented in the following table.',\r\n        11: '<strong>Where:</strong>',\r\n        12: 'time spent playing is a numerical variable',\r\n        13: 'gender is a qualitative nominal variable',\r\n        14: 'grade is a qualitative ordinal variable.',\r\n        15: 'STUDENT<br>NUMBER',\r\n        16: 'TIME<br>SPENT PLAYING (min)',\r\n        17: 'SEX',\r\n        18: 'GRADE',\r\n        19: 'f',\r\n        20: 'good',\r\n        21: 'm',\r\n        22: 'good',\r\n        23: 'f',\r\n        24: 'very good',\r\n        25: 'm',\r\n        26: 'good',\r\n        27: 'm',\r\n        28: 'very good',\r\n        29: 'm',\r\n        30: 'insufficient',\r\n        31: 'm',\r\n        32: 'good',\r\n        33: 'm',\r\n        34: 'good',\r\n        35: 'f',\r\n        36: 'excellent',\r\n        37: 'm',\r\n        38: 'good',\r\n        39: 'm',\r\n        40: 'very good',\r\n        41: 'f',\r\n        42: 'good',\r\n        43: 'f',\r\n        44: 'sufficient',\r\n        45: 'm',\r\n        46: 'good',\r\n        47: 'm',\r\n        48: 'good',\r\n        49: 'f',\r\n        50: 'very good',\r\n        51: 'f',\r\n        52: 'good',\r\n        53: 'm',\r\n        54: 'sufficient',\r\n        55: 'm',\r\n        56: 'excellent',\r\n        57: 'm',\r\n        58: 'very good',\r\n        59: 'm',\r\n        60: 'very good',\r\n        61: 'f',\r\n        62: 'insufficient',\r\n        63: 'm',\r\n        64: 'very good',\r\n        65: 'f',\r\n        66: 'very good',\r\n        67: 'TIME SPENT PLAYING ON SUNDAY',\r\n        68: 'TIME SPENT PLAYING ON MONDAY',\r\n\t\t69: '<strong>continuous variables</strong> - can take all values of an interval',\r\n\t\t70: '<strong>discrete variables</strong> - can take only some (but not all) values of an interval.'\r\n      },\r\n      'podaci-tablica-varabli': {\r\n        1: 'Name and surname',\r\n        2: 'Grade in Mathematics',\r\n        3: 'Grade in Biology',\r\n        4: 'Hours of absence',\r\n        5: 'Petar Petrić',\r\n        6: '5',\r\n        7: '4',\r\n        8: '20',\r\n        9: 'Ivan Ivić',\r\n        10: '4',\r\n        11: '5',\r\n        12: '45',\r\n        13: 'Marko Marković',\r\n        14: '5',\r\n        15: '4',\r\n        16: '130'\r\n      },\r\n      'podaci-zadatak': {\r\n        title: 'Data',\r\n        1: '<strong>Task 1.1.1.</strong>',\r\n        2: 'Data on daily habits of a group of persons in one day are collected as indicated in the following description of variables:',\r\n        3: 'Specify the type of each of the above-mentioned variables.',\r\n        4: '<strong>Variable</strong>',\r\n        5: '<strong>Values</strong>',\r\n        6: 'sex',\r\n        7: 'M, F',\r\n        8: 'currently married',\r\n        9: 'YES, NO',\r\n        10: 'number of newspaper browsed through',\r\n        11: '0, 1, 2, etc.',\r\n        12: 'number of TV news watched (not necessarily in entirety)',\r\n        13: '0, 1, 2, etc.',\r\n        14: 'number of coffees drank',\r\n        15: '0, 1, 2, etc.',\r\n        16: 'food costs',\r\n        17: 'number',\r\n        18: 'personal mood',\r\n        19: 'bad, good, great',\r\n        20: '<strong>Solution</strong>',\r\n        21: '<strong>Type</strong>',\r\n        22: 'qualitative nominal',\r\n        23: 'numerical',\r\n        24: 'qualitative ordinal',\r\n        25: '<strong>Task 1.1.2.</strong>',\r\n        26: '<strong>Create your own database</strong> having at least one qualitative ordinal, one qualitative nominal and one numerical variable.',\r\n        27: 'The minimum number of variables is 3'\r\n      },\r\n      'podaci-zadatak-interakcija': {\r\n        title: 'Task',\r\n        1: 'Enter the number of cases (table rows): ',\r\n        2: 'Enter the number of variables (table columns):',\r\n        3: 'Maximum is 10',\r\n        4: 'Maximum is 5',\r\n        5: 'Create table',\r\n        6: 'Export table to CSV file',\r\n        7: 'Attribute name',\r\n        8: 'Variable type',\r\n        9: 'Numerical variable',\r\n        10: 'Qualitative nominal variable',\r\n        11: 'Qualitative ordinal variable',\r\n        12: 'Enter the data',\r\n        13: 'Invalid input values.',\r\n        14: 'The maximum number of cases is 10! Repeat the entry.',\r\n        15: 'The maximum number of variables is 5! Repeat the entry.',\r\n        16: 'All table values must be entered.',\r\n        17: 'The minimum number of variables is 3'\r\n      },\r\n      'frekvencije-i-relativne-frekvencije': {\r\n        title: 'Frequencies and relative frequencies',\r\n        1: 'A frequency and relative frequency table is a form of reporting on data.',\r\n        2: 'It is presented for a selected variable.',\r\n        3: '<strong>The frequency</strong> of a category is the number of recorded variable values that belong to that category.',\r\n        4: '<strong>The relative frequency</strong> of a category is the frequency divided by the total number of data for that variable.',\r\n        5: 'Usual symbols',\r\n        6: 'frequency ⇒ <i>f</i>',\r\n        7: 'number of data of the selected variable ⇒ <i>n</i>',\r\n        8: 'relative frequency ⇒ <div class=\"fraction\" top=\"f\" bottom=\"n\"></div>.',\r\n        9: '<strong>Frequency and relative frequency table</strong>',\r\n        10: 'Frequencies and relative frequencies of categories are presented in tables. Relative frequencies are most often expressed in percentages.',\r\n        11: 'CATEGORY',\r\n        12: 'FREQUENCY',\r\n        13: 'RELATIVE <br> FREQUENCY (%)',\r\n        14: 'total',\r\n        15: '100',\r\n        16: '<strong>Grouping data into classes</strong>',\r\n        17: 'If a variable has a lot of different values, and if we want to present data in a frequency and relative frequency table, it is useful to group the values into <strong>classes</strong>.',\r\n        18: 'The need for grouping often arises in the case of numerical data. The <strong>grouping of values by intervals</strong> is usually applied.',\r\n        19: 'Different classes should not contain the same values.',\r\n        20: 'Grouping classes are carefully selected to highlight important data characteristics',\r\n        21: '<strong>Example 1.2.1.</strong>',\r\n        22: 'The class master of a particular class is monitoring how much time his students spend playing computer games. For that purpose, he asked the students to keep records of the aforementioned and he recorded data on the amount of time they spent playing computer games on Sunday in a table. He added data on the sex of students and the grade they got in the last Mathematics exam. Data are presented in the following table.',\r\n        23: 'student <br> number',\r\n        24: 'time spent <br> playin',\r\n        25: 'sex',\r\n        26: 'grade',\r\n        27: 'f',\r\n        28: 'good',\r\n        29: 'm',\r\n        30: 'good',\r\n        31: 'f',\r\n        32: 'very good',\r\n        33: 'm',\r\n        34: 'good',\r\n        35: 'm',\r\n        36: 'very good',\r\n        37: 'm',\r\n        38: 'insufficient',\r\n        39: 'm',\r\n        40: 'good',\r\n        41: 'm',\r\n        42: 'good',\r\n        43: 'f',\r\n        44: 'excellent',\r\n        45: 'm',\r\n        46: 'good',\r\n        47: 'm',\r\n        48: 'very good',\r\n        49: 'f',\r\n        50: 'good',\r\n        51: 'f',\r\n        52: 'sufficient',\r\n        53: 'm',\r\n        54: 'good',\r\n        55: 'm',\r\n        56: 'good',\r\n        57: 'f',\r\n        58: 'very good',\r\n        59: 'f',\r\n        60: 'good',\r\n        61: 'm',\r\n        62: 'sufficient',\r\n        64: 'm',\r\n        65: 'excellent',\r\n        66: 'm',\r\n        67: 'very good',\r\n        68: 'm',\r\n        69: 'very good',\r\n        70: 'f',\r\n        71: 'insufficient',\r\n        72: 'm',\r\n        73: 'very good',\r\n        74: 'f',\r\n        75: 'very good',\r\n        76: '<strong>Example 1.2.2.</strong>',\r\n        77: 'The following tables present the frequencies and relative frequencies of the numerical variable <strong>time spent playing</strong> for the table from the previous example. One table does not contain data grouped into classes, while the other does.',\r\n        78: 'TIME SPENT <br> PLAYING <br> (min)',\r\n        79: 'FREQUENCY',\r\n        80: 'RELATIVE <br> FREQUENCY <br> %',\r\n        81: 'TOTAL',\r\n        82: 'Frequency table and relative frequency table.'\r\n      },\r\n      'frekvencije-i-relativne-frekvencije-primjer': {\r\n        1: 'CATEGORY',\r\n        2: 'FREQUENCY',\r\n        3: 'RELATIVE FREQUENCY (%)',\r\n        4: 'Select a table variable to display the frequency and relative frequency table.',\r\n        5: 'Frequency and relative frequency table'\r\n      },\r\n      'frekvencije-i-relativne-frekvencije-zadatak': {\r\n        title: 'Frequencies and relative frequencies',\r\n        1: '<strong>Task 1.2.1.</strong>',\r\n        2: 'For the table from the previous example, group the data relating to the variable <i>time spent playing</i> so that each interval has a length of 30. Create a corresponding frequency and relative frequency table. Answer the following questions:',\r\n        3: 'What is the percentage of children who played computer games for more than three hours?',\r\n        4: 'What is the percentage of children who played computer games for less than two hours? Is the frequency and relative frequency table of the grouped data sufficient to answer this questions?',\r\n        5: '<strong>Solution</strong>',\r\n        6: 'TIME SPENT PLAYING (min)',\r\n        7: 'FREQUENCY',\r\n        8: 'RELATIVE FREQUENCY (%)',\r\n        9: '[0, 30]',\r\n        10: '<30, 60]',\r\n        11: '<60, 90]',\r\n        12: '<90, 120]',\r\n        13: '<120, 150]',\r\n        14: '<150, 180]',\r\n        15: '<180, 210]',\r\n        16: '<210, 240]',\r\n        17: '<240, 270]',\r\n        18: 'total',\r\n        19: '5',\r\n        20: '3',\r\n        21: '7',\r\n        22: '2',\r\n        23: '0',\r\n        24: '1',\r\n        25: '24',\r\n        26: '20.8',\r\n        27: '12.5',\r\n        28: '29.2',\r\n        29: '8.3',\r\n        30: '0',\r\n        31: '4.2',\r\n        32: 'Three children, or 12.5%, played computer games for more than three hours.',\r\n        33: 'Sixteen children, or 66.7%, played computer games for less than two hours. This piece of data cannot be derived only from the data grouped in this manner. We have to use the table with ungrouped data from the previous example.'\r\n      },\r\n      'stupicasti-dijagram-i-histogram': {\r\n        title: 'Bar graph and histogram',\r\n        1: '<strong>Bar graph </strong> is used to present the frequencies or relative frequencies of the selected variable categories. It consists of bars assigned to categories with lengths proportional to the frequency or relative frequency of categories.',\r\n        2: '<strong>Histogram </strong> is used to present numerical data. Before creating a histogram, it is necessary to group data into intervals and create a frequency table of the grouped data.  A histogram is drawn in a coordinate system by placing bars above the corresponding intervals. The bar height is proportionate to the interval frequency.',\r\n        3: '<strong>Example 1.3.1.</strong>',\r\n        4: 'The class master of a particular class is monitoring how much time his students spend playing computer games. For that purpose, he asked the students to keep records of the aforementioned and he recorded data on the amount of time they spent playing computer games on Sunday in a table. He added data on the sex of students and the grade they got in the last Mathematics exam. Data are presented in the following table.',\r\n        5: 'STUDENT<br>NUMBER',\r\n        6: 'TIME<br>SPENT PLAYING',\r\n        7: 'SEX',\r\n        8: 'GRADE',\r\n        9: 'f',\r\n        10: 'good',\r\n        11: 'm',\r\n        12: 'good',\r\n        13: 'f',\r\n        14: 'very good',\r\n        15: 'm',\r\n        16: 'good',\r\n        17: 'm',\r\n        18: 'very good',\r\n        19: 'm',\r\n        20: 'insufficient',\r\n        21: 'm',\r\n        22: 'good',\r\n        23: 'm',\r\n        24: 'good',\r\n        25: 'f',\r\n        26: 'excellent',\r\n        27: 'm',\r\n        28: 'good',\r\n        29: 'm',\r\n        30: 'very good',\r\n        31: 'f',\r\n        32: 'good',\r\n        33: 'f',\r\n        34: 'sufficient',\r\n        35: 'm',\r\n        36: 'good',\r\n        37: 'm',\r\n        38: 'good',\r\n        39: 'f',\r\n        40: 'very good',\r\n        41: 'f',\r\n        42: 'good',\r\n        43: 'm',\r\n        44: 'sufficient',\r\n        45: 'm',\r\n        46: 'excellent',\r\n        47: 'm',\r\n        48: 'very good',\r\n        49: 'm',\r\n        50: 'very good',\r\n        51: 'f',\r\n        52: 'insufficient',\r\n        53: 'm',\r\n        54: 'very good',\r\n        55: 'f',\r\n        56: 'very good',\r\n        57: 'The following tool can be used to draw bar graphs for the qualitative variables from the previous table. A bar graph of frequencies or relative frequencies can be drawn. Note that the graphs are the same in shape, but the values of the bar heights are different.',\r\n        58: '<strong>Example 1.3.2.</strong>',\r\n        59: 'The following tool can be used to draw a histogram for the variable <i>time spent playing</i> from the previous example. Select the minimum and the maximum value and the number of intervals to which the set will be divided for the display of histogram.'\r\n\r\n      },\r\n      'stupcasti-dijagram-i-histogram-primjer': {\r\n        1: 'UNIQUE REPETITIONS',\r\n        2: 'FREQUENCY',\r\n        3: 'RELATIVE FREQUENCY (%)',\r\n        4: 'Frequency bar chart',\r\n        5: 'Person frequency',\r\n        6: 'Women',\r\n        7: 'Men',\r\n        8: 'Relative frequency bar chart',\r\n        9: 'Relative person frequency',\r\n        10: 'The minimum and maximum recorded value of game time: ',\r\n        11: 'The lower limit value for the histogram: ',\r\n        12: 'Start of the array',\r\n        13: 'The upper limit value for the histogram: ',\r\n        14: 'End of the array',\r\n        15: 'Enter the number of segments to which you want to split a string:',\r\n        16: 'Number of segments',\r\n        17: 'Create table',\r\n        18: 'TIME SPENT PLAYING (min)',\r\n        19: 'FREQUENCY',\r\n        20: 'RELATIVE FREQUENCY (%)',\r\n        21: 'Frequency histogram',\r\n        22: 'Relative frequency histogram',\r\n        23: 'Frequency bar chart',\r\n        24: 'Grade frequency',\r\n        25: 'insufficient',\r\n        26: 'sufficient',\r\n        27: 'good',\r\n        28: 'very good',\r\n        29: 'excellent',\r\n        30: 'Bar chart of relative frequencies',\r\n        31: 'Grade relative frequency',\r\n        32: 'Inserted values must be numbers',\r\n        33: 'total',\r\n        34: 'To begin, select the column within the gender or grade data',\r\n        35: 'To begin, select the time played column.',\r\n        36: 'Game time frequency',\r\n        37: 'Game time relative frequency',\r\n        38: 'Empty input of any variable is not viable.',\r\n        39: 'Selected array can not be divided into the inserted number of subsets.'\r\n      },\r\n      'stupicasti-dijagram-i-histogram-zadatak': {\r\n        title: 'Bar graph and histogram',\r\n        1: '<strong>Task 1.3.1.</strong>',\r\n        2: 'The table below shows the following data on surveyed respondents: the <i>number of examinations</i> variable shows the total number of examinations, the <i>supplementary health insurance</i> variable indicates whether the insured person has a supplementary health insurance or not (1 – yes; 0 – no) and the <i>price</i> variable contains the price of the most expensive medical examination of the respondent (expressed in kuna)',\r\n        3: 'NUMBER OF <br> EXAMINATIONS',\r\n        4: 'SUPPLEMENTARY <br> HEALTH INSURANCE',\r\n        5: 'PRICE',\r\n        6: 'Which variable is appropriate for presentation by a bar graph? Select that variable to see the presentation of data by a bar graph.',\r\n        7: 'Select the <i>price</i> variable to open the data grouping tool and enter the required parameters to see the corresponding frequency and relative frequency table and histogram, as well as to determine the percentage in which the most expensive medical examination cost more than 200 kuna and in which percentage it cost more than 150 kuna.',\r\n        8: '<strong>Solution</strong>',\r\n        9: 'The most expensive medical examination cost more than 200 kuna in 30% of cases, and more than 150 kuna in 67.5% of cases.'\r\n      },\r\n      'stupcasti-dijagram-i-histogram-zadatak-interakcija': {\r\n        1: 'NUMBER OF EXAMINATIONS',\r\n        2: 'SUPPLEMENTARY HEALTH INSURANCE',\r\n        3: 'PRICE',\r\n        4: 'Specified arrays',\r\n        5: 'Array elements frequency',\r\n        6: 'Array relative frequency',\r\n        7: 'Minimum and maximum of',\r\n        8: 'The lower limit value for the histogram: ',\r\n        9: 'Start of the array',\r\n        10: 'The upper limit value for the histogram: ',\r\n        11: 'End of the array',\r\n        12: 'Enter the number of segments to which you want to split a string:',\r\n        13: 'Number of segments',\r\n        14: 'Create table',\r\n        15: 'Frequencies bar chart of ',\r\n        16: 'Frequency of',\r\n        17: 'Relative frequency of',\r\n        18: ' examination number',\r\n        19: ' examination price',\r\n        20: ' additional health insurance',\r\n        21: 'Starting number must be smaller than the ending number',\r\n        22: 'Ending array number must be in the selected array',\r\n        23: 'Starting array number must be in the selected array',\r\n        24: 'Relative frequency bar chart of',\r\n        25: 'Ending array number must be larger than the starting number'\r\n      },\r\n      'prosjek': {\r\n        title: 'Mean',\r\n        1: '<strong>Arithmetic mean </strong> or <strong>average</strong> of data 𝑥<sub>1</sub> , 𝑥<sub>2</sub> , … , 𝑥<sub>𝑛</sub>  is the sum of all data divided by the total number of data.',\r\n        2: 'Mean is a measure of central tendency of a numerical data set.',\r\n        3: '<strong>Sensitivity of the mean to outliers</strong>',\r\n        4: 'Outliers are data whose value is much bigger or much smaller than the value of other data. If data are added a value that deviates significantly from the mean of existing values, the new mean will change greatly.',\r\n        5: '<strong>Example 1.4.1.</strong>',\r\n        6: 'TIME SPENT <br> PLAYING (min)',\r\n        7: 'GENDER',\r\n        8: 'If number 4 is added to the existing set, the mean will amount to 4.181.',\r\n        9: 'If number 50 is added to the existing set, the mean will amount to 8.36.',\r\n        10: 'Select one number and add it to the existing set. Observe how the mean changes.',\r\n        11: 'm',\r\n        12: 'good',\r\n        13: 'f',\r\n        14: 'very good',\r\n        15: 'm',\r\n        16: 'good',\r\n        17: 'm',\r\n        18: 'very good',\r\n        19: 'm',\r\n        20: 'insufficient',\r\n        21: 'm',\r\n        22: 'good',\r\n        23: 'm',\r\n        24: 'good',\r\n        25: 'f',\r\n        26: 'excellent',\r\n        27: 'm',\r\n        28: 'good',\r\n        29: 'm',\r\n        30: 'very good',\r\n        31: 'f',\r\n        32: 'good',\r\n        33: 'f',\r\n        34: 'sufficient',\r\n        35: 'm',\r\n        36: 'good',\r\n        37: 'm',\r\n        38: 'good',\r\n        39: 'f',\r\n        40: 'very good',\r\n        41: 'f',\r\n        42: 'good',\r\n        43: 'm',\r\n        44: 'sufficient',\r\n        45: 'm',\r\n        46: 'excellent',\r\n        47: 'm',\r\n        48: 'very good',\r\n        49: 'm',\r\n        50: 'very good',\r\n        51: 'f',\r\n        52: 'insufficient',\r\n        53: 'm',\r\n        54: 'very good',\r\n        55: 'f',\r\n        56: 'very good',\r\n        57: 'STUDENT <br> NUMBER',\r\n        58: 'GRADE',\r\n        59: 'f',\r\n        60: 'good',\r\n        61: 'The average time students spent playing games on Sunday amounts to 89.96. Add one item and observe how the average and histogram change.',\r\n        62: '<strong>Example 1.4.2.</strong>',\r\n        63: 'The class master of a particular class is monitoring how much time his students spend playing computer games. For that purpose, he asked the students to keep records of the aforementioned and he recorded data on the amount of time they spent playing computer games on Sunday in a table. He added data on the sex of students and the grade they got in the last Mathematics exam. Data are presented in the following table.',\r\n        64: 'The mean of the data set 3, 5, 7, 2, 1, 7, 4, 3, 5, 5 amounts to',\r\n\t65: 'For starters, choose variable time spent playing.'\r\n      },\r\n      'prosjek-tablica': {\r\n        1: '1',\r\n        2: '2',\r\n        3: '3',\r\n        4: '4',\r\n        5: '5',\r\n        6: '6',\r\n        7: '7',\r\n        8: '8',\r\n        9: '9',\r\n        10: '10',\r\n        11: '11',\r\n        12: '12',\r\n        13: '13',\r\n        14: '14',\r\n        15: '15',\r\n        16: '16',\r\n        17: '17',\r\n        18: '18',\r\n        19: '19',\r\n        20: '20',\r\n        21: '21',\r\n        22: '22',\r\n        23: '23',\r\n        24: '24'\r\n      },\r\n      'prosjek-interakcija': {\r\n        1: 'Initial series of numbers: ',\r\n        2: 'Insert a new array element: ',\r\n        3: 'Insert a number',\r\n        4: 'Create graph',\r\n        5: 'Mean of the default array: ',\r\n        6: 'Mean of the array with a new element: ',\r\n        7: 'Initial distribution of the series and average',\r\n        8: 'Added element and new average',\r\n        9: 'Sorted time list:',\r\n        10: 'Time spent playing',\r\n        11: 'Array elements frequency',\r\n        12: 'Array relative frequency',\r\n        13: 'Frequency chart',\r\n        14: 'New array element must be a number',\r\n        15: 'New array element value is needed.',\r\n      },\r\n      'prosjek-zadatak': {\r\n        title: 'Mean',\r\n        1: '<strong>Task 1.4.1.</strong>',\r\n        2: 'Analysing the prices of food products, a market analyst noticed that the same products do not have the same price in different shopping malls. After observing eleven shopping malls, he recorded the prices of the product with the largest differences in the prices.',\r\n        3: 'SHOP <br> NUMBER',\r\n        4: 'PRICE',\r\n        5: 'The following tool can be used to calculate the average price of the product for the set of selected shopping malls. How much will the average decrease if we exclude the first one from the set of selected shopping malls, and how much if we exclude the eleventh one?',\r\n        6: '<strong>Task 1.4.2.</strong>',\r\n        7: 'The following two data sets are given:',\r\n        8: '0, 1, 2, 3, −1, −2, −3, 0.5, 0.7, 0.25, −1, −0.45',\r\n        9: '−100, 100, 150, −75, −250, 200, −25',\r\n        10: 'Calculate the mean of each data set. How are these sets similar? Does the mean express sufficient information on the data set?',\r\n        11: '<strong>Solution</strong>',\r\n        12: 'The average price for all shops is 52.88. If we exclude the first shopping mall, the average price will amount to 53.62, and if we exclude the eleventh one, the average price will amount to 48.67.',\r\n        13: 'The mean is 0 in both cases. The sets have the same mean although they differ significantly. Therefore, the mean does not give sufficient information on the data set.',\r\n        14: 'Select the prices to calculate the average by clicking on a particular price.',\r\n        15: 'By clicking on each price it enters the average price calculation.'\r\n\r\n      },\r\n      'prosjek-zadatak-interakcija': {\r\n        1: 'SHOP NUMBER',\r\n        2: 'PRICE',\r\n        3: 'Average price of all stores: ',\r\n        4: 'Average price of chosen stores: '\r\n      },\r\n      medijan: {\r\n        title: 'Median and mode',\r\n        1: '<strong>Median </strong> is a measure of central tendency of numerical data.',\r\n        2: 'It is the number that breaks down a sorted data set into two parts in such a manner that:',\r\n        3: 'each part contains the same number of data',\r\n        4: 'the data from the first part are not bigger than the data from the second part',\r\n        5: 'We thus get a number that is bigger than or equal to at least 50% of data, but at the same time, smaller than or equal to at least 50% of data.',\r\n        6: 'To obtain the <strong>median of a data</strong> set, data should first be sorted by size. ',\r\n        7: '<strong>The following is the median calculation algorithm:</strong>',\r\n        8: 'The following data set is given: 𝑥<sub>1</sub> , 𝑥<sub>2</sub> , … , 𝑥<sub>𝑛</sub>.',\r\n        9: 'Data are sorted by size, from the smallest to the biggest.',\r\n        10: 'If <div class=\"fraction\" top=\"𝑛\" bottom=\"2\"></div> is not a natural number, the item of data on the first position larger than <div class=\"fraction\" top=\"𝑛\" bottom=\"2\"></div> is the median.',\r\n        11: 'If <div class=\"fraction\" top=\"𝑛\" bottom=\"2\"></div> is a natural number, the median is the mean of data on the positions <div class=\"fraction\" top=\"𝑛\" bottom=\"2\"></div> and <div class=\"fraction\" top=\"𝑛\" bottom=\"2\"></div> + 1. ',\r\n        12: 'Compared to the mean, the median is less sensitive to <strong>outliers</strong>. Outliers are data whose value is much bigger or much smaller than the value of other data.',\r\n        13: '<strong>Example 1.5.1.</strong>',\r\n        14: 'For the following data:',\r\n        16: 'To calculate the median, we need to sort this set from the smallest to the largest number:',\r\n        18: 'There are 11 data in this set (odd number). Median is the item of data in the middle (sixth) position in the sorted data set, i.e. median is 5.',\r\n        19: '<strong>Example 1.5.2.</strong>',\r\n        20: 'The following data are given:',\r\n        22: 'To calculate the median, we need to sort this set from the smallest to the largest number:',\r\n        24: 'There are 10 data in this set (even number). Since <div class=\"fraction\" top=\"10\" bottom=\"2\"></div> = 5, the median is the mean of the values on the fifth and the sixth position in the ordered set, that is, <div class=\"fraction\" top=\"(4 + 5)\" bottom=\"2\"></div> = 4.5.',\r\n        25: '<strong>Example 1.5.3.</strong>',\r\n        27: 'The mean is 4.2, and the median 4.5.',\r\n        28: 'If number 50 is added to the existing set, the mean will amount to 8.36 and the median to 5.',\r\n        29: 'Select a number, add it to this set and observe how the median and the mean change.',\r\n\t\t30: '<strong>Mode</strong> is also a measure of central tendency suitable for all types of variables. It is the value of the data that occurs most often in the data set. If each value of the data set appears only once, then there is no mode. If several values appear the same many times (and the most often), then a data set has several modes - these are all the values that appear most often.',\r\n\t\t31: 'The most frequent number in this data set is 5 (it occurs 4 times) so mode is 5.'\r\n      },\r\n      'median-interaction': {\r\n        1: 'Initial median: ',\r\n        2: 'Initial number array: ',\r\n        3: 'Insert a new array number: ',\r\n        4: 'Insert a number',\r\n        5: 'Calculate and draw',\r\n        6: 'Default array average',\r\n        7: 'Array average with a new number',\r\n        8: 'Initial distribution of array elements',\r\n        9: 'Average',\r\n        10: 'Median',\r\n        11: 'New array distribution',\r\n        12: 'New average',\r\n        13: 'New median',\r\n        14: 'Sort the array',\r\n        15: 'Calculate median',\r\n        16: 'New array element must be a number',\r\n        17: 'New array element value is needed',\r\n        18: 'Result median:',\r\n      },\r\n      'medijan-zadatak': {\r\n        title: 'Median',\r\n        1: '<strong>Task 1.5.1.</strong>',\r\n        2: 'The class master of a particular class is monitoring how much time his students spend playing computer games. For that purpose, he asked the students to keep records of the aforementioned and he recorded data on the amount of time they spent playing computer games on Sunday in a table. He added data on the sex of students and the grade they got in the last Mathematics exam. Data are presented in the following table.',\r\n        3: 'Can we say that at least 50% of students spent less time playing games than the average time of playing in the class?',\r\n        4: '<strong>Solution</solution>',\r\n        5: 'The average is 89.96, while the median is 75 and is lower than the average. Therefore, the answer to the above question is affirmative.'\r\n      },\r\n      'minimum-maksimum-i-raspon': {\r\n        title: 'Minimum, maximum and range',\r\n        1: 'Let 𝑥<sub>1</sub> , 𝑥<sub>2</sub> , … , 𝑥<sub>𝑛</sub> be given data.',\r\n        2: '<strong>Minimum</strong> is the smallest number in the given data set and is denoted by 𝑥<sub>𝑚𝑖𝑛</sub>.',\r\n        3: '<strong>Maximum</strong> is the largest number in the given data set and is denoted by 𝑥<sub>𝑚𝑎𝑥</sub>.',\r\n        4: '<strong>Range</strong> is the difference between the minimum and the maximum:',\r\n        5: 'formula',\r\n        6: 'Range is a rough measure of dispersion of data.',\r\n        7: '<strong>Example 1.6.1.</strong>',\r\n        8: 'For the following data:',\r\n        9: '3, 5, 7, 2, 1, 7, 4, 3, 5, 5',\r\n        10: 'it is easy to calculate',\r\n        11: '𝑥𝑚𝑖𝑛 = 1',\r\n        12: '𝑥𝑚𝑎𝑥 = 7',\r\n        13: '𝑟𝑎𝑠𝑝𝑜𝑛 = 6',\r\n        14: 'range'\r\n      },\r\n      'minimum-maksimum-i-raspon-interakcija': {\r\n        1: 'Data: ',\r\n        2: 'Sorted array: ',\r\n        3: 'Minimum: ',\r\n        4: 'Maximum: ',\r\n        5: 'Range: ',\r\n        6: 'Sort the array',\r\n        7: 'Calculate min, max and range'\r\n      },\r\n      'minimum-maksimum-i-raspon-zadatak': {\r\n        title: 'Minimum, maximum and range',\r\n        1: '<strong>Task 1.6.1.</strong>',\r\n        2: 'The class master of a particular class is monitoring how much time his students spend playing computer games. For that purpose, he asked the students to keep records of the aforementioned and he recorded data on the amount of time they spent playing computer games on Sunday in a table. He added data on the sex of students and the grade they got in the last Mathematics exam. Data are presented in the following table.',\r\n        3: 'Specify the minimum, the maximum and the range of data of the variable time spent playing.',\r\n        4: '<strong>Solution</strong>',\r\n        5: 'The minimum is 0, the maximum is 244 and the range is 244.'\r\n      },\r\n      'kvartili-i-interkvartilni-raspon': {\r\n        title: 'Quartiles and interquartile range',\r\n        1: '<strong>Interquartile range</strong> is a measure of dispersion of data. It is defined by <strong>quartiles</strong>.',\r\n        2: '<strong>Quartile</strong> is the number that breaks down a sorted data set into two parts in such a manner that:',\r\n        3: 'one part contains a quarter of data and the other part contains three quarters of data',\r\n        4: 'the data from the first part are not bigger than the data from the second part.',\r\n        5: 'There are two quartiles: <strong>the lower quartile</strong>, which will be denoted by 𝑄<sub>1</sub>, and <strong>the upper quartile</strong>, which will be denoted by 𝑄<sub>3</sub>.',\r\n        6: '<strong>Lower quartile</strong> divides the first quarter of a sorted data set from the other three quarters. We thus get a number that is bigger than or equal to at least 25% of data, but at the same time, smaller than or equal to at least 75% of data.',\r\n        7: '<strong>Upper quartile</strong> divides the first three quarters of a sorted data set from the last quarter. We thus get a number that is bigger than or equal to at least 75% of data, but at the same time, smaller than or equal to at least 25% of data.',\r\n        8: 'Note the similarity between the idea of using the quartile and the median.',\r\n        9: 'Min',\r\n        10: 'Q<sub>1</sub>',\r\n        11: 'Median',\r\n        12: 'Q<sub>3</sub>',\r\n        13: 'Max',\r\n        14: 'Sorted <br> data',\r\n        15: 'Position in <br> a sorted set',\r\n        16: '<strong>Interquartile range</strong> is the difference between the upper and the lower quartile:',\r\n        17: 'formula',\r\n        18: '<strong>Example 1.7.1.</strong>',\r\n        19: 'The following set of 18 data is given:',\r\n        20: '5, 2, 3, 2, 5, 2, 4, 5, 1, 7, 6, 1, 4, 6, 7, 4, 7, 4',\r\n        21: 'Position',\r\n        22: 'interquartile',\r\n        23: 'range',\r\n        24: 'so',\r\n        25: 'The following data set is given: x<sub>1</sub>,x<sub>2</sub>,…,x<sub>n</sub>.',\r\n        26: 'Data are sorted by size, from the smallest to the biggest.',\r\n        27: '<strong>Lower quartile<strong>, Q<sub>1</sub>',\r\n        28: 'If <div class=\"fraction\" top=\"𝑛\" bottom=\"4\"></div> is not a natural number, the item of data on the first position larger than <div class=\"fraction\" top=\"𝑛\" bottom=\"4\"></div> is the lower quartile.',\r\n        29: 'If <div class=\"fraction\" top=\"𝑛\" bottom=\"4\"></div> is a natural number, the lower quartile is the mean of data on the positions <div class=\"fraction\" top=\"𝑛\" bottom=\"4\"></div> and <div class=\"fraction\" top=\"𝑛\" bottom=\"4\"></div> + 1.',\r\n        30: '<strong>Upper quartile<strong>, Q<sub>3</sub>',\r\n        31: 'If 3<div class=\"fraction\" top=\"𝑛\" bottom=\"4\"></div> is not a natural number, the item of data on the first position larger than 3<div class=\"fraction\" top=\"𝑛\" bottom=\"4\"></div> is the upper quartile.',\r\n        32: 'If 3<div class=\"fraction\" top=\"𝑛\" bottom=\"4\"></div> is a natural number, the upper quartile is the mean of data on the positions 3<div class=\"fraction\" top=\"𝑛\" bottom=\"4\"></div> and 3<div class=\"fraction\" top=\"𝑛\" bottom=\"4\"></div> + 1.',\r\n        33: 'For those who want to learn more'\r\n      },\r\n      'kvartili-i-interkvartilni-raspon-interakcija': {\r\n        1: 'Default array: ',\r\n        2: 'Create table',\r\n        3: 'Sorted data',\r\n        4: 'Position label',\r\n        5: 'Calculate the quartiles',\r\n        6: ', so Q1 is: ',\r\n        7: ', so Q3 is: ',\r\n        8: 'Interquartile range is: ',\r\n        9: 'Median is: '\r\n      },\r\n      'kvartili-i-interkvartilni-raspon-zadatak': {\r\n        title: 'Quartiles and interquartile range',\r\n        1: '<strong>Task 1.7.1.</strong>',\r\n        2: 'The class master of a particular class is monitoring how much time his students spend playing computer games. For that purpose, he asked the students to keep records of the aforementioned and he recorded data on the amount of time they spent playing computer games on Sunday in a table. He added data on the sex of students and the grade they got in the last Mathematics exam. Data are presented in the following table.',\r\n        3: 'Calculate the lower and the upper quartile as well as the interquartile range of data of the variable <i>time spent playing</i> and answer the following questions:',\r\n        4: 'Is it true that more than 75% of children played games for less than two hours?',\r\n        5: 'Is it true that less than 25% of children played games for more than two hours?',\r\n        6: 'Is it true that more than 25% of children played games for less than half an hour?',\r\n        7: '<strong>Solution</strong>',\r\n        8: 'Answers: ',\r\n        9: 'The upper quartile is 129.5 minutes. Therefore, the statement is not true.',\r\n        10: 'The upper quartile is 129.5 minutes. Therefore, the statement is true.',\r\n        11: 'The lower quartile is 49 minutes. Therefore, the statement is not true.'\r\n      },\r\n      'varijanca-i-standardna-devijacija': {\r\n        title: 'Variance and standard deviation',\r\n        1: 'Variance and standard deviation are the measures of dispersion of data, which characterise the spread of data around the mean.',\r\n        2: '<strong>Variance</strong> is the average squared deviation of a set of data from their mean. If <i>n</i> is the number of data, their variance is <i>s</i><sup>2</sup>.',\r\n        3: 'For the set of data 𝑥<sub>1</sub>, 𝑥<sub>2</sub>, … ,𝑥<sub>𝑛</sub>,the variance is given as follows:',\r\n        4: 'formula',\r\n        5: '<strong>Standard deviation</strong> is the square root of the variance. Standard deviation of the sample is denoted by <i>s</i>.',\r\n        6: 'formula',\r\n        7: '<strong>Example 1.8.1.</strong>',\r\n        8: 'For the following data:',\r\n        9: '3, 5, 7, 2, 1, 7, 4, 3, 5, 5',\r\n        10: 'the mean is 4,2. The calculation of the variance can be illustrated by the following table.',\r\n        11: 'DATA',\r\n        12: 'DEVIATION FROM <br> THE MEAN',\r\n        13: 'SQUARED DEVIATION <br> FROM THE MEAN',\r\n        14: 'total',\r\n        15: 'The variance is <div class=\"fraction\" top=\"35.6\" bottom=\"9\"></div> = 3.96, and the standard deviation is 1.99.',\r\n\t\t16: 'The variance of the population with N units is denoted as σ<sup>2</sup>. For a population with N units, the variance is given as follows:',\r\n\t\t17: 'The notation for the standard deviation of the population is σ.'\r\n      },\r\n      'varijanca-i-standardna-devijacija-zadatak': {\r\n        title: 'Variance and standard deviation',\r\n        1: '<strong>Task 1.8.1.</strong>',\r\n        2: 'The following two data sets are given:',\r\n        3: '0, 1, 2, 3, -1, -2, -3, 0.5, 0.7, 0.25, -1, -0.45',\r\n        4: '-100, 100, 150, -75, -250, 200, -25',\r\n        5: 'Calculate the mean and the standard deviation of each data set.',\r\n        6: 'How are these sets similar? Does the mean express sufficient information on the data set? Do you consider standard deviation an important information when reporting on data?',\r\n        7: '<strong>Task 1.8.2.</strong>',\r\n        8: 'The class master of a particular class is monitoring how much time his students spend playing computer games. For that purpose, he asked the students to keep records of the aforementioned and he recorded data on the amount of time they spent playing computer games on Sunday in a table. He added data on the sex of students and the grade they got in the last Mathematics exam. Data are presented in the following table.',\r\n        9: 'Use a spreadsheet to calculate the variance and the standard deviation for the variable <i>time spent playing</i>.',\r\n        10: '<strong>Solution task 1.8.1.</strong>',\r\n        11: 'The mean of the first set is 0 and the standard deviation is 1.65.',\r\n        12: 'The mean of the second set is 0 and the standard deviation is 158.77.',\r\n        13: 'The means are the same, while the differences are present in the standard deviation.',\r\n        14: 'The mean is 89.96.',\r\n        15: 'TIME SPENT PLAYING (min)',\r\n        16: 'DEVIATION FROM THE MEAN',\r\n        17: 'SQUARED DEVIATION FROM THE MEAN',\r\n        18: '47',\r\n        19: '177',\r\n        20: '124',\r\n        21: '135',\r\n        22: '69',\r\n        23: '88',\r\n        24: '0',\r\n        25: '69',\r\n        26: '120',\r\n        27: '63',\r\n        28: '57',\r\n        29: '79',\r\n        30: '244',\r\n        31: '99',\r\n        32: '76',\r\n        33: '166',\r\n        34: '193',\r\n        35: '19',\r\n        36: '74',\r\n        37: '51',\r\n        38: '20',\r\n        39: '189',\r\n        40: '<strong>total</strong>',\r\n        41: '-42.96',\r\n        42: '87.04',\r\n        43: '34.04',\r\n        44: '45.04',\r\n        45: '-20.96',\r\n        46: '-1.96',\r\n        47: '-89.96',\r\n        48: '-20.96',\r\n        49: '30.04',\r\n        50: '-89.96',\r\n        51: '-26.96',\r\n        52: '-32.96',\r\n        53: '-10.96',\r\n        54: '154.04',\r\n        55: '-89.96',\r\n        56: '9.04',\r\n        57: '-13.96',\r\n        58: '76.04',\r\n        59: '103.04',\r\n        60: '-70.96',\r\n        61: '-15.96',\r\n        62: '-38.96',\r\n        63: '-69.96',\r\n        64: '99.04',\r\n        65: '1845.56',\r\n        66: '1845.56',\r\n        67: '1158.72',\r\n        68: '2028.60',\r\n        69: '439.32',\r\n        70: '3.84',\r\n        71: '8092.80',\r\n        72: '439.32',\r\n        73: '902.40',\r\n        74: '8092.80',\r\n        75: '726.84',\r\n        76: '1086.36',\r\n        77: '120.12',\r\n        78: '23728.32',\r\n        79: '8092.80',\r\n        80: '81.72',\r\n        81: '194.88',\r\n        82: '5782.08',\r\n        83: '10617.24',\r\n        84: '5035.32',\r\n        85: '254.72',\r\n        86: '1517.88',\r\n        87: '4894.40',\r\n        88: '9808.92',\r\n        89: '102520.96',\r\n        90: 'The variance is 4457.43 and the standard deviation is 66.76.',\r\n        91: '<strong>Solution task 1.8.2.</strong>',\r\n      },\r\n      'kutijasti-dijagram': {\r\n        title: 'Box plot',\r\n        1: '<strong>Box plot</strong> (or box-and-whisker plot) is used to present the relation between the minimum, the maximum, the lower and the upper quartile and the median of data.',\r\n        2: 'If data contain outliers (data whose values are much greater or much smaller the values of other data), they are also indicated in this type of graph.',\r\n        3: '<strong>Example 1.9.1.</strong>',\r\n        4: 'The following set of 20 data is given:',\r\n        5: '1, 0, 9, 1.1, 1.1, 0.8, 1.1, 1.2, 0.7, 1, 0.6, 0.9, 1.3, 1.1, 0.7, 1, 1.1, 1, 1.3',\r\n        6: 'The figure presents data in a box plot and the values of the minimum, the maximum, the lower and the upper quartile and the median are indicated.',\r\n        7: 'Start interaction to see the box plot we get when we add number 2 to the set . Note that number 2 is the outlier and that the maximum of data without that value is displayed (1.3).',\r\n        8: '<strong>Example 1.9.2.</strong>',\r\n      },\r\n      'kutijasti-dijagram-interakcija': {\r\n        1: 'Sort',\r\n        2: 'Unsorted:',\r\n        3: 'Sorted:',\r\n        4: 'correct',\r\n        5: 'median',\r\n        6: 'incorrect'\r\n      },\r\n      'kutijasti-dijagram-zadatak': {\r\n        title: 'Box plot',\r\n        1: '<strong>Task 1.9.2.</strong>',\r\n        2: 'The figure below shows three box plots. Can we identify which statement applies to which plot:',\r\n        3: 'At least 25% of data are equal to the minimum.',\r\n        4: 'At least 75% of data are smaller than or equal to the median.',\r\n        5: 'At least 25% of data are equal to the maximum.',\r\n        6: 'The median and the upper quartile are equal.',\r\n        7: '<strong>Solution</strong>',\r\n        8: 'Statement:',\r\n        13: 'applies to plot 1',\r\n        14: 'applies to plot 3',\r\n        15: 'applies to plot 2',\r\n        16: 'applies to plot 3.'\r\n      },\r\n      'dijagram-rasprsenosti-i-standardna-devijacija': {\r\n        title: 'Scatter plot ',\r\n        1: 'If data on two numerical values are collected for particular individuals, it is useful to present the pairs of data in a <strong>scatter plot</strong>. Such a plot is suitable for detecting the correlation between variables.',\r\n        2: '<strong>A scatter plot</strong> consists of pairs of data marked by points in a coordinate system. ',\r\n        3: '<strong>Example 1.10.1.</strong>',\r\n        4: 'The following pairs of data are given:',\r\n        5: 'The following figure shows their scatter plot.',\r\n        6: 'NEXT CHAPTER:',\r\n        7: '2. Basic concepts of probability',\r\n        8: 'Clicking the \"Even number has fallen\" button will display a new set of all possible outcomes and a new set of favorable outcomes with additional information that the number of dice would turn to the even number.'\r\n      },\r\n      'dijagram-rasprsenosti-i-standardna-devijacija-zadatak': {\r\n        title: 'Scatter plot',\r\n        1: '<strong>Task 1.10.1.</strong>',\r\n        2: 'The class master of a particular class is monitoring how much time his students spend playing computer games. For that purpose, he asked the students to keep records of the aforementioned and he recorded data on the amount of time they spent playing computer games on Sunday and on Monday in a table. Data are presented in the following table.',\r\n        3: 'The following figure shows the scatter plot of the variable time spent playing games on Sunday and on Monday. Do you notice any correlation?',\r\n        4: '<strong>Solution</strong>',\r\n        5: 'There is a correlation in terms of growth. Based on this plot, it can be concluded that those children who spend a lot of time playing games on Sundays also spend a lot of time playing games on Mondays.'\r\n      }\r\n    },\r\n    osnove_vjerojatnosti: {\r\n      chapterNumber: '&mdash; Chapter 2 &mdash;',\r\n      title: 'Basic concepts of probability',\r\n      'vjerojatnost': {\r\n        title: 'Probability',\r\n        1: '<strong>Probability of an event</strong> is a number that expresses the degree of belief in the occurrence of that event.',\r\n        2: '<strong>Event</strong> is a subset of the set of all possible outcomes of an experiment.',\r\n        3: '<strong>Set of all possible outcomes</strong> of an experiment is a unit denoted by Ω.',\r\n        4: '<strong>Example 2.1.1.</strong>',\r\n        5: 'When a coin is tossed, it can land either tails up (denoted by 𝑝) or heads up (denoted by 𝑔). It follows that the set of all possible outcomes of tossing a coin is a two-member set',\r\n        6: 'Ω = {𝑝, 𝑔}',\r\n        7: 'An experiment consists of tossing a coin twice in a row. Every time, it lands either on 𝑝 or on 𝑔. The outcome of one performance of the subject experiment can be presented by an ordered pair, in which the first element is the outcome of the first toss and the second element is the outcome of the second toss. Therefore, the outcomes of the subject experiment are ordered pairs (𝑝, 𝑝), (𝑝, 𝑔), (𝑔, 𝑝) and (𝑔, 𝑔), while the set of all possible outcomes is a four-member set',\r\n        8: 'Ω = {(𝑝, 𝑝), (𝑝, 𝑔), (𝑔, 𝑝), (𝑔, 𝑔)}',\r\n        9: 'When rolling a die with sides numbered from 1 to 6, any of these numbers may appear as an outcome. It follows that the set of all possible outcomes of one die roll is a six-member set',\r\n        10: 'Ω = {1, 2, 3, 4, 5, 6}.',\r\n        11: 'We know that an element of the set &#937; will occur when performing the experiment. In this context, we say that we are sure that &#937; will happen, and even more often, we say that we are 100% sure that &#937; will happen. We thus express by a number the degree of belief in the occurrence of &#937;.',\r\n        12: 'Event A is part of the set &#937;, so the degree of belief in the occurrence of A is expressed by a percentage lower than or equal to 100%.',\r\n        13: 'Since percentage is a number with denominator 100, the degree of belief in the occurrence of Ω is expressed by number 1, and the degree of belief in the occurrence of event A by a number from the interval [0, 1].',\r\n        14: '<strong>Probability</strong> is defined as function P, which assigns the numbers from the interval [0, 1] to the events, so that the following applies: ',\r\n        15: 'The probability of the set  &#937; is 𝑃(Ω) = 1, ',\r\n        16: 'If events  and  are parts of the set , which do not have the same experiment outcomes, the probability that 𝐴 or 𝐵 will occur (𝐴 ∪ 𝐵) is equal to the sum of their probabilities:',\r\n        17: 'formula',\r\n        18: 'The second requirement also applies to more than two events that do not have the same experiment outcomes.',\r\n        19: '<strong>Example 2.1.2.</strong>',\r\n        20: '<strong>Classical approach to calculating probability</strong>',\r\n        21: 'If an experiment has a finite number of outcomes that are all equally possible, the probability of event  is the quotient of the number of favourable outcomes and the number of all possible outcomes of that experiment.',\r\n        22: 'The number of favourable outcomes is the number of elements of event A and is denoted by k(A), while the number of all possible outcomes is the number of elements of set &#937; and is denoted by k(&#937;).',\r\n        23: 'Therefore, the probability of event A is calculated as follows:',\r\n        24: 'formula',\r\n        25: 'For example, the set of all possible outcomes of tossing a coin is Ω = {𝑝, 𝑔}. If the coin we are tossing is unbiased, there are no grounds to favour one of its sides and therefore, the probability that the coin will land tails up is equal to the probability that it will land heads up:',\r\n        26: 'formula',\r\n        27: '<strong>Example 2.1.3.</strong>',\r\n        28: '<strong>Statistical approach to calculating probability</strong>',\r\n        29: 'The set of all possible outcomes Ω does not have to be finite, nor do all outcomes have to be equally probable. In that case, the classical approach to calculating probability of event 𝐴 ⊆ Ω cannot be applied. One of the methods for calculating the probability of event A is based on independent repeated performance of the experiment.',\r\n        30: 'After each repetition of the experiment, we count how many times event A occurred. That number is referred to as the <strong>frequency of event</strong> A.',\r\n        31: 'In addition to the frequency, after each repetition of the experiment, we calculate the quotient of the frequency of event A and the number of experiment performances. That number is referred to as the <strong>relative frequency of event</strong> A.',\r\n        32: 'If increase in the number of experiment performances results in the grouping of relative frequencies of event  around one number, this number is taken as probability P(A).',\r\n        33: 'For example, by increasing the number of tosses of an unbiased coin, the relative frequencies of the coin landing heads up will group around <div class=\"fraction\" top=\"1\" bottom=\"2\"></div>. If we toss the coin 40 times, the grouping of these relative frequencies could be presented by the following line graph:',\r\n        34: 'However, the coin could be biased. What happens if we toss a coin that is twice as likely to land heads up as tails up? Perform this experiment many times and visualise the probability of the coin landing heads up.',\r\n        35: 'Interaction instructions:',\r\n        36: 'Question num. 1. -  Click \"Calculate probability\" to display the solution.',\r\n        37: 'Question num. 2. and 3. - Select 2 pairs of offered items and then click \"Calculate probability\". In the case of a correct selection, a solution will be displayed.',\r\n        38: 'Question num. 4. - Click \"Calculate probability\" to display the solution.'\r\n      },\r\n      'vjerojatnost-interakcija': {\r\n        1: 'What is the probability of a head flip in the first throw?',\r\n        2: 'Calculate probability',\r\n        3: 'Reset marked events',\r\n        4: 'What is the probability of a head flip in the second throw?',\r\n        5: 'Incorrectly selected events, try again.',\r\n        6: 'What is the probability of a head flip in two throws?',\r\n        7: 'Check the probabilities of the other two-parts of Ω. Also, determine the likelihood of some three-part parts of Ω.',\r\n        8: 'Relative frequencies of the coin landing heads up',\r\n        9: 'Number of coin tosses',\r\n        10: 'Ok'\r\n      },\r\n      'vjerojatnost-interakcija-2': {\r\n        1: 'Throw the coin',\r\n        2: 'Number of throws must be a positive integer greater than 0.',\r\n        3: 'Coin',\r\n        4: 'Number of throws',\r\n        5: 'Head count',\r\n        6: 'Tail count',\r\n        7: 'Regular coin',\r\n        8: 'The head falls twice as likely as the tail',\r\n        9: 'The tail falls twice as likely as the head',\r\n      },\r\n      'vjerojatnost-zadatak': {\r\n        title: 'Probablity',\r\n        1: '<strong>Task 2.1.1.</strong>',\r\n        2: 'Two brothers, both gamblers, are completely different – one of them is honest, while the other one is a cheater.',\r\n        3: 'The honest gambler is playing with an unbiased die. What is the probability that he will get an even number when rolling a die once?',\r\n        4: 'His brother decided to cheat and had a rolling die created on which some numbers are more likely to be rolled than others. Put yourself in his shoes and choose the numbers you would like to favour. Using the interactive tool, apply statistical approach to find out what is the probability of rolling an even number when rolling such a die.',\r\n        5: '<strong>Solution</strong>',\r\n        6: 'The set of all possible outcomes of die rolling is ',\r\n        7: 'The event “an even number rolled” (denoted by A), is the following part of Ω:',\r\n        8: 'Since the die is unbiased, applying the classical approach, it follows that the probability of the honest gambler getting an even number when rolling the die is',\r\n        9: 'In the following table, enter the probability of rolling each number on the die. Bear in mind that, as stated in the text of the task, you assign larger probabilities to even numbers and that the sum of the six probabilities amounts to 1. For example:',\r\n        10: 'Outcome',\r\n        11: 'Probability'\r\n      },\r\n      'vjerojatnost-zadatak-interakcija': {\r\n        1: 'Outcome',\r\n        2: 'Probability',\r\n        3: 'The probability that the even number falls',\r\n        4: 'The probability that the odd number falls',\r\n        5: 'Throw the dice',\r\n        6: 'Dice',\r\n        7: 'Invalid number!',\r\n        8: 'The probabilities were not well chosen (the sum must be 1)',\r\n        9: 'Enter the number of dice throws:',\r\n        10: 'Number of throws',\r\n        11: 'Probability of an even number falling (%)',\r\n        12: 'Calculate probability'\r\n      },\r\n      'uvjetna-vjerojatnost': {\r\n        title: 'Conditional probability',\r\n        1: 'With additional information on the outcome of an experiment, the probability of an event may differ from the probability of the same event without the subject information.',\r\n        2: 'Let A be the event whose probability we are interested in. In other words, A is a set of favourable outcomes of an experiment. If we know that event B, for which P (B) > 0, occurred when performing the experiment, the set of favourable outcomes changes. More precisely, the set of favourable outcomes is not the whole A anymore, but A ∩ B.',\r\n        3: '<strong>Example 2.2.1.</strong>',\r\n        4: 'In a game of chance, the goal is to get a prime number by rolling a die.',\r\n        5: 'The set of all possible outcomes of die rolling is &Omega; = {1, 2, 3, 4, 5, 6}, and the set of favourable outcomes is the set of all prime numbers from &Omega;, that is, the three-member set {2, 3, 5}.',\r\n        6: 'However, with the additional information that an even number was rolled, the set of favourable outcomes changes.',\r\n        7: 'If it is known that event A was realised such that P (B > 0), the probability of the realisation of event A is referred to as the <strong>conditional probability of event</strong> A given B. It is denoted by P(A | B) and defined as follows:',\r\n        8: '<strong>Example 2.2.2.</strong>',\r\n        9: 'In an experiment in which an unbiased coin is tossed two times in a row, the set of all possible outcomes is &omega; = (p,p), (p,g), (g,p), (g,g) and all outcomes are equally probable.',\r\n        10: 'The probability of the coin landing on the same side in both tosses, whereby this event is denoted by A = (p,p), (g,g), is calculated according to the classical approach and it amounts to <div class=\"fraction\" top=\"1\" bottom=\"2\"></div>.',\r\n        11: 'However, if it is known that the outcome of the first or the second toss is p, we know that the following event was realised:',\r\n        12: 'B = {(𝑝, 𝑝), (𝑝, 𝑔), (𝑔, 𝑝)}, 𝑃(𝐵) = 3/4',\r\n        13: 'With this additional piece of information, the probability of the coin landing on the same side in both tosses, that is, the probability of event A given B is',\r\n        14: '1 𝑃(𝐴 ∩ 𝐵) 4 1 𝑃(𝐴|𝐵) = = = . 𝑃(𝐵) 3 3 4',\r\n        15: 'Note also that, given B, the probability of outcome (g,g) is 0.'\r\n      },\r\n      'uvjetna-vjerojatnost-interakcija': {\r\n        1: '(Set of all outcomes):',\r\n        2: 'A set of favorable outcomes:',\r\n        3: 'Even number has fallen',\r\n        4: 'Realized event',\r\n        5: 'A new set of favorable outcomes',\r\n        6: '3. Random Variable'\r\n      },\r\n      'uvjetna-vjerojatnost-zadatak': {\r\n        title: 'Conditional probability',\r\n        1: '<strong>Task 2.2.1.</strong>',\r\n        2: 'Using the interactive tool, calculate the probability of rolling a six when rolling a die that is not necessarily unbiased, with additional information that arbitrarily selected event B was realised. Select the probabilities of the outcomes of die rolling and the realised event B by yourself.',\r\n        3: 'The sum of all probabilities for each throw must be equal to 1.'\r\n      },\r\n      'uvjetna-vjerojatnost-zadatak-interakcija': {\r\n        1: 'Outcome',\r\n        2: 'Probablity',\r\n        3: 'Insert a number',\r\n        4: 'Probability of a six realization with a conditional on B',\r\n        5: 'The sum of all elements must be equal to 1. Repeat the entry!',\r\n        6: 'The inserted numbers must be positive.',\r\n        7: 'The input of text is not allowed',\r\n        8: 'Event elements of B are selected by clicking on the desired outcomes in the first row of the table. You should also enter the probabilities for all event outcomes.',\r\n        9: 'All input fields are required',\r\n        10: 'It is neccesary to select at least one outcome from the first table row.'\r\n      }\r\n    },\r\n    statisticko_zakljucivanje: {\r\n      chapterNumber: '&mdash; Chapter 5 &mdash;',\r\n      title: 'Statistical inference',\r\n      'populacija_i_uzorak': {\r\n        title: 'Population and sample',\r\n        1: 'In statistical inference, the data we manage are considered the values recorded on one part of the <stron>population</strong> called the <strong>sample</strong>. A typical example are pre-election polls, where a part of the voting-eligible population is selected, and based on their responses, a conclusion on the outcome of the election is trying to be reached.',\r\n        2: 'By collecting <a href=\"../opisivanje-podataka/podaci\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">data</a> on a sample regarding a characteristic of a population – variable 𝑋 – a set of 𝑥<sub>1</sub>, 𝑥<sub>2</sub>, ... , 𝑥<sub>𝑛</sub> numbers is obtained, where n is the <strong>sample size</strong>.',\r\n        3: 'Statistical conclusions derived from a sample have some degree of uncertainty for the following reasons:',\r\n        4: 'Data are based on incomplete data (for example, pre-election polls are carried out only on a part of the population with the aim of predicting the outcome of the election).',\r\n        5: 'Data have a characteristic of randomness (for example, the outcome of tossing a coin cannot be predicted).',\r\n        6: 'Therefore, the sample obtained is perceived as the realisation of 𝑛 <a href=\"../slucajna-varijabla/slucajna-varijabla\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">random variables</a> 𝑋<sub>1</sub>, 𝑋<sub>2</sub>, ... , 𝑋<sub>𝑛</sub>, called the <strong>random sample</strong>.',\r\n        7: 'A random sample is a <strong>simple random sample</strong> if the following applies:',\r\n        8: '𝑋<sub>1</sub>, 𝑋<sub>2</sub>, ... , 𝑋<sub>𝑛</sub> are all equally distributed as random variable (population characteristic),',\r\n        9: '𝑋<sub>1</sub>, 𝑋<sub>2</sub>, ... , 𝑋<sub>𝑛</sub> are mutually independent.',\r\n        10: 'Data collection is often designed so that these two assumptions are met. For example, a pre-election poll cannot be carried out only among pensioners, but the sample has to be <strong>representative</strong> so that the typical characteristics of the population relevant to the poll are represented.',\r\n        11: 'Therefore, a sample consists of realisations of independent random variables equally distributed as a characteristic in the entire population 𝑋. It is thus said that  𝑥<sub>1</sub>, 𝑥<sub>2</sub>, ... , 𝑥<sub>𝑛</sub> is a <strong>sample from variable</strong> 𝑋 or <strong>distributions of variable</strong> 𝑋.',\r\n        12: 'Based on the values from the sample, the conclusions on the distribution of <a href=\"../slucajna-varijabla/slucajna-varijabla\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">random variable</a> are made 𝑋. The distribution of variable 𝑋 may be completely unknown or only its type may be known, while its parameters may be unknown (for example, 𝑋 has a <a href=\"../distribucije/normalna-distribucija\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">normal distribution</a> with unknown expectation and variance).',\r\n        13: '<strong>Example 5.1.1.</strong>',\r\n        14: 'In 2014, the Croatian Bureau of Statistics conducted the survey on household consumption expenditures as well as on socioeconomic and demographic characteristics of households. A total of 2029 randomly selected households were surveyed and, inter alia, the following data were recorded:',\r\n        15: 'values of total annual expenditures, ',\r\n        16: 'type of a housing unit (house or dwelling), ',\r\n        17: 'number of household members.',\r\n        18: 'The population in this survey consists of all households in the Republic of Croatia and the sample consists of the surveyed households. The sample size is 2029. There are three variables:',\r\n        19: 'Data on total annual expenditures are characterised by a continuous distribution. Since there is no valid reason to make an assumption about the type of distribution, it is considered completely unknown.',\r\n        20: 'The variable representing the type of a housing unit can have only two outcomes. If the outcomes are denoted by 0 (house) and 1 (dwelling), it is a <a href=\"../distribucije/bernoulijeva-distribucija\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">Bernoulli random variable</a> with unknown parameter 𝑝',\r\n        21: 'Therefore, the type of distribution is known and only one parameter is unknown.',\r\n        22: 'Data on the number of household members are characterised by a discrete distribution with possible values 0, 1, 2, .... The probabilities of observing these values are unknown.'\r\n      },\r\n      'populacija_i_uzorak_zadatak_1': {\r\n        title: 'Population and sample task',\r\n        1: 'In an experiment where a coin is tossed, the coin lands tails up two times in two tosses. The experiment is repeated 200 times. What is the population and what is the sample in this experiment? Which variable is observed and what can we say about its distribution?',\r\n        2: '<strong>Solution</strong>',\r\n        3: 'The coin tossing experiment can be repeated an arbitrary number of times, so the population in this experiment is infinite. The sample consists of 200 repetitions. The experiments are independent and the distribution of possible outcomes is always the same because the same coin is tossed each time. Therefore, it is a <strong>simple random sample</strong>.',\r\n        4: 'The observed variable is the number of tails in two tosses. The variable can take on three values: 0, 1 i 2. The probability of tails 𝑝 in one toss is unknown, but it is known that the distribution of the variable number of tails is formed as follows: ',\r\n        5: '<strong>Task 5.1.1.</strong>'\r\n      },\r\n      'procjena_proporcije_vjerojatnosti': {\r\n        title: 'Proportion/probability estimate',\r\n        1: 'Let be 𝑥<sub>1</sub>, 𝑥<sub>2</sub>, ... , 𝑥<sub>𝑛</sub> the sample from variable 𝑋, which can have only two outcomes. The outcomes can be denoted by 0 and 1, so it is a sample from the <a href=\"../distribucije/bernoulijeva-distribucija\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">Bernoulli distribution</a>',\r\n        2: 'where 𝑝 is unknown. Parameter 𝑝 is the probability of realising value 1, that is, the proportion of 1 value in the total population. Unknown parameter 𝑝 can be <strong>estimated</strong> by the <a href=\"../opisivanje-podataka/frekvencije-i-relativne-frekvencije\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">relative frequency</a> of value 1: ',\r\n        3: 'The same principle can be applied when variable 𝑋 has more than two outcomes. The probability of each realisation is then estimated by the relative frequency of that realisation in the sample. For example, if 𝑋 has distribution',\r\n        4: 'the estimate for 𝑝<sub>1</sub> is the relative frequency of units in the sample. The obtained estimate of the distribution of 𝑋 is called <stong>empirical distribution</strong>.',\r\n        5: '<strong>Example 5.2.1.</strong>',\r\n        6: 'We are tossing a coin for which it is unknown whether it is unbiased or not. If the outcome “tails up” is denoted by 1 and the outcome “heads up” by 0, a sample from the Bernoulli distribution is obtained',\r\n        7: 'where 𝑝 is the unknown probability of the coin landing tails up.',\r\n        8: 'It is noticeable that, as a rule, the greater the number of tosses, the closer the estimate to the actual value. It is also guaranteed by the <a href=\"../slucajna-varijabla/ocekivanje/dodatni-zadaci\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">law of large numbers</a>.'\r\n      },\r\n      'procjena_proporcije_vjerojatnosti_interakcija': {\r\n        1: 'Population parameter p:',\r\n        2: 'Number of throws:',\r\n        3: 'Throw',\r\n        4: 'Estimation',\r\n        5: 'Sample size n = ',\r\n        6: 'Proportion/probability estimate',\r\n        7: 'Tails',\r\n        8: 'Heads',\r\n        9: 'Parameters were not chosen well.',\r\n        10: 'Probability must be in the interval [0, 1]',\r\n        11: 'Insert the numbers',\r\n        12: 'Number of throws must be larger than 0'\r\n      },\r\n      'procjena_proporcije_vjerojatnosti_zadatak_1': {\r\n        title: 'Proportion/probability estimate task',\r\n        1: 'According to the survey conducted by the Croatian Bureau of Statistics, out of 2029 surveyed households in the Republic of Croatia, 1635 households live in a privately-owned dwelling or house with no outstanding housing loan, 160 of them live in a privately-owned dwelling or house with outstanding housing loan, 77 live in a rented dwelling or house and 156 in a rented dwelling or house free of charge.',\r\n        2: 'Based on these data, estimate the distribution of the variable that can be used to describe the dwellings of the entire population.',\r\n        3: '<strong>Solution</strong>',\r\n        4: 'Possible realisations of variable X representing the type of dwelling are the following:',\r\n        5: 'privately-owned dwelling or house with no outstanding housing loan',\r\n        6: 'privately-owned dwelling or house with outstanding housing loan',\r\n        7: 'rented dwelling or house',\r\n        8: 'rented dwelling or house free of charge.',\r\n        9: 'Distribution (empirical distribution) estimate is',\r\n        10: '<stong>Task 5.2.1.</strong>'\r\n      },\r\n      'procjena_ocekivanja_i_varijance': {\r\n        title: 'Expectation and variance estimate',\r\n        1: 'If 𝑥<sub>1</sub>, 𝑥<sub>2</sub>, ... , 𝑥<sub>𝑛</sub> is a sample from variable 𝑋 with unknown expectation 𝜇 = 𝐸[𝑋], parameter 𝜇 is estimated by the <a href=\"../opisivanje-podataka/prosjek\" class=\"topic-link\">arithmetic mean</a> of the sample',\r\n        2: 'The unknown variance of 𝜎<sup>2</sup> = 𝑉𝑎𝑟(𝑋) variable is estimated by the <a href=\"../opisivanje-podataka/varijanca-i-standardna-devijacija\" class=\"topic-link\" target=\"_blank\" rel=\"noopener noreferrer\">variance</a> of the sample',\r\n        3: 'The estimate for <strong>standard deviation</strong> 𝜎 is the <a href=\"../opisivanje-podataka/varijanca-i-standardna-devijacija\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">standard deviation</a> of sample 𝑠<sub>𝑛</sub>.',\r\n        4: '<strong>Example 5.3.1.</strong>',\r\n        5: 'Data on the measured heights of 100 men from a population are available. The expectation and variance of the height in the subject population should be estimated.',\r\n        6: 'Based on the following tool, it is possible to calculate the estimates for the samples of different sizes randomly selected from the original sample of 100. Observe what happens with the expectation and variance estimates on such smaller samples.'\r\n      },\r\n      'procjena_ocekivanja_i_varijance_interakcija': {\r\n        1: 'Data histogram: ',\r\n        2: 'Sample size: ',\r\n        3: 'Expectation assessment <span class=\"math-symbol\">𝜇<sup>^</sup></span>= 𝑥̅',\r\n        4: 'Variance assessment <span class=\"math-symbol\">𝜎<sup>^</sup></span>',\r\n        5: 'The size of the subsample must be an integer from 0 to 100!',\r\n        6: 'Take subsample',\r\n        7: 'Data: ',\r\n      },\r\n      'pouzdani_interval_za_ocekivanje': {\r\n        title: 'Confidence interval for expectation',\r\n        1: 'Instead of estimating a parameter with one number, we can estimate the interval which contains that number with some probability, usually  0.95 or  0.99. Such interval is called the confidence interval.',\r\n        2: 'If a sample is characterised by a normal distribution with an unknown expectation 𝜇 and an unknown variance, the interval calculated according to the formula',\r\n        3: 'contains the actual value of expectation 𝜇 in approximately 100𝛾% cases.',\r\n        4: 'In the formula above, 𝛾 is the <strong>confidence level</strong>, usually 0.95 or 0.99. Number 𝑡<sub>𝑛−1,𝛾</sub> is determined as follows:',\r\n        5: 'for a random variable 𝑇<sub>𝑛−1</sub>,  with Student’s t-distribution with 𝑛−1 degrees of freedom. Graphically, it means determining an interval distributed symmetrically around 0, above which the density function of Student’s t-distribution closed the area 𝛾.',\r\n        6: 'Due to its relation to the t-distribution, the confidence interval is often called the <strong>t-interval</strong>. It is also used when a sample is not from normal distribution, but is large enough (at least 30 data) and the sample distribution is not very asymmetric.',\r\n        7: '<strong>Example 5.4.1.</strong>',\r\n        8: 'The following tool can be used to simulate the calculation of 100 confidence intervals for samples from the normal distribution.'\r\n      },\r\n      'pouzdani_interval_za_ocekivanje_interakcija': {\r\n        1: 'Expectation 𝜇:',\r\n        2: 'Variance 𝜎<sup>2</sup>:',\r\n        3: 'Confidence level 𝛾:',\r\n        4: 'Sample size 𝑛:',\r\n        5: 'Insert a number',\r\n        6: 'Generate 100 samples',\r\n        7: 'The confidence level must be less than 1. Re-enter the data!',\r\n        8: 'Entered value must be a number!',\r\n        9: 'grey – a number of reliable intervals that contain real value 𝜇',\r\n        10: 'red – a number of reliable intervals that do not contain real value 𝜇'\r\n      },\r\n      'pouzdani_interval_za_ocekivanje_zadatak_1': {\r\n        title: 'Confidence interval for expectation task',\r\n        1: 'According to the survey conducted by the Croatian Bureau of Statistics, households in the Republic of Croatia spend an average of 5494 kuna per year on clothing and footwear, with a standard deviation of 197.78 kuna. Data are based on 2029 surveyed households.',\r\n        2: 'Using the following calculator, calculate a 95% confidence interval for the expected expenditure on clothing and footwear.',\r\n        3: 'Compare the obtained interval with the intervals you would obtain if (with other values unchanged):',\r\n        4: 'a) standard deviation was 100',\r\n        5: 'a) sample size was 1000',\r\n        6: 'c) confidence was 0.99.',\r\n        7: 'How the confidence interval changes by changing the standard deviation/sample size/confidence level if other values remain unchanged?',\r\n        8: '<strong>Solution</strong>',\r\n        9: 'The interval is shorter for a smaller standard deviation – if the dispersion is smaller, an equally confident estimate can be given using a shorter interval. The interval is longer for a smaller sample size – if there are fewer data, the interval has to be longer with an equal confidence level. The interval is longer for a greater confidence – if we want a greater confidence, we have to use a longer interval.',\r\n        10: 'Arithmetic mean <span class=\"math-symbol\"><i>x&#772;</i></span><sub><i>n</i></sub>:',\r\n        11: 'Standard deviation of the sample <span class=\"math-symbol\"><i>s&#772;</i></span><sub><i>n</i></sub>:',\r\n        12: 'Confidence level 𝛾',\r\n        13: 'Sample size 𝑛',\r\n        14: '<strong>Task 5.4.1.</strong>'\r\n      },\r\n      'pouzdan-interval-za-procjenu-i-vjerojatnost': {\r\n        title: 'Confidence interval for proportion/probability',\r\n        1: 'We can often hear statements such as “80% of users have noticed improvements in the beauty of hair/whiteness of teeth/cleanliness of laundry”. A lot of ambiguity can be hidden in such statements. For example, we rarely know the size of the sample, and 80% can even refer to four out of five users.',\r\n        2: 'Instead of estimating by one number, an unknown proportion of a characteristic in a population can be estimated by a <strong>confidence interval for proportion</strong>',\r\n        3: 'formula',\r\n        4: 'where 𝑝&#770; is relative frequency, 𝑛 is sample size was and <i>z</i><sub>𝛾</sub> is a number determined as follows ',\r\n        5: 'formula',\r\n        6: 'for a random variable Z, which has a standard <a href=\"../distribucije/normalna-distribucija\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">normal distribution</a>. Graphically, it means determining an interval distributed symmetrically around 0, above which the density function of standard normal distribution closes the area 𝛾.',\r\n        7: 'The calculated interval will contain the actual value of proportion 𝑝 in approximately 100𝛾% cases. To apply the subject interval, it is necessary to have a large enough sample.',\r\n        8: '<strong>Example 5.5.1.</strong>',\r\n        9: 'In a coin tossing experiment, we want to estimate the probability of the outcome “tails up” by a confidence interval. The following tool can be used to observe how confidence intervals, as a rule, become shorter as the sample size increases.',\r\n        10: '<strong>Example 5.5.2.</strong>',\r\n        11: 'According to the survey conducted by the Croatian Bureau of Statistics, 26.4% of households in the Republic of Croatia have a dwelling as a housing unit. Data are based on 2029 surveyed households. Using the following calculator, we can calculate a 95% confidence interval for the proportion of the households living in dwellings.'\r\n      },\r\n      'pouzdan-interval-za-procjenu-i-vjerojatnost-interakcija': {\r\n        1: 'Tails probability 𝑝: ',\r\n        2: 'Confidence level 𝛾: ',\r\n        3: 'Number of throws 𝑛: ',\r\n        4: 'Throw',\r\n        5: 'The confidence level must be less than 1. Re-enter the data!',\r\n        6: 'Insert a number',\r\n        7: 'Entered values must be positive',\r\n        8: 'Inserted values must be numbers',\r\n        9: 'Probability must be in range [0, 1]'\r\n      },\r\n      'pouzdan-interval-za-procjenu-i-vjerojatnost-interakcija-2': {\r\n        1: 'Relative frequency <i class=\"math-symbol\">p̂</i>:',\r\n        2: 'Confidence level ',\r\n        3: 'Sample size ',\r\n        4: 'Calculate',\r\n        5: 'Reliable interval',\r\n        6: 'Inserted values must be positive',\r\n        7: 'Inserted values must be numbers',\r\n        8: 'All values must be inserted',\r\n        9: 'Relative frequency must be between 0 and 1.',\r\n        10: 'Confidence level must be between 0 and 1.'\r\n      },\r\n      'pouzdan-interval-za-procjenu-i-vjerojatnost-zadatak': {\r\n        title: 'Confidence interval for proportion/probability',\r\n        1: '<strong>Task 5.5.1.</strong>',\r\n        2: 'Let us assume that only two candidates A and B are participating in an election. The aim of the poll is to predict the winner. Out of 1000 polled citizens, 577 of them stated they will vote for candidate A. Using the calculator for confidence interval, calculate the 95% confidence interval for the proportion of votes for candidate A.',\r\n        3: '<strong>Solution</strong>',\r\n        4: 'The estimate of the proportion of votes for candidate A is 0.577 (or 57.5%), while the confidence interval is [0.5464 ,  0.6076] (or [54.64%, 60.76%]). ',\r\n        5: 'Confidence intervals are often presented in the form 0.577±0.0306, that is, 57.7%±3.06%. Therefore, when talking about the poll results in the media, we can often hear a note saying “statistical error amounts to ±3%“. It is actually a half of the length of the confidence interval, and it is usually assumed that the confidence level is 0.95.'\r\n      },\r\n      'testiranje-statistickih-hipoteza': {\r\n        title: 'Testing statistical hypotheses',\r\n        1: 'Let us assume that we are playing a game in which we win if we toss a coin and it lands tails up. After 10 tosses, the coin landed tails up 2 times and heads up 8 times. If the coin were unbiased, ideally, we would expect 5 tails and 5 heads. Is the deviation we obtained only accidental (bad luck) or we can suspect that we have been deceived?',\r\n        2: 'The answer can be obtained by setting these two statements as <strong>statistical hypotheses</strong> and by testing their validity. One hypothesis is called the <strong>null-hypothesis</strong> and is denoted by <i>H<sub>0</sub></i>, while the contrary one is called the <strong>alternative hypothesis</strong> and is denoted by <i>H<sub>1</sub></i>. In this case, hypotheses are',\r\n        3: '<i>H<sub>0</sub></i>: the coin is unbiased',\r\n        4: '<i>H<sub>1</sub></i>: the coin is biased; it favours heads.',\r\n        5: 'By tossing the coin, a sample from the Bernoulli distribution with parameter <i>p</i>, which represents the probability of the coin landing tails up. Hypotheses can be expressed as statements about an unknown parameter',\r\n        6: '<i>H<sub>0</sub></i>: p = 0.5',\r\n        7: '<i>H<sub>1</sub></i>: p < 0.5',\r\n        8: '<strong>Example 5.6.1.</strong>',\r\n        9: 'The following simulator can be used to repeat the game consisting of  tosses of an unbiased coin. We can observe how many times the game ended in  tails or less.',\r\n        10: 'If the coin is unbiased, what is the probability of getting only 2 tails or less in 10 tosses? That probability can be calculated correctly. The number of tails in 10 tosses of an unbiased coin has a <a href=\"../distribucije/binomna-distribucija\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">binomial distribution</a> with parameters 10 and 0.5 and therefore, the probability of the coin landing tails up 2 times or less in 10 tosses is 0.0547. This probability is called the p<strong>-value</strong> – the probability of obtaining the observed or even more extreme sample under the condition that the null-hypothesis is valid. In this context, the p-value indicates how strong the evidence against <i>H<sub>0</sub></i> is.',\r\n        11: 'Are two tails sufficient evidence against <i>H<sub>0</sub></i>? We cannot reach a correct conclusion because something like that can also happen with an unbiased coin. However, we can control the probability of making a mistake by rejecting the null-hypothesis by determining in advance the amount of probability we allow for that kind of mistake.  This number is called the <strong>significance level</strong>, which is usually set at 0.05.',\r\n        12: 'In that case, the p-value is higher that the usual significance level, 0.0547 > 0.05. When the coin is unbiased, the outcome of the game is not improbable so there is no reason to reject the null-hypothesis.',\r\n        13: 'How many tails would be sufficient evidence for rejecting the null-hypothesis? Let us assume that the coin landed tails up only once in ten tosses. The p-value is then 0.0107. The coin would land tails up only one in approximately one of 100 games with unbiased coin. It is so improbable that, with the 0.05 confidence level, it could be said that the coin is biased and it favours heads.',\r\n        14: 'This example illustrates only one of many statistical tests that can be applied to different problems and types of hypotheses.'\r\n      },\r\n      'testiranje-statistickih-hipoteza-interakcija': {\r\n        1: 'Number of repetitions N: ',\r\n        2: 'Repeat 10 throws N times',\r\n        3: 'Number of runs of 10 throws: ',\r\n        4: 'Number of runs with 2 or fewer tails: ',\r\n        5: 'Relative frequency: ',\r\n        6: 'Values',\r\n        7: 'Inserted values must be positive and above 0',\r\n        8: 'Inserted values must be numbers',\r\n        9: 'Expectation must be a positive number',\r\n        10: 'All values must be inserted'\r\n      },\r\n      'testiranje-statistickih-hipoteza-zadatak': {\r\n        title: 'Testing statistical hypotheses',\r\n        1: '<strong>Task 5.6.1.</strong>',\r\n        2: 'A test was conducted on a sample of 50 persons on whether they can recognise the difference between expensive and cheap wine. Each respondent was given unmarked glasses of expensive and cheap wine and was asked to guess the type of wine. A total of 34 of them correctly identified the type of wine after tasting. Can we say that people can identify the type of wine based on its taste with the 0.05 confidence level?',\r\n        3: '<strong>Solution</strong>',\r\n        4: 'It is a sample from the Bernoulli distribution in which value 1 indicates that a person identified the wine correctly. Hypotheses can be set as follows: ',\r\n        5: '<i>H<sub>0</sub></i>: p=0.5 (accidentally guess the type of wine)',\r\n        6: '<i>H<sub>1</sub></i>: p>0.5 (can recognise the type of wine)',\r\n        7: 'p-value amounts to 0.0078. Therefore, with the 0.05 confidence level, we can reject the null-hypothesis. In conclusion, people can recognise the difference in the types of wine.'\r\n      },\r\n      'jednostavna-linearna-regresija': {\r\n        title: 'Simple linear regression',\r\n        1: 'When examining the relationship between two continuous variables X and Y, we take a sample of data pairs:',\r\n        2: 'formula',\r\n        3: 'Such data pairs can be drawn in a coordinate system, thus obtaining a <a href=\"../opisivanje-podataka/dijagram-rasprsenosti-i-standardna-devijacija\" class=\"topic-link\" target=\"_blank\" rel=\"noopener noreferrer\">scatter plot</a>.',\r\n        4: '<strong>Regression methods</strong> can be used to describe the relationship between variables X and Y. If the points shown in the scatter diagram appear to be scattered around a line, then it makes sense to observe the linear connection between X and Y; therefore, we are talking about <strong>linear regression</strong>. It means that a line',\r\n        5: 'y = ax + b',\r\n        6: 'should be found for parameters <strong><i>a</i></strong> and <strong><i>b</i></strong> so that the line describes the relationship between the two variables. Parameter <strong><i>a</i></strong> is the <strong>slope</strong> of the line and <strong><i>a</i></strong> > 0 indicates that the relationship between X and Y is a growing one, and <strong><i>a</i></strong> < 0 that the relationship is a declining one.',\r\n        7: 'Parameters <strong><i>a</i></strong> and <strong><i>b</i></strong> are unknown and we need to estimate them based on data. Identifying parameters <strong>a</strong> and <strong>b</strong> means identifying a line that best describes the relationship between the variables. It can be done using the <strong>method of least squares</strong>, by minimising the sum of squares of vertical deviations of all points from the line. Vertical distances of points from the line are shown in the following figure.',\r\n        8: '<strong>Example 5.7.1.</strong>',\r\n        9: 'Using the following tool, we can select one of the given sets of data pairs and try to set the line that best describes the data.'\r\n      },\r\n      'jednostavna-linearna-regresija-interakcija': {\r\n        1: 'Data 1',\r\n        2: 'Data 2',\r\n        3: 'Data 3',\r\n        4: 'Display the regression line estimate',\r\n        5: '<strong>Description: </strong>Variable X contains monthly gross volume indices of industrial production in the period from 2011 to 2013, while variable Y contains monthly data on the number of persons in employment in the same period.',\r\n        6: '<strong>Description: </strong>A producer has introduced a new product and distributed it into stores at different prices. After a while, data on the number of products sold according to their prices were collected. It is noticeable that a higher price indicates a lower number of products sold, that is, the relationship between the variables is a declining one. ',\r\n        7: '<strong>Description: </strong>Simulated data scattered around the line with one outlier. It is noticeable that only one outlier significantly affects the position of the regression line.',\r\n      }\r\n    },\r\n    slucajna_varijabla: {\r\n      chapterNumber: '&mdash; Chapter 3 &mdash;',\r\n      title: 'Random variable',\r\n      slucajna_varijabla: {\r\n        title: 'Random variable',\r\n        1: '<strong>Random variable</strong> is a function that assigns real numbers to the outcomes of an experiment (elements of the set Ω). It is usually denoted by a capital letter, for example, 𝑋.',\r\n        2: 'A set of all values that a random variable 𝑋 can take on is referred to as the image of a random variable and is denoted by 𝓡<i>(X)</i>.',\r\n        3: 'We are often interested in the probability of a random variable 𝑋 realising with the values from a set 𝐴 ⊆ R. The event we are interested in is {𝜔 ∈ Ω: 𝑋(𝜔) ∈ 𝐴} ⊆ Ω, denoted abbreviated by (𝑋 ∈ 𝐴).',\r\n        4: '<strong>Example 3.1.1.</strong>',\r\n        5: 'When tossing a coin two times in a row, we are interested in the number of times the coin will land tails side up. We define function 𝑋, which assigns to each outcome from the set',\r\n        6: 'the number of tails in the ordered pair representing that outcome:',\r\n        7: 'Experiment outcome',\r\n        8: 'Value of <i>X</i>',\r\n        9: '2',\r\n        10: '1',\r\n        11: '1',\r\n        12: '0',\r\n        13: 'The image of the subject random variable 𝑋 is the following set:',\r\n        14: 'Analogically, we define another random variable, denoted by <i>Y</i>, which assigns the number of heads to each outcome of this experiment. The image of the subject random variable is the set 𝓡(𝑌) = {0, 1, 2}.',\r\n        15: 'It is noticeable that we can define several random variables on the same Ω.'\r\n      },\r\n      slucajna_varijabla_zadatak_1: {\r\n        title: 'Random variable task',\r\n        1: 'An experiment consists of rolling a dice twice in a row. Define the random variable that assigns the sum of the numbers rolled to the outcomes of that experiment.',\r\n        2: '<strong>Solution</strong>',\r\n        3: 'The following outcomes may be realised when rolling a die twice in a row:',\r\n        4: 'The figure above shows the set of all possible outcomes of the subject experiment. It can be written as a set as follows:',\r\n        5: 'whereby each outcome is represented by an ordered pair of the numbers rolled.',\r\n        6: 'The random variable which assigns the sum of the numbers rolled to the outcomes of the subject experiment is defined as follows:',\r\n        7: 'The image of the random variable 𝑋 is the set <i>𝓡(X)</i> = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.',\r\n        8: '<strong>Task 3.1.1.</strong>',\r\n        9: '<strong>Task 3.2.1.</strong>'\r\n      },\r\n      diskretna_slucajna_varijabla: {\r\n        title: 'Discrete random variable',\r\n        1: '<strong>Discrete random variable</strong> 𝑋 is characterised by: ',\r\n        2: 'finite {𝑥<sub>1</sub>, 𝑥<sub>2</sub>, ... , 𝑥<sub>𝑛</sub>} or',\r\n        3: 'countable {𝑥<sub>1</sub>, 𝑥<sub>2</sub>, ... , 𝑥<sub>𝑛</sub>, ... }',\r\n        4: 'set of values 𝓡(𝑋).',\r\n        5: 'If the probabilities 𝑃(𝑋 = 𝑥<sub>𝑖</sub>) are known for all possible values of 𝑥<sub>𝑖</sub> from 𝓡(𝑋), we say that the <strong>distribution of discrete random variable</strong> 𝑋 is known, and it is written in a <strong>distribution table</strong>:',\r\n        6: 'where 𝑝<sub>𝑖</sub> denotes  𝑃(𝑋 = 𝑥<sub>𝑖</sub>), 𝑖 = 1,2,...',\r\n        7: 'Using a distribution table, we calculate the probability of 𝑋 realising from a set 𝐴 ⊆ 𝓡(𝑋).',\r\n        8: 'This probability is equal to the sum of probabilities 𝑝<sub>𝑖</sub> for all 𝑥<sub>𝑖</sub> from 𝐴:',\r\n        9: '<strong>Example 3.2.1.</strong>',\r\n        10: 'When tossing an unbiased coin two times in a row, the set of all possible outcomes is Ω = {(𝑝, 𝑝), (𝑝, 𝑔), (𝑔, 𝑝), (𝑔, 𝑔)} and all outcomes are equally probable:',\r\n        11: 'Random variable 𝑋, which assigns the number of tails to each outcome of the experiment, is discrete and has the following image:',\r\n        12: 'The probabilities of realising the elements of the image 𝓡<i>(X)</i> are the following:',\r\n        13: 'Therefore, the distribution of the subject random variable 𝑋 is given in table',\r\n        14: 'For example, the probability of the coin landing tails up at least once is',\r\n        15: 'Except by a table, the distribution can also be presented graphically:',\r\n        16: 'However, the coin we are tossing does not have to be unbiased. For example, the coin may be twice as likely to land on heads as on tails. It means that the outcomes of two consecutive tosses are not equally probable:',\r\n        17: 'In this case, the distribution of the random variable, which assigns the number of tails to the outcomes of this experiment, is given in table',\r\n        18: 'Now, the probability of the coin landing tails up at least once is',\r\n        19: 'and the graphical presentation of the distribution is given in the following figure:',\r\n        20: 'Using the interactive part, let us examine how the distribution of X and P(X ≥ 1) changes as the probability of the coin landing tails up changes:'\r\n      },\r\n      diskretna_slucajna_varijabla_interakcija: {\r\n        1: 'The probability of tails realization: ',\r\n        2: 'Probability is not chosen well',\r\n        3: 'Calculate probability P(X>=1)',\r\n        4: 'Calculate probability',\r\n        5: 'Probabilities',\r\n        6: '0 tails',\r\n        7: '1 tail',\r\n        8: 'The probability value must be a number',\r\n        9: '2 tails',\r\n        10: 'Probability',\r\n        11: 'Please insert the probability value'\r\n      },\r\n      diskretna_slucajna_varijabla_zadatak_1: {\r\n        title: 'Discrete random variable task',\r\n        1: 'An experiment consists of rolling a dice, which does not have to be unbiased, twice in a row. Calculate the distribution of the random variable that assigns the sum of the numbers rolled to the outcomes of the subject experiment. Using the interactive tool, calculate the probability of rolling the numbers whose sum is less than five.',\r\n        2: '<strong>Solution</strong>',\r\n        3: 'The die does not have to be unbiased. The random variable which assigns the sum of the numbers rolled to the outcomes of the subject experiment is denoted by 𝑋. The probability of rolling the numbers whose sum is less than five is',\r\n        4: 'where 𝑝<sub>2</sub>, 𝑝<sub>3</sub>, 𝑝<sub>4</sub>, 𝑝<sub>5</sub> are the probabilities from the distribution table of random variable 𝑋.'\r\n      },\r\n      diskretna_slucajna_varijabla_zadatak_interakcija: {\r\n        1: 'Dice throw outcome',\r\n        2: 'Outcome probability',\r\n        3: 'Probabilities were not chosen well (sum must be 1)',\r\n        4: 'Distribution of X',\r\n        5: 'Calculate probability',\r\n        6: 'Probabilities',\r\n        7: 'Calculate probability',\r\n        8: 'In the following table, enter the probabilities of rolling the numbers indicated on the sides of the dice. By clicking on the “Distribution of X” button, the distribution table of the random variable whose value is the sum of the numbers rolled in two consecutive rolls appears, while by clicking on the “Calculate probability” button, the probability that the sum of the numbers rolled is an element of the arbitrary subset of the image of the random variable X is written, whereby p<sub>i</sub> indicates P(X=i).',\r\n        9: 'Click on the second table row probabilities to form a subset on which the probability will be calculated.',\r\n        10: 'It is necessary to select some of the table probabilities!'\r\n      },\r\n      neprekidna_slucajna_varijabla: {\r\n        title: 'Continuous random variable',\r\n        1: '<strong>Continuous random variable</strong> is characterised by image 𝓡(𝑋), which is not a discrete set. ',\r\n        2: 'For example, 𝓡(𝑋) may be an interval or even a whole set of real numbers.',\r\n        3: '<strong>Distribution</strong> of a continuous random variable 𝑋 is given by a non-negative function 𝑓,<strong> density function</strong>, for which the area between the graph of that function and the 𝑥-axis is equal to 1.',\r\n        4: 'The probability of the continuous random variable 𝑋 realising with the values of a set 𝐴 ⊆ <i>R</i> is equal to the area under the graph of the density  𝑓 function above the set 𝐴, as presented in the following figure:',\r\n        5: '<strong>Example 3.3.1.</strong>',\r\n        6: 'The random variable 𝑋 whose image is interval (𝑎, 𝑏), −∞ < 𝑎 < 𝑏 < ∞, and all equally long intervals of (𝑎, 𝑏) are equally probable, is given by density function',\r\n        7: 'For example, for 𝑎 = -1 and 𝑏 = 1, this random variable may be applied to describe an error in the measuring result of a precision measuring instrument, with errors from equally long subintervals of (-1, 1) realising with equal probabilities. The density function graph for a = -1 and b = 1 is presented in the following figure:',\r\n        8: 'For example, for a = -1, b = 1, c = -1, d = 0, P(X ∈ (-1, 0)) is equal to the area of a rectangle with the length of its sides of 1 and <div class=\"fraction\" top=\"1\" bottom=\"2\"></div> :',\r\n        9: 'Analogically, for a = -1, b = 1, c = 12, d = 1, the following applies:',\r\n        10: 'Using the interactive tool, try to calculate the probability P(<i>c < X < d</i>) for the above-mentioned distribution for different values 𝑎 and 𝑏.'\r\n      },\r\n      neprekidna_slucajna_varijabla_interakcija: {\r\n        1: 'Starting value',\r\n        2: 'Ending value',\r\n        3: 'Draw the density function chart',\r\n        4: 'Determine the probability P(c < X < d)',\r\n        5: 'Parameters are not selected well. Number a must be less than b!',\r\n        6: 'Second interval start',\r\n        7: 'Second interval end',\r\n        8: 'Parameters are not selected well. Number c must be less than d!',\r\n        9: 'Values must be numbers',\r\n        10: 'Subinterval values must be in the interval range.',\r\n        11: 'All input values must be inserted'\r\n      },\r\n      neprekidna_slucajna_varijabla_zadatak_1: {\r\n        title: 'Continuous random variable task',\r\n        1: 'Random variable given by the density function',\r\n        2: 'can be used to describe the time between two consecutive realisations of the observed event, for example, the arrival of a tram at a tram stop. Number <i>λ</i> is the parameter of this distribution. Using the interactive tool for <i>λ</i> = 1, calculate the probability that the following time will pass between two',\r\n        3: '<strong>Solution</strong>',\r\n        4: 'The density function graph for <i>λ</i> = 1 is presented in the following figure:',\r\n        5: 'The required probabilities are the following:',\r\n        6: 'a) 𝑃(0<𝑋<1)=0.6321',\r\n        7: 'The probability that less than 1 minute will pass between two consecutive arrivals of a tram at a tram stop is 0.6321.',\r\n        8: 'b) 𝑃(1<𝑋<2)=0.2325',\r\n        9: 'The probability that from 1 to 2 minutes will pass between two consecutive arrivals of a tram at a tram stop is 0.2325.',\r\n        10: 'c) 𝑃(𝑋 > 2) = 0.1353',\r\n        11: 'The probability that more than 2 minutes will pass between two consecutive arrivals of a tram at a tram stop is 0.1353.',\r\n        12: 'Graphical presentations of the density function and the required probabilities:',\r\n        13: 'less than 1 minute,',\r\n        14: 'between 1 i 2 minutes,',\r\n        15: 'more than 2 minutes,',\r\n        16: 'Change the values of parameter <i>λ</i> and analyse the results.',\r\n        17: '<strong>Task 3.3.1.</strong>',\r\n        18: 'Probability for element between 0 and 1',\r\n        19: 'Probability that the element is between 1 and 2',\r\n        20: 'Probability for element greater than 2'\r\n      },\r\n      neprekidna_slucajna_varijabla_zadatak_interakcija: {\r\n        1: 'Insert a number',\r\n        2: 'Draw the density function chart',\r\n        3: 'Determine the probability P(c < X < d)',\r\n        4: 'Density function chart',\r\n        5: 'Values must be numbers',\r\n        6: 'Values c and d must not be equal.',\r\n        7: 'Values d must be larger than c.',\r\n        8: 'All values must be inserted.'\r\n      },\r\n      funkcija_distribucije: {\r\n        title: 'Distribution function',\r\n        1: '<strong>Distribution function</strong> 𝐹 of a random variable 𝑋 assigns to each real number the probability of event (𝑋 ≤ 𝑥): ',\r\n        2: 'For a discrete random variable 𝑋, the value of the distribution function is calculated using a <a href=\"../slucajna-varijabla/diskretna-slucajna-varijabla\" class=\"topic-link\" target=\"_blank\" rel=\"noopener noreferrer\">distribution table</a>. For an arbitrary 𝑥, the value 𝐹(𝑥) is the sum of probabilities 𝑝<sub>𝑖</sub> for those 𝑥<sub>𝑖</sub> ∈ 𝓡(𝑋) that are smaller than or equal to 𝑥:',\r\n        3: '<strong>Example 3.4.1.</strong>',\r\n        4: 'The distribution of the discrete random variable 𝑋 which, when tossing an unbiased coin two times in a row, records tails, is given in the following table:',\r\n        5: 'The values of the distribution function of 𝑋 in the points of its image are the following:',\r\n        6: 'The distribution function 𝑋 of is given as follows:',\r\n        7: 'and its graph is presented in the following figure: ',\r\n        8: 'It is noticeable that the distribution function of the discrete random variable has a value rise p<sub>i</sub>=P(X=x<sub>i</sub>) in each x<sub>i</sub>∈𝓡(X), that it grows monotonously and is limited (by the line y=0 from the bottom and by the line y=1 from the top).',\r\n        9: '<strong>Example 3.4.2.</strong>',\r\n        10: 'The continuous random variable 𝑋, whose image is interval (-1, 1), and all equally long subintervals of (-1, 1) are equally probable, is given by the density function',\r\n        11: 'Let us show the value of the distribution function of 𝑋 in point 𝑥 = <div class=\"fraction\" top=\"1\" bottom=\"2\"></div> by graphical presentations of the density function and the distribution function of the subject random variable:',\r\n        12: 'The function above is an example of the density function given as follows:',\r\n        13: 'For some other <i>a</i> and <i>b</i> and an arbitrary 𝑥, let us observe the density function and the distribution function graphs as well as probability P(X≤x) on these graphs.',\r\n        14: 'What if the coin that is tossed is biased? Let us examine how the distribution function of X changes as the probability of the coin landing tails up changes:',\r\n        15: 'For a continuous random variable 𝑋, the value of the distribution function is calculated using a <a href=\"../slucajna-varijabla/neprekidna-slucajna-varijabla\" class=\"topic-link\" target=\"_blank\" rel=\"noopener noreferrer\">density function</a>. For an arbitrary 𝑥, the <i>F(</i>𝑥<i>)</i> is equal to the area under the graph of its density function above the interval (-∞, 𝑥].'\r\n      },\r\n      funkcija_distribucije_dodatni_zadaci: {\r\n        title: 'Learn more: how to calculate probability P(X∈A)?',\r\n        1: 'The probability of a random variable X realising from interval (a, b) can be calculated using the value of the distribution function in points a and b:',\r\n        2: 'P X∈(a, b)=P a<X≤b=P X≤b-P X≤a=F b-F (a).',\r\n        3: 'The probabilities of X realising from intervals(a, b), [a, b] and(a, b) are calculated in a similar way.',\r\n        4: 'In case of a discrete random variable (link to the topic) with the distribution table',\r\n        5: 'X~(x1 x2 ... p1 p2 ... xn…  pn…)',\r\n        6: 'each of these probabilities is the sum of probabilities pi=P(X = xi) for all xi from the observed interval.',\r\n        7: 'In case of a continuous random variable (link to the topic) , each of these probabilities is equal to the area under the density function graph above the interval A the probabilities P(a<X≤b),',\r\n        8: 'P (a≤X<b), P (a≤X≤b) i P (a<X≤b) are equal, because for a continuous random variable, P X=x = 0 for each number X.'\r\n      },\r\n      funkcija_distribucije_interakcija: {\r\n        1: 'The probability of tails realization:',\r\n        2: 'Distribution of X',\r\n        3: 'Distribution function of X',\r\n        4: 'Distribution function chart',\r\n        5: 'Discrete random variable chart',\r\n        6: 'The probability must be a number',\r\n        7: 'The probability must be in the range [0, 1]',\r\n        8: 'Empty probability input value is not valid.'\r\n      },\r\n      funkcija_distribucije_interakcija_2: {\r\n        1: 'Density function chart',\r\n        2: 'Distribution function chart',\r\n        3: 'The value of x is not in the interval between a and b',\r\n        4: 'Inserted values must be numbers',\r\n        5: 'Probablity P(X ≤ ',\r\n        6: 'Plase insert all values'\r\n      },\r\n      ocekivanje: {\r\n        title: 'Expectation',\r\n        1: '<strong>Expectation</strong> of a random variable 𝑋 is the number that indicates the centre of the probability distribution of that random variable. It is denoted by 𝐸[𝑋] or 𝜇 .',\r\n        2: 'The expectation of a random variable does not have to exist, but if it does, it is calculated as follows:',\r\n        3: 'For a <a href=\"../slucajna-varijabla/diskretna-slucajna-varijabla\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\" target=\"_blank\" rel=\"noopener noreferrer\">discrete random variable</a> 𝑋 with the distribution table',\r\n        4: 'the expectation is the sum of the products of each value  𝑥<sub>𝑖</sub> with the associated value 𝑝<sub>𝑖</sub> :',\r\n        5: 'For a <a href=\"../slucajna-varijabla/neprekidna-slucajna-varijabla\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\" target=\"_blank\" rel=\"noopener noreferrer\">continuous random variable</a> 𝑋 with density function 𝑓, the expectation is calculated using the area between the 𝑥-axis and the graph of the function 𝑥𝑓(𝑥), by subtracting the area between the graph of the negative part of the function 𝑥𝑓(𝑥) and the x-axis from the area between the x-axis and the graph of the positive part of the function 𝑥𝑓(𝑥).',\r\n        6: '<strong>Example 3.5.1.</strong>',\r\n        7: 'The distribution of the random variable which assigns the numbers on the sides of a die to the outcomes of rolling an unbiased die is given by the following table:',\r\n        8: 'The expectation of the subject random variable is the following number:',\r\n        9: 'The following figure shows the distribution graph and the expectation position of the subject random variable:',\r\n        10: 'It is noticeable that in this case, the expectation is the arithmetic mean of the values which the random variable can take on. ',\r\n        11: 'However, this does not have to be the case. If the die we are rolling is biased, due to the changes in the distribution of the random variable , the 𝑋 expectation will not be the arithmetic mean of the numbers from its image. Let us observe how the expectation changes due to the changes in the distribution.',\r\n        12: '<strong>Example 3.5.2.</strong>',\r\n        13: 'The continuous random variable 𝑋 whose image is interval (−1, 1), and all equally long subintervals of (−1, 1) are equally probable, is given by the density function',\r\n        14: 'Since the function 𝑥𝑓(𝑥) used to calculate the expectation is odd, the expectation is 0.',\r\n        15: 'The following figures show the area between the x-axis and the graph of function 𝑥𝑓(𝑥) used to calculate the expectation and the graph of the density function 𝑓  with marked expectation on the x-axis:',\r\n        16: 'Using the interactive tool, let us observe the area between the x-axis and the graph of function 𝑥𝑓(𝑥), as well as the graph of the general density function',\r\n        17: 'with marked expectation on the x-axis.',\r\n        18: '<strong>Example 3.5.3.</strong>',\r\n        19: 'Let (𝑋𝑛, 𝑛 ∈ 𝑁) be a set of random variables describing the outcomes of consecutive rolls of an unbiased die. Random variable 𝑋𝑛 takes on value 1 if number 6 rolls in the th 𝑛-roll. Otherwise, it takes on value 0. The distribution of 𝑋𝑛 is given by table',\r\n        20: 'It is noticeable that arithmetic mean 𝑋𝑛 corresponds to the relative frequency of units. In addition, it is noticeable that the expectation of the relative frequency of units is 1/6.',\r\n        21: 'According to the weak law of large numbers, by increasing the number of die rolls, the probability of deviation of the relative frequency of units from 1/6 can be made arbitrarily small.'\r\n      },\r\n      ocekivanje_interakcija: {\r\n        1: 'Draw charts',\r\n        2: 'Chart of the function xf(x)',\r\n        3: 'Chart of the function f(x)',\r\n        4: 'All values must be inserted.',\r\n        5: 'Inserted values must be numbers.',\r\n        6: 'Number a must be smaller than number b.'\r\n      },\r\n      ocekivanje_interakcija_2: {\r\n        1: 'Draw the distribution and mark the expectation',\r\n        2: 'Expectation',\r\n        3: 'Probabilities were not chosen well (the sum must be 1)'\r\n      },\r\n      ocekivanje_dodatni_zadaci: {\r\n        title: 'For those who want to learn more',\r\n        1: 'Let (𝑋<sub>𝑛</sub>, 𝑛 ∈ 𝑁) be a set of independent, equally distributed random variables with expectation 𝜇, which describes the outcomes of experiment repetitions.',\r\n        2: 'The weak law of large numbers deals with the limits of the associated set of arithmetic means (<span class=\"overline\">𝑋</span><sub>𝑛</sub>, 𝑛 ∈ 𝑁), where',\r\n        3: 'According to the weak law of large numbers, the probability of deviation of arithmetic mean <span class=\"overline\">𝑋</span><sub>𝑛</sub> from expectation 𝜇 can be made arbitrarily small by selecting a large number of experiment repetitions, that is, number 𝑛.',\r\n        4: '<strong>For those who want to learn more - example 1</strong>',\r\n        5: 'Let (<i>X<sub>n</sub></i>, <i>n∈N</i>) be a set of random variables describing the outcomes of consecutive rolls of an unbiased die. Random variable X<sub>𝑛</sub> takes on value 1 if number n rolls in the 6<sup>th</sup> roll. Otherwise, it takes on value 0. The distribution of <i>X<sub>n</sub></i> is given by table',\r\n        6: 'It is noticeable that arithmetic mean <span class=\"overline\">X</span><sub>n</sub> corresponds to the relative frequency of units. In addition, it is noticeable that the expectation of the relative frequency of units is <div class=\"fraction\" top=\"1\" bottom=\"6\"></div>.',\r\n        7: 'According to the weak law of large numbers, by increasing the number of die rolls, the probability of deviation of the relative frequency of units from <div class=\"fraction\" top=\"1\" bottom=\"6\"></div> can be made arbitrarily small.',\r\n        8: '<strong>For those who want to learn more - example 2</strong>',\r\n        9: 'Let (<i>X<sub>n</sub>,  n∈N</i>) be a set of random variables describing the outcomes of consecutive coin tosses. Random variable <i>X<sub>n</sub></i> takes on value 1 if the coin lands heads up in the nth toss. If it lands tails up, it takes on value 0. With <i>p</i> denoting the probability of success (1), it follows that the distribution of <i>X<sub>n</sub></i> is given by table',\r\n        10: 'It is noticeable that arithmetic mean <span class=\"overline\">X</span><sub>n</sub> corresponds to the relative frequency of units. In addition, it is noticeable that the expectation of the relative frequency of units is 𝑝, 𝐸[<span class=\"overline\">𝑋</span><sub>𝑛</sub>] = 𝑝.',\r\n        11: 'According to the weak law of large numbers, by increasing the number of coin tosses, the probability of deviation of the relative frequency of units from expectation 𝑝 can be made arbitrarily small.',\r\n        12: '<strong>Expectation position</strong>',\r\n        13: 'If we wonder if there is a real number that is somehow “the closest” to the random variable, then in one way of measuring distance, it is precisely the expectation. The distance between the random variable <i>X</i> and number <i>a</i> is thus measured as expected squared deviation.',\r\n        14: 'Observing it as a function with an independent variable <i>a</i>,',\r\n        15: 'it follows that it reaches its minimum exactly at <i>a = E[X]</i>. Therefore, <i>E[X]</i> minimises the expected squared deviation from the random variable <i>X</i>.',\r\n        16: '<strong>Weak law of large numbers</strong>',\r\n        17: 'For those who want to learn more',\r\n        18: 'For those who want to learn more - example'\r\n\r\n      },\r\n      ocekivanje_dodatni_zadaci_interakcije: {\r\n        1: 'Number of throws: ',\r\n        2: 'Insert a number',\r\n        3: 'Throw the dice',\r\n        4: 'Number of throws must be greater than 0!',\r\n        5: 'Heads probability',\r\n        6: 'Number of throws',\r\n        7: 'Throw the coin',\r\n        8: 'Probability must be between 0 and 1.',\r\n        9: 'Number of throws can not be a string.',\r\n        10: 'Number of throws must be a whole number.',\r\n        11: 'Number of throws input is necessary.',\r\n        12: 'All values must be inserted.'\r\n      },\r\n      varijanca_i_standardna_devijacija: {\r\n        title: 'Variance and standard deviation',\r\n        1: '<strong>Variance</strong> of a random variable 𝑋 is a positive number that indicates the <strong>dispersion</strong> of the distribution of a random variable 𝑋 in relation to its expectation 𝐸[𝑋].',\r\n        2: 'It is denoted by 𝑉𝑎𝑟(𝑋) or 𝜎<sup> 2</sup> .',\r\n        3: 'More precisely, 𝑉𝑎𝑟(𝑋) is the expected squared deviation of a random variable 𝑋 from its expectation:',\r\n        4: 'Square root of 𝑉𝑎𝑟(𝑋) is referred to as the <strong>standard deviation</strong> of a random variable 𝑋 and is denoted by 𝜎.',\r\n        5: '<strong>Example 3.6.1.</strong>',\r\n        6: 'The continuous random variable 𝑋 whose image is interval (𝑎, 𝑏), and all equally long subintervals of (𝑎, 𝑏) are equally probable, is given by the density function',\r\n        7: 'Using the interactive tool, let us observe the expectation and variance of the subject random variable for different values of parameters a and b:',\r\n        8: 'random variables with distribution on equally long intervals have equal variances',\r\n        9: 'comparing the variance of the random variable with distribution on the shorter interval and the random variable with distribution on the longer interval, the variation of the random variable with distribution on the longer interval is larger.'\r\n      },\r\n      varijanca_i_standardna_devijacija_interakcija: {\r\n        1: 'Calculate expectation and variance',\r\n        2: 'Draw density function chart',\r\n        3: 'Expectation: ',\r\n        4: 'Variance: ',\r\n        5: 'Original density function chart',\r\n        6: 'Expectation',\r\n        7: 'Expectation minus standard deviation',\r\n        8: 'Number b must be bigger than number a',\r\n        9: 'Expectation plus standard deviation',\r\n        10: '4. Distributions',\r\n        11: 'All values must be inserted.'\r\n      },\r\n      varijanca_i_standardna_devijacija_zadatak: {\r\n        1: 'Use an interactive tool to check the random variables variable X with a density function depending on the parameter value λ> 0',\r\n        2: '<strong>Solution</strong>',\r\n        3: 'By increasing the value of parameter λ, expectation and variance decrease.',\r\n        4: '<strong>Task 3.6.1.</strong>'\r\n      },\r\n      varijanca_i_standardna_devijacija_zadatak_interakcija: {\r\n        1: 'Calculate the expectation and variance',\r\n        2: 'Draw the density function chart',\r\n        3: 'Expectation: ',\r\n        4: 'Variance: ',\r\n        5: 'Original density function chart',\r\n        6: 'Expectation minus standard deviation',\r\n        7: 'Expectation plus standard deviation',\r\n        8: 'Expectation'\r\n      }\r\n    },\r\n    distribucije: {\r\n      chapterNumber: '&mdash; Chapter 4 &mdash;',\r\n      title: 'Distributions',\r\n      bernoulijeva_distribucija: {\r\n        title: 'Bernoulli distribution',\r\n        1: 'Random variable 𝑋 that describes an experiment with only <strong>two possible outcomes</strong>:',\r\n        2: '<strong>failure</strong> (denoted by 0), which is realised with probability (1 − 𝑝)',\r\n        3: '<strong>success</strong> (denoted by 1), which is realised with probability 𝑝',\r\n        4: 'has a Bernoulli distribution with parameter 𝑝 ∈ (0, 1) and distribution table',\r\n        5: '<strong>Expectation</strong> and <strong>variance</strong> of the Bernoulli distribution with parameter 𝑝 are',\r\n        6: '<strong>Example 4.1.1.</strong>',\r\n        7: 'When tossing a coin, it can land either on tails or on heads. If the coin we are tossing is unbiased, these two outcomes are equally probable. If we say that the outcome “heads up” is a success and denote it by 1, and the outcome “tails up” is a failure and denote it by 0, we describe the outcome of the coin toss with the random variable 𝑋 with the Bernoulli distribution with parameter 𝑝 = <div class=\"fraction\" top=\"1\" bottom=\"2\"></div> and by distribution table',\r\n        8: 'Expectation and variance are',\r\n        9: 'The following figure shows the graph of the subject Bernoulli distribution with marked expectation:',\r\n        10: 'If we are tossing a coin that is biased, the outcomes “tails up” (failure) and “heads up” (success) are not equally probable.',\r\n        11: 'Using the interactive tool, observe how the change in the probability of success <i>p</i> affects the change in the Bernoulli distribution, which describes the outcome of the coin toss, as well as the change in its expectation.'\r\n      },\r\n      bernoulijeva_distribucija_interakcija: {\r\n        1: 'Probability',\r\n        2: 'Distribution chart',\r\n        3: 'Expectation',\r\n        4: 'Variance',\r\n        5: 'The probability must be within the interval [0, 1]!',\r\n        6: 'The probability must be a number!'\r\n      },\r\n      bernoulijeva_distribucija_zadatak_1: {\r\n        title: 'Bernoulli distribution task',\r\n        1: 'a) In the game of Ludo, players roll an unbiased die, and when a six is rolled, it is considered success. If any of the numbers 1, 2, 3, 4, 5 is rolled, it is considered failure. Calculate the distribution, expectation and variance of the random variable used to describe the rolling of an unbiased die in this context. Present the distribution and the expectation position graphically using the interactive tool.',\r\n        2: 'b) Using the interactive tool, observe how the distribution and the expectation change when we roll a die that is biased, for example, when the probability of rolling a six is changed.',\r\n        3: '<strong>Solution</strong>',\r\n        4: 'a) Since the die is unbiased, the probability of realising success (rolling a six) in one roll is <div class=\"fraction\" top=\"1\" bottom=\"6\"></div> , therefore, in this case, the outcome of die roll is described by the Bernoulli random variable 𝑋 with parameter 𝑝 = <div class=\"fraction\" top=\"1\" bottom=\"6\"></div> and distribution table',\r\n        5: 'Expectation and variance are',\r\n        6: 'b) Using the interactive tool, the user draws distribution graphs with marked expectations for different values of parameter 𝑝.',\r\n        7: '<strong>Task 4.1.1.</strong>'\r\n      },\r\n      bernoulijeva_distribucija_zadatak_interakcija: {\r\n        1: 'Probability',\r\n        2: 'Distribution chart',\r\n        3: 'Expectation',\r\n        4: 'Variance',\r\n        5: 'The probability must be within the interval [0, 1]!'\r\n      },\r\n      binomna_distribucija: {\r\n        title: 'Binomial distribution',\r\n        1: 'A random variable 𝑋 that has successes in 𝑛 independent performances of the same experiment with only two possible outcomes (success and failure), whereby success is realised in each performance of the experiment with probability 𝑝, has a <strong>binomial distribution</strong> with parameters 𝑛 ∈ 𝑁 and 𝑝 ∈ (0, 1) , denoted by 𝑋~ℬ(𝑛, 𝑝).',\r\n        2: 'The image ℬ(𝑛, 𝑝) of distribution is 𝓡(𝑋) = {0, 1, 2, ... , 𝑛}, and the probabilities of realising the elements of the image are:',\r\n        3: '<strong>Expectation</strong> and <strong>variance</strong> ℬ(𝑛, 𝑝) of distribution are',\r\n        4: '<strong>Example 4.2.1.</strong>',\r\n        5: 'Let us assume that we are tossing a coin 20 times. If the coin we are tossing is unbiased, the number of occurrences of the outcome “heads up” in these 20 tosses is described by a random variable X with a binomial distribution with parameters n = 20 and p = <div class=\"fraction\" top=\"1\" bottom=\"2\"></div>. The expectation and variance of the subject distribution are:',\r\n        6: 'The following figure shows the graph of the subject distribution with marked expectation: ',\r\n        7: 'Using the interactive tool, we can calculate some interesting probabilities, for example the following:',\r\n        8: 'The probability of the coin landing heads up exactly 10 times is P(X=10) = 0.1762.',\r\n        9: 'The probability of the coin landing heads up less than 10 times is P(X<10) = 0.4119.',\r\n        10: 'The probability of the coin landing heads up at least 10 times is P(X≥10) = 0.5881.'\r\n      },\r\n      binomna_distribucija_interakcija: {\r\n        1: 'Distribution chart',\r\n        2: 'Expectation',\r\n        3: 'Variance',\r\n        4: 'Calculate the required probabilities',\r\n        5: 'Inserted values must be numbers',\r\n        6: 'Probability must be in range [0, 1]',\r\n        7: 'Number of throws must be a positive number',\r\n        8: 'For selected binomial distribution parameters n, p, and the value x from its image, determine the probabilities P(X=x), P(X<=x) and P(X>x).',\r\n        9: 'P(X<=x)',\r\n        10: 'P(X>x)',\r\n        11: 'The probability value must be inserted.',\r\n        12: 'All values must be inserted.',\r\n        13: 'Please enter the value between 0 and '\r\n      },\r\n      binomna_distribucija_zadatak_1: {\r\n        title: 'Binomial distribution task',\r\n        1: 'Using the interactive tool, calculate the probability of rolling a six more than 5 times in 50 die rolls. Is it more probable that a six will roll at least 5 times or at most 10 times?',\r\n        2: '<strong>Solution</strong>',\r\n        3: 'The following is the example of solution for the case of unbiased die:',\r\n        4: '𝑋 represents the number of rolling a six in 50 rolls of an unbiased die:',\r\n        5: 'The required probabilities are',\r\n        6: 'Therefore, it is more probable that a six will roll at least 5 times than at most 10 times.',\r\n        7: '<strong>Task 4.2.1.</strong>',\r\n        8: 'For the selected parameters n (number of dice rolls) and p (probability of realization of six) of the binomial distribution, we determine the probabilities P(X>5), P(X>=5) and P(X<=10).'\r\n      },\r\n      uniformna_distribucija: {\r\n        title: 'Uniform distribution',\r\n        1: 'A random variable 𝑋 with density function',\r\n        2: 'has a <strong>uniform distribution</strong> on interval (𝑎, 𝑏) and is denoted by 𝑿~𝓤(𝒂, 𝒃). Real numbers 𝑎 and 𝑏, −∞ < 𝑎 < 𝑏 < ∞, are parameters of the subject distribution.',\r\n        3: 'The density function of the uniform distribution reflects the fact that equally long subintervals of (𝑎,𝑏) are equally probable.',\r\n        4: 'The probability of the random variable 𝑋~𝒰(𝑎, 𝑏) realising from interval (𝑐, 𝑑), 𝑎 ≤ 𝑐 < 𝑑 ≤ 𝑏, is equal to the area under the graph of the density function above interval (𝑐, 𝑑):',\r\n        5: 'Expectation and variance 𝒰(𝑎, 𝑏) of distribution are',\r\n        6: 'The subject distribution was discussed in detail in the section on continuous random variables (link to the topic).',\r\n        7: '<strong>Example 4.3.1.</strong>',\r\n        8: 'Let us observe density function graphs of uniform distributions with different intervals, with marked expectations.',\r\n        9: 'For example, 𝒰(5, 10) distribution is given by density function',\r\n        10: 'Furthermore, 𝒰(−1,1) distribution is given by density function'\r\n      },\r\n      uniformna_distribucija_zadatak_1: {\r\n        title: 'Uniform distribution task',\r\n        1: 'The specification of a precision measuring instrument for mass indicated that the measured mass deviates from the actual mass by less than 1 𝜇𝑔 and that the distribution of error is uniform. Using the interactive tool, calculate the following:',\r\n        2: 'a) probability that the measured mass is smaller than the actual one',\r\n        3: 'b) probability that the measured mass is bigger than the actual one.',\r\n        4: '<strong>Solution</strong>',\r\n        5: 'The error in the measurement of mass is described by a random variable 𝑋 with a uniform distribution at interval (−1, 1). The density function of 𝒰(−1, 1) distribution is',\r\n        6: ', which is presented graphically in the previous example.',\r\n        7: 'a) If the actual and the measured mass are equal, the error is zero. Therefore, the probability that the measured mass is smaller than the actual one, 𝑃(𝑋 < 0), is equal to the area under the density function graph of 𝒰(−1, 1) distribution above the interval (−1, 0).',\r\n        8: 'It is noticeable that the area in question is the area of a rectangle with the lengths of its sides of 1 and 1/2 ; therefore, the required probability is 𝑃(𝑋 < 0) = 1/2.',\r\n        9: 'b) The probability that the measured mass is bigger than the actual one is equal to the area under the density function graph of 𝒰(−1, 1) distribution above the interval (0, 1) and it amounts to 𝑃(𝑋 > 0) = 1/2.'\r\n      },\r\n      normalna_distribucija: {\r\n        title: 'Normal distribution',\r\n        1: 'A random variable 𝑍 with density function',\r\n        2: 'has a <strong>normal distribution</strong> with parameters 𝜇 ∈ 𝑅 i 𝜎 > 0 and , denoted by 𝑍~𝒩(𝜇, 𝜎).',\r\n        3: '<strong>Expectation</strong> and <strong>variance</strong> of 𝒩(𝜇, 𝜎) distribution are the following:',\r\n        4: 'Therefore, 𝜎 > 0 is a standard deviation of 𝒩(𝜇, 𝜎) distribution.',\r\n        5: 'A normal distribution with expectation 𝜇 = 0 and standard deviation 𝜎 = 1 is called standard normal distribution.',\r\n        6: '<strong>Example 4.3.1.</strong>',\r\n        7: 'Let us observe density function graphs of normal distributions with different parameters 𝜇 and 𝜎 .',\r\n        8: 'Let us fix the standard deviation at 𝜎 = 1 and take the values −1, 0, 1, 2 for expectation  𝜇. It is noticeable that the density function reaches its minimum at expectation 𝜇.',\r\n        9: 'Let us fix the expectation at 𝜇 = 0 and take the values 0.1, 0.5, 1, 5 for standard deviation 𝜎. It is noticeable that, with the fixed expectation 𝜇, the increase in the standard deviation causes a decrease in the maximum density function of the normal distribution, and the graph becomes increasingly “flattened”.',\r\n        10: 'On the density function graph 𝒩(𝜇,𝜎), we will mark expectation 𝜇 and limits of intervals (𝜇−𝜎, 𝜇+𝜎), (𝜇−2𝜎, 𝜇+2𝜎), (𝜇−3𝜎, 𝜇+3𝜎)',\r\n        11: 'Using the interactive tool, we can calculate that, for arbitrary 𝜇 ∈ 𝑅 and 𝜎 > 0 , the following applies',\r\n        12: 'It follows that random variable 𝑍~𝒩(𝜇, 𝜎) deviates from its expectation by more than one standard deviation with probability 31.73%, the probability that it deviates from its expectation by more than two standard deviations is 4.55%, and the probability that it deviates from its expectation by more than three standard deviations is 0.27%.'\r\n      },\r\n      normalna_distribucija_interakcija: {\r\n        1: 'Expectation',\r\n        2: 'Starting value',\r\n        3: 'Standard deviation',\r\n        4: 'Ending value',\r\n        5: 'Density function chart',\r\n        6: 'P(c < Z < d)',\r\n        7: 'The interval ending values c and d are not well selected!',\r\n        8: 'Expectation',\r\n        9: 'Variance',\r\n        10: 'Values must be numbers',\r\n        11: 'Wrong deviation input',\r\n        12: '5. Statistical inference',\r\n        13: 'All values must be inserted.',\r\n        14: 'Values c and d must be within the interval',\r\n        15: ' with the condition of c < d.'\r\n      },\r\n      normalna_distribucija_zadatak_1: {\r\n        title: 'Normal distribution task',\r\n        1: 'A standardised intelligence test is calibrated based on the assumption that the intelligence quotient in a population is a normally distributed property with expectation 𝜇 = 100 and standard deviation  𝜎 = 15. Using the interactive tool, calculate the following:',\r\n        2: 'a) probability that a randomly selected person from the population has an intelligence quotient higher than the expected',\r\n        3: 'b) probability that a randomly selected person from the population has an intelligence quotient between 85 and 115.',\r\n        4: '<strong>Solution</strong>',\r\n        5: 'The intelligence quotient in the population is described by a random variable 𝑍~𝒩(100, 15).',\r\n        6: 'a) Since 𝐸[𝑍] = 100, we are looking for probability 𝑃(𝑍 > 100). This probability is equal to the area under the density function graph of 𝒩(100, 15) distribution above the interval (100, ∞) and it amounts to <div class=\"fraction\" top=\"1\" bottom=\"2\"></div>.',\r\n        7: 'b) The required probability 𝑃(85 < 𝑍 < 115) is equal to the area under the density function graph of 𝒩(100, 15) distribution above the (85, 115) interval and it amounts to 0.6827.',\r\n        8: '<strong>Task 4.3.1.</strong>'\r\n      },\r\n      normalna_distribucija_zadatak_interakcija: {\r\n        1: 'Expectation',\r\n        2: 'Starting value',\r\n        3: 'Standard deviation',\r\n        4: 'Ending value',\r\n        5: 'Density function chart',\r\n        6: 'P(c < Z < d)',\r\n        7: 'The interval ending values c and d are not well selected!',\r\n        8: 'The deviation must be greater than 1!'\r\n      },\r\n      distribucija: {\r\n        title: 'Distribution',\r\n        1: 'If 𝑍1, ... , 𝑍𝑛 are independent standard normal random variables, the sum of their squares',\r\n        2: 'is a random variable with <strong>𝝌𝟐 distribution</strong> with parameter 𝑛 ∈ 𝑁 and is denoted by 𝑌~𝜒2(𝑛).',\r\n        3: 'Parameter 𝑛 is called <strong>the number of degrees of freedom</strong> of 𝜒2 distribution.',\r\n        4: '<strong>Expectation</strong> and <strong>variance</strong> of 𝜒2(𝑛) distribution are the following:',\r\n        5: '<strong>Example 4.5.1.</strong>',\r\n        6: 'Density function graphs of distributions 𝜒2(3), 𝜒2(5) i 𝜒2(7, and with marked expectation are presented in the following figures.',\r\n        7: 'Using the interactive tool, examine 𝜒2(𝑛) distributions for other values of parameter .'\r\n      },\r\n      studentova_t_distribucija: {\r\n        title: 'Student’s t distribution',\r\n        1: 'If 𝑍~𝒩(0, 1) and 𝑌~𝜒2(𝑛), the random variable',\r\n        2: 'has <strong>Student’s t distribution</strong> with 𝑛 degrees of freedom and is denoted by 𝑇 ~𝑡(𝑛).',\r\n        3: '<strong>Expectation</strong> and <strong>variance</strong> of 𝑡(𝑛) distribution are the following:',\r\n        4: '<strong>Example 4.6.1.</strong>',\r\n        5: 'Density function graphs of distributions 𝑡(3), 𝑡(5) i 𝑡(7), and with marked expectation are presented in the following figure.',\r\n        6: 'Using the interactive tool, examine 𝑡(𝑛) distributions for other values of parameter 𝑛.'\r\n      }\r\n    }\r\n  },\r\n  sl: {\r\n    validation_messages: {\r\n      must_be_number: 'Mora biti število',\r\n      must_be_positive_number: 'Mora biti pozitivno število',\r\n      new_start: 'Za nov izračun vpišite novo število metov.',\r\n      must_not_be_empty: 'mora biti vpisano'\r\n    },\r\n    chaptersTitle: 'Poglavja',\r\n    literatureTitle: 'Literatura',\r\n    about: 'O projektu',\r\n    contact: 'Kontakt',\r\n    nextChapterParagraph: 'Naslednje poglavje',\r\n    go_button: 'Začni!',\r\n    chapters_button: 'Poglavja',\r\n    task_button: 'Naloga',\r\n    example: 'Primer',\r\n    task: 'Naloga',\r\n    chapter1Title: 'Opis podatkov',\r\n    chapter2Title: 'Osnove verjetnosti',\r\n    chapter3Title: 'Slučajna spremenljivka',\r\n    chapter4Title: 'Porazdelitve',\r\n    chapter5Title: 'Statistično sklepanje',\r\n    buttonText: 'Pojdi na poglavje',\r\n    showTaskSolution: 'Prikaži rešitev',\r\n    hideTaskSolution: 'Skrij rešitev',\r\n    for_those_who_want_more: 'Za tiste, ki bi radi izvedeli več',\r\n    show_interaction: 'Prikaži interakcijo',\r\n    show_data: 'Prikaži podatke',\r\n    show_table: 'Prikaži tabelo',\r\n    show: 'Prikaži',\r\n    show_interaction_1_9_1: 'Prikaži interakcijo',\r\n    show_interaction_1_9_2: 'Prikaži interakcijo',\r\n    sidebar: {\r\n      lesson1: {\r\n        1: 'Podatki',\r\n        2: 'Frekvence in relativne frekvence',\r\n        3: 'Stolpčni grafikon in histogram',\r\n        4: 'Aritmetična sredina ali povprečje',\r\n        5: 'Mediana in modus',\r\n        6: 'Minimum, maksimum in variacijski razmik',\r\n        7: 'Kvartili in kvartilni razmik',\r\n        8: 'Varianca in standardni odklon',\r\n        9: 'Graf kvartilov',\r\n        10: 'Razsevni diagram'\r\n      },\r\n      lesson2: {\r\n        1: 'Verjetnost',\r\n        2: 'Pogojna verjetnost'\r\n      },\r\n      lesson3: {\r\n        1: 'Slučajna spremenljivka',\r\n        2: 'Diskretna slučajna spremenljivka',\r\n        3: 'Zvezna slučajna spremenljivka',\r\n        4: 'Porazdelitvena funkcija',\r\n        5: 'Pričakovana vrednost',\r\n        6: 'Varianca in standardni odklon'\r\n      },\r\n      lesson4: {\r\n        1: 'Bernoullijeva porazdelitev',\r\n        2: 'Binomska porazdelitev',\r\n        3: 'Normalna porazdelitev'\r\n      },\r\n      lesson5: {\r\n        1: 'Populacija in vzorec',\r\n        2: 'Ocena deleža/verjetnosti',\r\n        3: 'Ocena pričakovane vrednosti in variance',\r\n        4: 'Interval zaupanja za pričakovano vrednost',\r\n        5: 'Interval zaupanja za delež/verjetnost',\r\n        6: 'Preizkušanje statističnih domnev',\r\n        7: 'Enostavna linearna regresija'\r\n      }\r\n    },\r\n    literature: {\r\n      1: 'Bain, L.E., Engelhardt, M. (2008). Introduction to Probability and Mathematical Statistics. \tBROOKS/COLE Cengage Learning.',\r\n      2: 'Benšić, M., Šuvak, N. (2013). Primijenjena statistika. Sveučilište J.J. Strossmayera u Osijeku, Odjel za matematiku.',\r\n      3: 'Bhattacharyya, G.K., Johnson, R.A. (1977). Statistical Concepts and Methods. John Wiley and Sons.',\r\n      4: 'Benšić, M., Šuvak, N. (2014). Uvod u vjerojatnost i statistiku. Sveučilište J.J. Strossmayera u Osijeku, Odjel za matematiku.',\r\n      5: 'Elezović, N. (2007). Diskretna vjerojatnost. Element.',\r\n      6: 'Elezović, N. (2007). Slučajne varijable. Element.',\r\n      7: 'Elezović, N. (2007). Statistika i procesi. Element.',\r\n      8: 'Ross, S.M. (2017). Introductory statistics. Academic Press.',\r\n      9: 'Sarapa, N. (1987). Teorija vjerojatnosti. Školska knjiga.',\r\n      10: 'Tintle, N., Chance, B.L., Cobb, G.W., Rossman, A.J., Roy, S., Swanson, T., VanderStoep, J. \t(2015). Introduction to Statistical Investigations: High School Binding. John Wiley.'\r\n    },\r\n    title_tag: {\r\n      homepage: 'STEDy - spoznaj statistiko',\r\n      chapter_literature: 'Seznam poglavij - STEDy',\r\n      privacy_policy: 'Varovanje zasebnosti - STEDy',\r\n      opisivanje_podataka: 'Opis podatkov - STEDy',\r\n      osnove_vjerojatnosti: 'Osnove verjetnosti - STEDy',\r\n      slucajna_varijabla: 'Slučajna spremenljivka - STEDy',\r\n      distribucije: 'Porazdelitve - STEDy',\r\n      statisticko_zakljucivanje: 'Statistično sklepanje - STEDy',\r\n      chapter1: {\r\n        1: 'Podatki - Opis podatkov - STEDy',\r\n        2: 'Frekvence in relativne frekvence - Opis podatkov - STEDy',\r\n        3: 'Stolpčni grafikon in histogram - Opis podatkov - STEDy',\r\n        4: 'Aritmetična sredina ali povprečje - Opis podatkov - STEDy',\r\n        5: 'Mediana in modus - Opis podatkov - STEDy',\r\n        6: 'Minimim, maksimum in variacijski razmik - Opis podatkov - STEDy',\r\n        7: 'Kvartili in kvartilni razmik - Opis podatkov - STEDy',\r\n        8: 'Varianca in standardni odklon - Opis podatkov - STEDy',\r\n        9: 'Graf kvartilov - Opis podatkov - STEDy',\r\n        10: 'Razsevni diagram - Opis podatkov - STEDy',\r\n      },\r\n      chapter2: {\r\n        1: 'Verjetnost - Osnove verjetnosti - STEDy',\r\n        2: 'Pogojna verjetnost - Osnove verjetnosti - STEDy'\r\n      },\r\n      chapter3: {\r\n        1: 'Slučajna spremenljivka - Slučajna spremenljivka - STEDy',\r\n        2: 'Diskretna slučajna spremenljivka - Slučajna spremenljivka - STEDy',\r\n        3: 'Zvezna slučajna spremenljivka - Slučajna spremenljivka - STEDy',\r\n        4: 'Porazdelitvena funkcija - Slučajna spremenljivka - STEDy',\r\n        5: 'Pričakovana vrednost - Slučajna spremenljivka - STEDy',\r\n        6: 'Varianca in standardni odklon - Slučajna spremenljivka - STEDy'\r\n      },\r\n      chapter4: {\r\n        1: 'Bernoullijeva porazdelitev - Porazdelitve - STEDy',\r\n        2: 'Binomska porazdelitev - Porazdelitve - STEDy',\r\n        3: 'Normalna porazdelitev - Porazdelitve - STEDy',\r\n      },\r\n      chapter5: {\r\n        1: 'Populacija in vzorec - Statistično sklepanje - STEDy',\r\n        2: 'Ocena deleža/verjetnosti - Statistično sklepanje - STEDy',\r\n        3: 'Ocena pričakovane vrednosti in variance - Statistično sklepanje - STEDy',\r\n        4: 'Interval zaupanja za pričakovano vrednost - Statistično sklepanje - STEDy',\r\n        5: 'Interval zaupanja za delež/verjetnost - Statistično sklepanje - STEDy',\r\n        6: 'Preizkušanje statističnih domnev - Statistično sklepanje - STEDy',\r\n        7: 'Enostavna linearna regresija - Statistično sklepanje - STEDy',\r\n      },\r\n    },\r\n    meta_content: {\r\n      homepage: 'STEDy je interaktivni portal, namenjen izobraževanju in promociji statistične pismenosti z e-učenjem.',\r\n      chapter_literature: 'Abecedni seznam literature, uporabljene za izdelavo izobraževalnega portala Stedy.',\r\n      privacy_policy: 'Interaktivni izobraževalni portal Stedy upravlja hrvaški statistični urad. Urad namenja veliko pozornosti zaščiti osebnih podatkov uporabnikov Stedyja.',\r\n      opisivanje_podataka: 'STEDy - Opis podatkov',\r\n      osnove_vjerojatnosti: 'STEDy - Osnove verjetnosti',\r\n      slucajna_varijabla: 'STEDy - Slučajna spremenljivka',\r\n      distribucije: 'STEDy - Porazdelitve',\r\n      statisticko_zakljucivanje: 'STEDy - Statistično sklepanje',\r\n      chapter1: {\r\n        1: 'Podatke zbiramo o enotah (npr. ljudje, živali, rastline, države, mesta, podjetja itd.), ki jim rečemo enote ali primeri.',\r\n        2: 'Frekvenca kategorije je število zabeleženih vrednosti spremenljivke, ki pripadajo tej kategoriji. Relativna frekvenca kategorije je frekvenca, deljena s skupnim številom podatkov za to spremenljivko.',\r\n        3: 'Stolpčni grafikon se uporablja za prikaz frekvenc ali relativnih frekvenc kategorij izbrane spremenljivke. Histogram se uporablja za prikaz številskih podatkov.',\r\n        4: 'Aritmetična sredina ali povprečje podatkov je seštevek vseh podatkov, deljen s skupnim številom podatkov. Aritmetična sredina ali povprečje je primerno za številske spremenljivke in je ena od mer srednje vrednosti.',\r\n        5: 'Mediana je število, ki nabor podatkov, urejen po velikosti, razdeli na dva dela, pri čemer oba dela vsebujeta enako število podatkov in noben podatek iz prvega dela ni večji od podatkov iz drugega dela.',\r\n        6: 'Minimum je najmanjše število v naboru, maksimum pa največje število v naboru. Razpon je groba mera razpršenosti podatkov, tj. razlika med maksimumom in minimumom.',\r\n        7: 'Kvartilni razmik je mera razpršenosti podatkov. Definirana je s pomočjo kvartila. Razlikujemo med prvim, drugim (mediana) in tretjim kvartilom.',\r\n        8: 'Varianca in standardni odklon sta meri razpršenosti podatkov, ki označujeta razpršenost podatkov okoli povprečja.',\r\n        9: 'Graf kvartilov (angl. box plot ali box-and-whisker plot) prikazuje odnos med minimumom, maksimumom, prvim in tretjim kvartilom ter mediano podatkov.',\r\n        10: 'Če so za posameznike zbrani podatki o dveh številskih vrednostih, je pare podatkov koristno prikazati z razsevnim diagramom.'\r\n      },\r\n      chapter1_tasks: {\r\n        1: 'Ustvarite svojo bazo podatkov, ki ima vsaj eno opisno ordinalno, eno opisno imensko in eno številsko spremenljivko.',\r\n        2: 'Za vsako tabelo iz primera grupirajte podatke spremenljivke, tako da je vsak interval dolžine 30. Ustvarite ustrezno tabelo frekvenc in relativnih frekvenc.',\r\n        3:  'Za prikaz katere spremenljivke je primeren stolpčni grafikon? Izberite to spremenljivko za predstavitev podatkov s stolpčnim grafikonom.',\r\n        4: 'Dana sta naslednja podatkovna nabora. Izračunajte povprečje vsakega od njiju. Kako sta si nabora podobna? Ali daje povprečje dovolj informacij o podatkovnem naboru?',\r\n        5:  'Razrednik določenega razreda spremlja koliko časa učenci igrajo računalniške igrice. Zato je učence prosil…',\r\n        6: 'Razrednik določenega razreda spremlja koliko časa učenci igrajo računalniške igrice. Zato je učence prosil…',\r\n        7: 'Razrednik določenega razreda spremlja koliko časa učenci igrajo računalniške igrice. Zato je učence prosil…',\r\n        8: 'Dana sta naslednja podatkovna nabora. Izračunajte povprečje in standardni odklon vsakega od njiju. Kako sta si nabora podobna?',\r\n        9: 'Slika prikazuje tri grafe kvartilov. Ali lahko določimo kateremu grafu ustreza posamezna trditev…',\r\n        10: 'Slika prikazuje razsevni grafikon spremenljivke čas, porabljen za igranje igric v nedeljo in ponedeljek. Ali opazite kakšno povezanost spremenljivk?'\r\n      },\r\n      chapter2: {\r\n        1: 'Verjetnost dogodka je število, ki izraža stopnjo prepričanja, da se bo dogodek zgodil.',\r\n        2: 'Z dodatnimi informacijami o izidu poskusa se lahko verjetnost nekega dogodka razlikuje od verjetnosti istega dogodka brez teh informacij.'\r\n      },\r\n      chapter2_tasks: {\r\n        1: 'Brata, oba hazarderja, sta popolnoma drugačna - prvi je pošten, drugi pa goljufa. Pošteni hazarder igra s pošteno kocko…',\r\n        2: 'Z interaktivnim orodjem izračunajte verjetnost, da boste pri metu kocke, ki ni nujno poštena, z dodatno informacijo dobili šestico…'\r\n      },\r\n      chapter3: {\r\n        1: 'Slučajna spremenljivka je funkcija, ki izidom poskusa (elementom množice Ω) priredi realna števila. Običajno jo označimo z veliko črko, npr. X.',\r\n        2: 'Diskretna slučajna spremenljivka je označena s končnim ali števnim naborom vrednosti.',\r\n        3: 'Zvezna slučajna spremenljivka ima zalogo vrednosti Z(𝑋), ki ni diskretna. Z(𝑋) je lahko interval ali množica vseh realnih števil.',\r\n        4: 'Porazdelitvena funkcija 𝐹 slučajne spremenljivke 𝑋 vsakemu realnemu številu 𝑥 določa verjetnost dogodka (𝑋 ≤ 𝑥): F(x)=P(X≤x),x∈R.',\r\n        5: 'Pričakovana vrednost slučajne spremenljivke 𝑋 je število, ki prikazuje sredino verjetnostne porazdelitve te slučajne spremenljivke. Označujemo jo s 𝐸[𝑋] ali 𝜇.',\r\n        6: 'Varianca slučajne spremenljivke 𝑋 je pozitivno število, ki prikazuje razpršenost porazdelitve slučajne spremenljivke 𝑋 v odnosu do njene pričakovane vrednosti 𝐸[𝑋].'\r\n      },\r\n      chapter3_tasks: {\r\n        1: 'Poskus je sestavljen iz dveh zaporednih metov kocke. Določite zalogo vrednosti slučajne spremenljivke, ki izidom poskusa priredi vsoto vrženih pik.',\r\n        2: 'Poskus je sestavljen iz dveh zaporednih metov kocke, ki ni nujno poštena. Izračunajte porazdelitev slučajne spremenljivke X, ki določa…',\r\n        3: 'Z interaktivnim orodjem za λ=1 izračunajte verjetnost, da med dvema zaporednima prihodoma tramvaja…',\r\n        4: '',\r\n        5: 'Če se sprašujemo, ali obstaja realno število, ki je nekako \"najbližje\" slučajni spremenljivki, je to pri enem od načinov merjenju oddaljenosti prav pričakovana vrednost.',\r\n        6: 'Z interaktivnim orodjem preučite kako se pričakovana vrednost in varianca slučajne spremenljivke X spreminjata glede na vrednost parametra λ>0…'\r\n      },\r\n      chapter4: {\r\n        1: 'Slučajna spremenljivka 𝑋, ki opisuje poskus s samo dvema možnima izidoma, neuspeh (označen z 0) in uspeh (označen z 1), ima Bernoullijevo porazdelitev s parametrom 𝑝 ∈ (0, 1)…',\r\n        2: 'Binomska porazdelitev prikazuje verjetnost dogajanja medsebojno izključujočih dogodkov za vsako število dogodkov posebej.',\r\n        3: 'Normalna porazdelitev je funkcija z dvema parametroma, in sicer s povprečjem in standardnim odklonom.',\r\n      },\r\n      chapter4_tasks: {\r\n        1: 'Pri igri Človek ne jezi se igralci mečejo pošteno kocko. Uspeh je, če igralec vrže šestico. Če vržejo 1, 2, 3, 4 ali 5, je to…',\r\n        2: 'Z interaktivnim orodjem izračunajte verjetnost, da bo kocka v 50 metih več kot petkrat padla na šestico. Ali je bolj verjetno, da bo šestica…',\r\n        3: 'Standardizirani test inteligence je umerjen na podlagi predpostavke, da je inteligenčni količnik v populaciji normalno porazdeljena lastnost…',\r\n      },\r\n     chapter5: {\r\n        1: 'Pri statističnem sklepanju so podatki, ki so na voljo, vrednosti, zabeležene za del populacije, ki jo imenujemo vzorec.',\r\n        2: 'Naj bo x1, 𝑥2, ... , 𝑥n vzorec spremenljivke 𝑋, ki ima lahko le dva izida. Izida lahko označimo kot 0 in 1, torej gre za vzorec iz Bernoullijeve porazdelitve…',\r\n        3: 'Če je  𝑥1, 𝑥2, ... , 𝑥𝑛 vzorec spremenljivke 𝑋 z neznano pričakovano vrednostjo 𝜇 = 𝐸[𝑋], je parameter 𝜇 ocenjen s povprečjem vzorca…',\r\n        4: 'Namesto da bi ocenili parameter z enim številom, lahko ocenimo interval, ki z določeno verjetnostjo vsebuje to število, običajno 0,95 ali 0,99. Takšen interval se imenuje interval zaupanja.',\r\n        5: 'Namesto da bi neznani delež značilnosti v populaciji ocenili z enim številom, ga lahko ocenimo z intervalom zaupanja za delež.',\r\n        6: 'Predpostavimo, da igramo igro, v kateri vržemo kovanec in zmagamo, če pade na cifro. Po desetih metih je dvakrat padla cifra, osemkrat pa grb…',\r\n        7: 'Z regresijskimi metodami lahko opisujemo odnos med spremenljivkama X in Y. Če so točke, prikazane na razsevnem diagramu, videti razpršene',\r\n      },\r\n      chapter5_tasks: {\r\n        1: 'Pri metanju kovanca pade kovanec v dveh metih dvakrat na cifro. Poskus ponovimo 200-krat.',\r\n        2: 'Na Hrvaškem živi 1635 od 2029 anketiranih gospodinjstev v stanovanju ali hiši…',\r\n        3: '',\r\n        4: 'Na Hrvaškem gospodinjstva povprečno porabijo 5494 kun na leto za obleko in obutev…',\r\n        5: 'Predpostavimo, da na volitvah sodelujeta samo dva kandidata, A in B. Cilj ankete je napovedati zmagovalca.',\r\n        6: 'Na vzorcu 50 oseb so izvedli test, ali prepoznajo razliko med dragim in pocenim vinom.',\r\n        7: '',\r\n      },\r\n      cookies: {\r\n\t\t1: 'Spletno mesto Statističnega urada RS uporablja piškotke za analizo obiska ter za zagotavljanje spletne storitve in funkcionalnosti, saj teh brez piškotkov ne bi moglo nuditi. Ali se strinjate z namestitvijo piškotkov?',\r\n        2: 'O piškotkih.',\r\n        3: 'Ne strinjam se',\r\n        4: 'Strinjam se',\r\n      },\r\n    },\r\n    accessibility: {\r\n        1: 'Izjava o dostopnosti',\r\n        2: 'Statistični urad RS (dalje SURS) se zavezuje, da bo omogočal dostopnost v skladu z <a href=\"http://www.pisrs.si/Pis.web/pregledPredpisa?id=ZAKO7718\">Zakonom o dostopnosti spletišč in mobilnih aplikacij</a>.',\r\n        3: '<strong>Izjava o dostopnosti<strong>',\r\n        4: 'Ta izjava o dostopnosti se nanaša na spletno stran <a href=\"https://www.stat.si/stedy\">STEDy</a>. Spletna stran STEDy je z Zakonom o dostopnosti spletišč in mobilnih aplikacij skladna <strong>samo delno</strong>, in sicer toliko, kot je to zagotovil hrvaški statistični urad, od katerega jo je SURS prevzel, da bi jo priredil in prevedel v slovenščino.',\r\n        5: 'SURS spletne strani STEDy ni dodatno prilagodil <a href=\"https://www.w3.org/WAI/standards-guidelines/wcag/\">smernicam WCAG 2.0 ali WCAG 2.1 </a>(angl. Web Content Acessibility Guidelines) za dostopnost ranljivim skupinam, saj bi dodatna predelava prevzete spletne strani pomenila nesorazmerno finančno in kadrovsko breme.',\r\n        6: 'Za zagotavljanje zahtev glede dostopnosti so bile sistemsko zagotovljene nekatere prilagoditve, na primer:',\r\n        7: 'odzivno oblikovanje (angl. responsive) – postavitev vsebine se prilagaja ločljivosti zaslona;',\r\n        8: 'delna podpora za navigacijo s tipkovnico (prilagoditev za uporabnike, ki ne morejo uporabljati miške);',\r\n        9: 'delno ustrezni barvni kontrasti (med besedilom in ozadjem).',\r\n       10: '<strong>Povratne in kontaktne informacije</strong>',\r\n       11: 'SURS bo vesel vseh informacij o vaši uporabniški izkušnji pri uporabi spletne strani STEDy in tudi vseh vaših predlogov o morebitnih dodatnih prilagoditvah spletnega mesta za ranljive skupine.',\r\n       12: 'Tudi o morebitnih primerih vsebine, ki bi bila  neskladna z Zakonom o dostopnosti spletišč in mobilnih aplikacij, lahko prav tako obvestite SURS. Skušali jih bomo izboljšati ali vam omogočiti alternativne vire dostopa.',\r\n       13: 'Odgovor boste prejeli najpozneje v osmih dneh po prejemu obvestila ali prošnje. Če vam SURS v tem času ne bo mogel ustrezno odgovoriti, vam bo sporočil, kdaj bo odgovor na voljo in  zakaj je prišlo do zamude.',\r\n       14: 'Vse informacije, ki so dostopne na spletnih straneh SURS, tudi o njegovih drugih produktih, lahko dobite:',\r\n       15: 'po telefonu: <a href=\"tel:012416404\">01 241 64 04</a>,',\r\n       16: 'na elektronskem naslovu: <a href=\"mailto:gp.surs@gov.si\">gp.surs@gov.si</a>,',\r\n       17: 'osebno na Statističnem uradu RS (Litostrojska cesta 54, 1000 Ljubljana).',\r\n       18: 'Nekatere informacije o delovanju SURS so dostopne tudi na SURS-ovi predstavitveni strani na <a href=\"https://www.gov.si/drzavni-organi/vladne-sluzbe/statisticni-urad/\">gov.si</a>.',\r\n       19: '<strong>Priprava izjave o dostopnosti</strong>',\r\n       20: 'Ta izjava je bila pripravljena 1. oktobra 2021 na podlagi samoocene, nazadnje pregledana pa 5. oktobra 2021.',\r\n       21: '<strong>Izvršilni postopek</strong>',\r\n       22: 'Če opazite kakršno koli neupoštevanje določil Zakona o dostopnosti spletišč in mobilnih aplikacij, lahko to prijavite inšpektorjem za informacijsko družbo, po navadni ali elektronski pošti na naslov:',\r\n       23: 'Uprava Republike Slovenije za informacijsko varnost<br>MINISTRSTVO ZA JAVNO UPRAVO<br>Tržaška cesta 21<br>1000 Ljubljana<br><a href=\"tel:014784778\">01 478 47 78</a><br><a href=\"mailto:gp.uiv@gov.si\">gp.uiv@gov.si</a>',\r\n    },\r\n    privacy_cookies: {\r\n       title: 'O spletni strani STEDy in piškotkih',\r\n       1: 'Spletno stran STEDy je razvil Hrvaški državni statistični urad skupaj z univerzo J. J. Strossmayerja v Osijeku. Njeno izdelavo je sofinanciral Eurostat, evropski statistični urad. Prevod in priredbo v slovenščini je pripravil Statistični urad RS (dalje SURS). Prevod v slovenščino je recenziralo Statistično društvo Slovenije.',\r\n       2: '<strong>Spremljanje analitike obiska</strong>',\r\n       3: 'SURS zbira med uporabo spletne strani STEDy podatke o uporabi (analitika obiska). Za ta namen in za  optimalno delovanju spletne strani ter za zagotavljanje dobre uporabniške izkušnje lahko na naprave uporabnikov shranjuje piškotke.',\r\n       4: '<strong>Podatki o uporabi</strong>',\r\n       5: 'Podatki o uporabi so na primer podatki o napravi, ki jih uporabniki uporabljajo za dostop do spleta, naslov internetnega protokola v računalniku (npr. naslov IP), vrsta brskalnika, različica brskalnika, spletne strani znotraj STEDy, ki so jih uporabniki obiskali, čas in datum obiska, čas, preživet na teh spletnih straneh, edinstveni identifikatorji naprav in drugi diagnostični podatki.',\r\n       6: 'Tako zbrane podatke SURS uporablja:',\r\n       7: 'za zagotavljanje in vzdrževanje spletne strani;',\r\n       8: 'za spremljanje uporabe spletne strani;',\r\n       9: 'za odkrivanje, preprečevanje in reševanje tehničnih težav, povezanih z uporabo spletne strani;',\r\n      10: 'za zagotavljanje pomoči in podpore uporabnikom;',\r\n      11: 'za analize ali zagotavljanje informacij za izboljšanje spletne strani.',\t\r\n      12: '<strong>Piškotki</strong>',\r\n      13: 'SURS spremlja dejavnosti, povezanih s spletno stranjo STEDy, in zbira določene informacije s pomočjo piškotkov. Piškotki so datoteke z majhno količino podatkov, ki lahko vsebujejo anonimni enolični identifikator in se v vaš brskalnik naložijo s spletne strani, ki jo uporabljate, ter se shranijo na vašo napravo.',\r\n      14: 'Primeri piškotkov, ki jih uporablja SURS:',\r\n      15: '<strong>začasni ali sejni piškotki</strong> – s temi SURS upravlja spletno stran;',\r\n      16: '<strong>funkcionalni ali preferenčni piškotki</strong> – s temi si SURS zapomni vaše preference in različne nastavitve;',\r\n      17: '<strong>varnostni piškotki</strong> – te SURS uporablja za zagotavljanje varnosti.',\r\n      18: 'IZDAJATELJ',\r\n      19: 'ŽIVLJENJSKA DOBA PIŠKOTKOV',\r\n      20: 'NAMEN',\r\n      21: 'IME PIŠKOTKA',\r\n      22: 'Statistični urad',\r\n      23: 'Sejni (1), dnevni (1), letni (3).',\r\n      24: 'Gre za lastne piškotke, namenjene spremljanju analitike obiska spletne strani STEDy (orodje Piwik), beleženju uporabnikove odločitve, ali je piškotke sprejel ali ne, in za varnost.',\r\n      25: 'pk_id, pk_ref, pk_ses, piwik_agreement, RequestVerificationToken, stat.si.STEDy.analytics',\r\n      26: '<strong>Upravljanje piškotkov</strong>',\r\n      27: 'Piškotki, ki jih uporablja spletna stran STEDy, se vam na računalnik oz. mobilno napravo naložijo le, če izberete možnost »Strinjam se«. Če izberete to možnost, se na vašem računalniku namestijo vsi piškotki, navedeni v zgornji tabeli. Če izberete nasprotno možnost (»Se ne strinjam«), se vam piškotki ne bodo naložili,  vaš obisk se ne bo beležil, vendar vam lahko tudi nekatere funkcionalnosti spletne strani ne bodo delovale.',\r\n      28: 'Večina spletnih brskalnikov sprejme piškotke samodejno. Delovanje spletnega brskalnika lahko v nastavitvah spremenite tako, da računalnik piškotke zavrne ali da prej, preden se piškotek shrani, prejmete opozorilo. Namestitev piškotkov v brskalniku lahko tudi popolnoma preprečite za vse spletne strani, ki jih boste obiskali. Piškotke, ki so že shranjeni na vašem računalniku, lahko izbrišete.',\r\n      29: 'Povezave do navodil, kako lahko izključite piškotke na vašem spletnem brskalniku:',\r\n      30: '<a href=\"https://support.mozilla.org/en-US/kb/cookies-information-websites-store-on-your-computer?redirectlocale=en-US&redirectslug=Cookies\">Mozilla Firefox</a>',\r\n      31: '<a href=\"https://support.google.com/chrome/answer/95647?hl=en\">Chrome</a>',\r\n      32: '<a href=\"https://support.apple.com/guide/safari/manage-cookies-and-website-data-sfri11471/mac\">Safari</a>',\r\n      33: '<a href=\"https://support.microsoft.com/en-us/microsoft-edge/delete-cookies-in-microsoft-edge-63947406-40ac-c3b8-57b9-2a946a29ae09\">Edge</a>',\r\n      34: 'Informacije o uporabi piškotkov v brskalnikih mobilnih telefonov ter navodila, kako zavrniti ali izbrisati te piškotke, boste našli v priročniku za uporabo mobilne naprave.',\r\n      35: '<strong>Vaše nastavitve piškotkov</strong>',\r\n      36: 'Svojo odločitev o piškotkih na spletni strani STEDy lahko kadarkoli spremenite.',\r\n      37: 'Spremeni odločitev'\r\n    },\r\n    table_head: {\r\n      1: 'ŠTEVILKA UČENCA',\r\n      2: 'ČAS IGRANJA (min)',\r\n      3: 'SPOL',\r\n      4: 'OCENA'\r\n    },\r\n    student_table: {\r\n      table_head: {\r\n        student_number: 'ŠTEVILKA UČENCA',\r\n        play_time: 'ČAS IGRANJA (min)',\r\n        sex: 'SPOL',\r\n        grade: 'OCENA'\r\n      },\r\n      table_body: {\r\n        1: '1',\r\n        2: '2',\r\n        3: '3',\r\n        4: '4',\r\n        5: '5',\r\n        6: '6',\r\n        7: '7',\r\n        8: '8',\r\n        9: '9',\r\n        10: '10',\r\n        11: '11',\r\n        12: '12',\r\n        13: '13',\r\n        14: '14',\r\n        15: '15',\r\n        16: '16',\r\n        17: '17',\r\n        18: '18',\r\n        19: '19',\r\n        20: '20',\r\n        21: '21',\r\n        22: '22',\r\n        23: '23',\r\n        24: '24',\r\n        47: '47',\r\n        177: '177',\r\n        124: '124',\r\n        135: '135',\r\n        69: '69',\r\n        88: '88',\r\n        0: '0',\r\n        120: '120',\r\n        63: '63',\r\n        57: '57',\r\n        79: '79',\r\n        244: '244',\r\n        99: '99',\r\n        76: '76',\r\n        166: '166',\r\n        193: '193',\r\n        74: '74',\r\n        51: '51',\r\n        data20: '20',\r\n        data19: '19',\r\n        189: '189',\r\n        zene: 'ž',\r\n        muskarci: 'm',\r\n        nedovoljan: 'nezadostno',\r\n        dovoljan: 'zadostno',\r\n        dobar: 'dobro',\r\n        vrlo_dobar: 'zelo dobro',\r\n        odlican: 'odlično'\r\n      }\r\n    },\r\n    frequency_table_big: {\r\n      table_head: {\r\n        play_time: 'ČAS IGRANJA (min)',\r\n        frequency: 'FREKVENCA',\r\n        relative_frequency: 'RELATIVNA FREKVENCA (%)'\r\n      },\r\n      table_body: {\r\n        1: '0',\r\n        2: '19',\r\n        3: '20',\r\n        4: '47',\r\n        5: '51',\r\n        6: '57',\r\n        7: '63',\r\n        8: '69',\r\n        9: '74',\r\n        10: '76',\r\n        11: '79',\r\n        12: '88',\r\n        13: '99',\r\n        14: '120',\r\n        15: '124',\r\n        16: '135',\r\n        17: '166',\r\n        18: '177',\r\n        19: '189',\r\n        20: '193',\r\n        21: '244',\r\n        22: '3',\r\n        23: '1',\r\n        24: '0,12',\r\n        25: '0,04',\r\n        26: '2',\r\n        27: '0,08'\r\n      }\r\n    },\r\n    frequency_table_small: {\r\n      table_head: {\r\n        play_time: 'ČAS IGRANJA (min)',\r\n        frequency: 'FREKVENCA',\r\n        relative_frequency: 'RELATIVNA FREKVENCA (%)'\r\n      },\r\n      table_body: {\r\n        1: '0',\r\n        2: '<0, 60]',\r\n        3: '<60, 120]',\r\n        4: '> 120',\r\n        5: 'skupaj'\r\n      }\r\n    },\r\n    socials: {\r\n      facebook: 'https://www.facebook.com/StatSlovenija/',\r\n      instagram: 'https://www.instagram.com/statslovenija/',\r\n      youtube: 'https://www.youtube.com/user/StatSlovenia',\r\n      linkedin: '',\r\n      github: ''\r\n    },\r\n    homepage: {\r\n      intro: '<span>STEDy - spoznaj statistiko</span>',\r\n      about_section: {\r\n        1: 'Mislite, da je statistika prezapletena? Da nikakor ni za vas?',\r\n        2: 'Zavedamo se, da ste se računanja odstotkov naučili že v osnovni šoli, hkrati pa tudi tega, da je precej verjetno, da so intervali, kvartili in vrste porazdelitev ostali za vas megleno področje. Upamo, da ne za dolgo.',\r\n        3: 'Zdaj imate na voljo statistični izobraževalni portal <strong>STEDy</strong> in ta vam bo le v nekaj korakih razložil statistične pojme, ki se včasih zdijo zelo zapleteni. Če pa ste ljubitelj statistike že od nekdaj, je ta aplikacija natančno to, kar potrebujete, da boste svoje znanje razširili, obnovili ali preizkusili! STEDy je namenjen vsem – širši javnosti, učiteljem, profesorjem, učencem, dijakom in študentom ter ljubiteljem statistike.',\r\n        4: 'Pri razlaganju statističnih pojmov smo se skušali izogniti najpogostejši metodi, zato se STEDy ne omejuje samo na teoretično ozadje, temveč vam ponuja tudi praktične primere, interaktivne vizualizacije in naloge, s katerimi lahko takoj preverite svoje razumevanje statistike in njeno uporabnost.',\r\n        5: 'Statistična pismenost je v današnjem času, ko smo preplavljeni s številnimi informacijami in podatki, zelo koristna in uporabna veščina, saj nam pomaga, da statistične podatke, kadar naletimo nanje, lažje razumemo in jih znamo tudi kritično ovrednotiti. Ne glede na to, ali je statistika del vašega vsakdana in vam pomaga, da so odločitve, ki jih sprejemate, podprte z dejstvi, ali pa zgolj ovira, ki bi jo radi premagali, upamo, da bo STEDy odličen pomočnik pri reševanju vaših statističnih izzivov.',\r\n        6: 'Pripnite si pasove, potopite se v čarobni svet števil in se poigrajte s podatki!',\r\n        7: 'Statistični izobraževalni portal STEDy je pripravil hrvaški statistični urad skupaj z univerzo J. J. Strossmayerja v Osijeku kot del Eurostatovega projekta Support for statistical literacy actions in the area of a competition, gamification and e-learning. Pri projektu so sodelovali profesorica Mirta Benšić, docent Danijel Grahovac in izredni profesor Nenad Šuvak.',\r\n        8: 'Gradivo je prevedel v slovenščino in priredil Statistični urad Republike Slovenije.'\r\n      },\r\n      contact: {\r\n        1: 'Imate vprašanja? Stopite v stik z nami!',\r\n        2: 'Poizvedbe, sporočila in komentarje lahko pošljete na <a href=\"mailto: gp.surs@gov.si\">gp.surs@gov.si</a>',\r\n        3: 'Stopite v stik z nami'\r\n      },\r\n      footer: {\r\n        1: 'O STEDy in piškotkih',\r\n        2: 'Hrvaški statistični urad',\r\n        3: 'Spletno stran je razvil hrvaški statistični urad skupaj z univerzo J. J. Strossmayerja v Osijeku.</br> Njeno izdelavo je sofinanciral Eurostat, evropski statistični urad. Prevedel in priredil jo je Statistični urad RS.',\r\n        4: 'Odprtokodni projekt',\r\n        5: 'Dostopnost'\r\n      }\r\n    },\r\n    privacy_policy: {\r\n      title: 'Varovanje zasebnosti',\r\n      1: 'Spletno stran <a href=\"www.stedy.hr\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"link\">www.stedy.hr</a> upravlja hrvaški statistični urad (v nadaljevanju urad). Veliko pozornost namenja zaščiti osebnih podatkov uporabnikov omenjene spletne strani.',\r\n      2: 'Politika varovanja zasebnosti (v nadaljevanju politika) ureja način uporabe podatkov, ki jih urad obdeluje ali zbira, ko uporabniki obiščejo to spletno stran. Urad zbira vaše osebne podatke le, če nam jih izrecno date na voljo in se strinjate, da jih uporabimo.',\r\n      3: 'Med različnimi oblikami interakcije na spletni strani <a href=\"www.stedy.hr\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"link\">www.stedy.hr</a> urad zbira vaše osebne podatke, kot je vaš e-poštni naslov, pa tudi druge podatke, na primer piškotke in podatke o uporabi.',\r\n      4: 'Piškotki',\r\n      5: 'Za spremljanje dejavnosti, povezanih s to spletno stranjo, in za zbiranje določenih informacij uporabljamo piškotke in podobne tehnologije sledenja. Piškotki so datoteke z majhno količino podatkov, ki lahko vključujejo anonimni enolični identifikator in se v vaš brskalnik pošljejo s spletne strani, ki jo uporabljate, ter se shranijo na vašo napravo. Uporabljajo se tudi tehnologije sledenja kot so svetilniki (beacons), oznake (tags) in skripti (scripts), ki se uporabljajo za zbiranje informacij in sledenje informacijam ter za izboljšanje in analizo navad uporabe prej omenjene spletne strani.',\r\n      6: 'Brskalniku lahko naročite, naj zavrne vse piškotke ali sporoči, ko je piškotek poslan. Vendar pa, če piškotkov ne sprejmete, nekaterih delov spletne strani morda ne boste mogli uporabljati.',\r\n      7: 'Primer piškotkov, ki jih uporabljamo:',\r\n      8: '<strong>začasni ali sejni piškotki</strong> – z njimi upravljamo našo spletno stran',\r\n      9: '<strong>funkcionalni ali preferenčni piškotki</strong> – z njimi si zapomnimo vaše preference in različne nastavitve',\r\n      10: '<strong>varnostni piškotki</strong> – uporabljamo jih zaradi varnosti.',\r\n      11: 'Podatki o uporabi',\r\n      12: 'Podatki o uporabi lahko vključujejo informacije, kot so podatki o napravi, ki jo uporabljate za internetno povezavo, naslov internetnega protokola v računalniku (npr. naslov IP), vrsta brskalnika, različica brskalnika, spletne strani, ki jih obiskujete, čas in datum vašega obiska, čas, preživet na teh spletnih straneh, edinstveni identifikatorji naprav in drugi diagnostični podatki.',\r\n      13: '<strong>Uporaba podatkov</strong>',\r\n      14: 'Urad zbrane podatke uporablja:',\r\n      15: 'za zagotavljanje in vzdrževanje spletne strani',\r\n      16: 'za spremljanje uporabe spletne strani',\r\n      17: 'za odkrivanje, preprečevanje in reševanje tehničnih težav, povezanih z uporabo spletne strani',\r\n      18: 'za zagotavljanje pomoči in podpore uporabnikom',\r\n      19: 'za analize ali zagotavljanje dragocenih informacij za izboljšanje spletne strani',\r\n      20: 'da omogoča uporabnikom sodelovanje v interaktivnih funkcijah spletne strani',\r\n      21: 'za obveščanje uporabnikov o spremembah na spletni strani.',\r\n      22: '<strong>Prenos podatkov</strong>',\r\n      23: 'Vaši podatki, vključno z osebnimi podatki, se lahko prenašajo in vzdržujejo na računalnikih zunaj vaše države ali zunaj Evropske unije ali druge državne jurisdikcije, kjer se zakoni o varstvu podatkov lahko razlikujejo od zakonov Evropske unije.',\r\n      24: 'Če se nahajate zunaj Republike Hrvaške in se odločite, da nam boste posredovali svoje podatke, upoštevajte, da podatke, vključno z osebnimi podatki, prenesemo v Republiko Hrvaško in jih tam obdelujemo.',\r\n      25: 'Urad bo sprejel vse potrebne ukrepe, da bo zagotovil varno obdelavo vaših podatkov v skladu s to politiko varovanja zasebnosti ter to, da se vaši osebni podatki ne bodo prenašali, če za njihovo zaščito ne bo vzpostavljen ustrezen nadzor.',\r\n      26: 'Urad lahko vaše osebne podatke posreduje tretjim osebam samo v naslednjih primerih: ',\r\n      27: 'če obstaja zakonska obveznost ali izrecno zakonsko pooblastilo',\r\n      28: 'če za opravljanje določenih storitev najamemo obdelovalca, ki deluje izključno po naročilu urada, pri čemer urad sprejme vse ukrepe za varstvo podatkov',\r\n      29: 'če je podatke treba posredovati tretjim osebam za izvedbo pogodbe s posameznikom, na katerega se osebni podatki nanašajo.',\r\n      30: 'Pri prenosu podatkov posameznika, na katerega se osebni podatki nanašajo, urad dosledno spoštuje načelo omejitve obdelave s prenosom najmanjše količine potrebnih podatkov in spoštovanjem vseh drugih ustreznih načel varstva podatkov. Tretje osebe imajo dostop do vaših osebnih podatkov samo za izvajanje storitev v imenu urada in se zavezujejo, da bodo ohranile zaupnost vaših osebnih podatkov in da jih bodo uporabljale le v skladu s posebnim namenom, za katerega se prenašajo',\r\n      31: '<strong>Varnost podatkov</strong>',\r\n      32: 'Varnost vaših podatkov je za nas pomembna, vendar ne pozabite, da noben način prenosa prek interneta ali način elektronskega shranjevanja ni povsem varen. Čeprav si prizadevamo za komercialno sprejemljiva sredstva za varstvo vaših osebnih podatkov, ne moremo zagotoviti njihove popolne varnosti.',\r\n      33: '<strong>Analitika</strong>',\r\n      34: 'Urad lahko za spremljanje in analizo uporabe spletne strani najame neodvisne ponudnike storitev.',\r\n      35: '<strong>Google Analitics</strong>',\r\n      36: 'Google Analytics je storitev spletne analitike, ki jo ponuja Google in ki spremlja in poroča o prometu na spletni strani. Google zbrane podatke uporablja za sledenje uporabi in spremljanje uporabe te spletne strani. Ti podatki se delijo z drugimi Googlovimi storitvami. Google lahko zbrane podatke uporabi za kontekstualizacijo in prilagajanje oglasov lastne oglaševalske mreže',\r\n      37: 'Če želite onemogočiti, da so vaše dejavnosti na tej spletni strani na voljo Google Analytics, lahko namestite dodatek za brskalnik za izključitev storitve Google Analytics. Dodatek preprečuje, da bi JavaScript Google Analytics (ga.js, analytics.js in dc.js) z Google Analytics delil informacije o dejavnostih obiskovalcev.',\r\n      38: 'Za več informacij o Googlovih praksah glede zasebnosti obiščite spletno stran Google Privacy & Terms website: <a href=\"https://policies.google.com/privacy?hl=en\" class=\"link\" target=\"_blank\" rel=\"noopener noreferrer\">https://policies.google.com/privacy?hl=en</a>',\r\n      39: '<strong>Povezave do drugih strani</strong>',\r\n      40: 'Ta spletna stran lahko vsebuje povezave do drugih spletnih strani, ki jih ne upravlja urad. Priporočamo vam, da pregledate politiko varovanja zasebnosti vsake spletne strani, ki jo obiščete. Urad nima nadzora nad vsebino, politiko varovanja zasebnosti ali prakso spletnih strani ali storitev tretjih oseb in za to ne prevzema nobene odgovornosti.',\r\n      41: '<strong>Varovanje zasebnosti oseb, mlajših od 18 let</strong>',\r\n      42: 'To spletno stran lahko uporabljajo tudi osebe, mlajše od 18 let. Urad ne zbira osebnih podatkov o osebah, mlajših od 18 let. Če ste starš ali skrbnik in veste, da nam je vaš otrok priskrbel osebne podatke, se obrnite na urad. Če urad ugotovi, da so bili osebni podatki oseb, mlajših od 18 let, zbrani brez veljavnega soglasja starša ali skrbnika, bo razumno in v najkrajšem možnem času izvedel naslednje korake:',\r\n      43: 'podatke odstranil iz uradovih evidenc',\r\n      44: 'če izbris ni mogoč, bo zagotovil, da se osebni podatki ne bodo uporabljali za noben drug namen',\r\n      45: 'podatkov ne bo v nobenem primeru dal nobeni tretji osebi.',\r\n      46: '<strong>Spremembe politike varovanja zasebnosti</strong>',\r\n      47: 'Urad si pridržuje pravico do spremembe te politike z objavo nove politike na tej spletni strani. Priporočamo vam, da jo redno pregledujete glede morebitnih sprememb te politike. Spremembe te politike veljajo, ko so objavljene na tej spletni strani.',\r\n      48: 'Vaše pravice',\r\n      49: 'Kar zadeva obdelavo osebnih podatkov imate pravico uveljavljati naslednje pravice: ',\r\n      50: 'pravica do dostopa do osebnih podatkov',\r\n      51: 'pravica do popravka osebnih podatkov',\r\n      52: 'pravica do izbrisa osebnih podatkov (\"pravica do pozabe\") ',\r\n      53: 'pravica do omejitve obdelave',\r\n      54: 'pravica do prenosa podatkov ',\r\n      55: 'pravica do pritožbe.',\r\n      56: 'Kako lahko uveljavljate svoje pravice?',\r\n      57: 'Za uresničevanje prej omenjenih pravic in s svojimi vprašanji v zvezi z vašimi osebnimi podatki se lahko obrnete na naše uradnike za varstvo podatkov tako, da pošljete e-sporočilo na <a href=\"mailto: gp.surs@gov.si\" class=\"link\">gp.surs@gov.si</a> .',\r\n      58: 'Zahteve in poizvedbe bomo obdelali brez nepotrebnega odlašanja in v skladu z zakonskimi obveznostmi ter vas o sprejetih ukrepih pisno obvestili.',\r\n      59: 'Če menite, da urad deluje nezakonito in te zadeve ne morete rešiti v sodelovanju z nami, imate pravico vložiti pritožbo pri nadzornem organu za varstvo osebnih podatkov v Republiki Hrvaški - Agencija za zaštitu osobnih podataka (AZOP).'\r\n    },\r\n    opisivanje_podataka: {\r\n      chapterNumber: '&mdash; 1. poglavje &mdash;',\r\n      title: 'Opis podatkov',\r\n      table: {\r\n        rank: 'ŠTEVILKA UČENCA',\r\n        time: 'ČAS IGRANJA (min)',\r\n        sex: 'SPOL',\r\n        grade: 'OCENA',\r\n        freq: 'FREKVENCA',\r\n        relFreq: 'RELATIVNA FREKVENCA (%)'\r\n      },\r\n      game_time: {\r\n        1: '47',\r\n        2: '177',\r\n        3: '124',\r\n        4: '135',\r\n        5: '69',\r\n        6: '88',\r\n        7: '0',\r\n        8: '120',\r\n        9: '63',\r\n        10: '57',\r\n        11: '79',\r\n        12: '244',\r\n        13: '99',\r\n        14: '76',\r\n        15: '166',\r\n        16: '193',\r\n        17: '19',\r\n        18: '74',\r\n        19: '51',\r\n        20: '20',\r\n        21: '189',\r\n        22: 'skupaj'\r\n      },\r\n      sex: {\r\n        1: 'ž',\r\n        2: 'm',\r\n        3: 'skupaj'\r\n      },\r\n      grade: {\r\n        1: 'nezadostno',\r\n        2: 'zadostno',\r\n        3: 'dobro',\r\n        4: 'zelo dobro',\r\n        5: 'odlično',\r\n        6: 'skupaj'\r\n      },\r\n      resultTable: {\r\n        1: 'KATEGORIJA',\r\n        2: 'FREKVENCA',\r\n        3: 'RELATIVNA FREKVENCA (%)'\r\n      },\r\n      podaci: {\r\n        title: 'Podatki',\r\n        1: 'Podatke zbiramo o <strong>enotah</strong> (npr. ljudje, živali, rastline, države, mesta, podjetja itd.), ki jim rečemo <strong>enote</strong> ali <strong>primeri</strong>.',\r\n        2: 'Lastnosti, ki nas zanimajo o posameznikih, se imenujejo <strong>spremenljivke</strong>.',\r\n        3: 'Evidenca zbranih podatkov je prikazana v <strong>tabelah</strong>.',\r\n        4: '<strong>Vrste spremenljivk:</strong>',\r\n        5: '<strong>številske spremenljivke</strong> – vrednosti teh spremenljivk so števila:',\r\n        6: '<strong>opisne spremenljivke</strong> – vrednosti teh spremenljivk niso številske ampak neštevilske vrednosti, imenovane <strong>kategorije</strong>. Opisne spremenljivke delimo v dve skupini:',\r\n        7: '<strong>nominalne (ali imenske) spremenljivke</strong> – med kategorijami spremenljivk ni naravnega reda (npr. spol, barva, ime mesta, rod živali itd.);',\r\n        8: '<strong>ordinalne (ali vrstne) spremenljivke</strong> – med kategorijami spremenljivk obstaja naravni red (npr. strokovna izobrazba osebe, ocena strinjanja od sploh se ne strinjam do popolnoma se strinjam itd.). Kategorije ordinalnih spremenljivk so običajno oštevilčene.',\r\n        9: '<strong>Primer 1.1.1.</strong>',\r\n        10: 'Razrednik določenega razreda spremlja, koliko časa porabijo njegovi učenci za igranje računalniških igric. Zato je učence prosil, naj vodijo evidenco, v tabelo pa je zapisal podatke o tem, koliko časa so v nedeljo preživeli pri igranju računalniških igric. Dodal je podatke o spolu učencev in oceni, ki so jo dobili na zadnjem izpitu iz matematike. Podatki so predstavljeni v naslednji tabeli.',\r\n        11: '<strong>Pri čemer:</strong>',\r\n        12: 'je čas igranja številska spremenljivka',\r\n        13: 'spol opisna imenska spremenljivka',\r\n        14: 'ocena pa opisna ordinalna spremenljivka.',\r\n        15: 'ŠTEVILKA<br>UČENCA',\r\n        16: 'ČAS<br>IGRANJA (min)',\r\n        17: 'SPOL',\r\n        18: 'OCENA',\r\n        19: 'ž',\r\n        20: 'dobro',\r\n        21: 'm',\r\n        22: 'dobro',\r\n        23: 'ž',\r\n        24: 'zelo dobro',\r\n        25: 'm',\r\n        26: 'dobro',\r\n        27: 'm',\r\n        28: 'zelo dobro',\r\n        29: 'm',\r\n        30: 'nezadostno',\r\n        31: 'm',\r\n        32: 'dobro',\r\n        33: 'm',\r\n        34: 'dobro',\r\n        35: 'ž',\r\n        36: 'odlično',\r\n        37: 'm',\r\n        38: 'dobro',\r\n        39: 'm',\r\n        40: 'zelo dobro',\r\n        41: 'ž',\r\n        42: 'dobro',\r\n        43: 'ž',\r\n        44: 'zadostno',\r\n        45: 'm',\r\n        46: 'dobro',\r\n        47: 'm',\r\n        48: 'dobro',\r\n        49: 'ž',\r\n        50: 'zelo dobro',\r\n        51: 'ž',\r\n        52: 'dobro',\r\n        53: 'm',\r\n        54: 'zadostno',\r\n        55: 'm',\r\n        56: 'odlično',\r\n        57: 'm',\r\n        58: 'zelo dobro',\r\n        59: 'm',\r\n        60: 'zelo dobro',\r\n        61: 'ž',\r\n        62: 'nezadostno',\r\n        63: 'm',\r\n        64: 'zelo dobro',\r\n        65: 'ž',\r\n        66: 'zelo dobro',\r\n        67: 'ČAS IGRANJA V NEDELJO',\r\n        68: 'ČAS IGRANJA V PONEDELJEK',\r\n\t\t69: '<strong>zvezne spremenljivke</strong> - lahko zavzamejo vse vrednosti nekega intervala;',\r\n        70: '<strong>nezvezne (ali diskretne) spremenljivke </strong> - lahko zavzamejo le nekatere (ne vse) vrednosti nekega intervala;'\r\n      },\r\n      'podaci-tablica-varabli': {\r\n        1: 'Ime in priimek',\r\n        2: 'Ocena pri matematiki',\r\n        3: 'Ocena pri biologiji',\r\n        4: 'Število ur odsotnosti',\r\n        5: 'Janez Novak',\r\n        6: '5',\r\n        7: '4',\r\n        8: '20',\r\n        9: 'Franc Horvat',\r\n        10: '4',\r\n        11: '5',\r\n        12: '45',\r\n        13: 'Andrej Kovačič',\r\n        14: '5',\r\n        15: '4',\r\n        16: '130'\r\n      },\r\n      'podaci-zadatak': {\r\n        title: 'Podatki',\r\n        1: '<strong>Naloga 1.1.1.</strong>',\r\n        2: 'Podatki o navadah skupine ljudi v enem dnevu so zbrani v spodnjem opisu spremenljivk:',\r\n        3: 'Določite vrsto vsake od navedenih spremenljivk.',\r\n        4: '<strong>Spremenljivka</strong>',\r\n        5: '<strong>Vrednosti</strong>',\r\n        6: 'spol',\r\n        7: 'M, Ž',\r\n        8: 'poročen',\r\n        9: 'DA, NE',\r\n        10: 'število prelistanih dnevnih časopisov',\r\n        11: '0, 1, 2 itd.',\r\n        12: 'število gledanih televizijskih novic (ne nujno v celoti)',\r\n        13: '0, 1, 2 itd.',\r\n        14: 'število popitih kav',\r\n        15: '0, 1, 2 itd.',\r\n        16: 'stroški za hrano',\r\n        17: 'število',\r\n        18: 'osebno počutje',\r\n        19: 'slabo, dobro, izvrstno',\r\n        20: '<strong>Rešitev</strong>',\r\n        21: '<strong>Vrsta</strong>',\r\n        22: 'opisna imenska',\r\n        23: 'številska',\r\n        24: 'opisna ordinalna',\r\n        25: '<strong>Naloga 1.1.2.</strong>',\r\n        26: '<strong>Ustvarite svojo podatkovno bazo</strong>, ki ima vsaj eno ordinalno, eno imensko in eno številsko spremenljivko.',\r\n        27: 'Najmanjše število spremenljivk je 3'\r\n      },\r\n      'podaci-zadatak-interakcija': {\r\n        title: 'Naloga',\r\n        1: 'Vpišite število primerov (vrstice v tabeli): ',\r\n        2: 'Vpišite število spremenljivk (stolpci v tabeli):',\r\n        3: 'Največ 10',\r\n        4: 'Največ 5',\r\n        5: 'Ustvarite tabelo',\r\n        6: 'Izvozite tabelo v datoteko CSV',\r\n        7: 'Ime opisne spremenljivke',\r\n        8: 'Vrsta spremenljivke',\r\n        9: 'Številska spremenljivka',\r\n        10: 'Opisna imenska spremenljivka',\r\n        11: 'Opisna ordinalna spremenljivka',\r\n        12: 'Vpišite podatke',\r\n        13: 'Nepravilne vrednosti.',\r\n        14: 'Največje število primerov je 10! Ponovite vnos.',\r\n        15: 'Največje število spremenljivk je 5! Ponovite vnos.',\r\n        16: 'V tabelo je treba vnesti vse vrednosti.',\r\n        17: 'Najmanjše število spremenljivk je 3'\r\n      },\r\n      'frekvencije-i-relativne-frekvencije': {\r\n        title: 'Frekvence in relativne frekvence',\r\n        1: 'Frekvenčna porazdelitev je oblika poročanja o podatkih, poda se lahko s frekvenčno tabelo  ali s tabelo relativnih frekvenc.',\r\n        2: 'Predstavljena je za izbrano spremenljivko.',\r\n        3: '<strong>Frekvenca</strong> kategorije je število zabeleženih vrednosti spremenljivk, ki pripadajo tej kategoriji.',\r\n        4: '<strong>Relativna frekvenca</strong> kategorije je frekvenca, deljena s skupnim številom podatkov za to spremenljivko.',\r\n        5: 'Običajne oznake',\r\n        6: '<i>f</i> je frekvenca',\r\n        7: '<i>n</i> je število enot izbrane spremenljivke',\r\n        8: '<div class=\"fraction\" top=\"f\" bottom=\"n\"></div> je relativna frekvenca.',\r\n        9: '<strong>Frekvenčna tabela in tabela relativnih frekvenc</strong>',\r\n        10: 'Frekvence in relativne frekvence kategorij so predstavljene v tabelah. Relativne frekvence so najpogosteje izražene v odstotkih.',\r\n        11: 'KATEGORIJA',\r\n        12: 'FREKVENCA',\r\n        13: 'RELATIVNA <br> FREKVENCA (%)',\r\n        14: 'skupaj',\r\n        15: '100',\r\n        16: '<strong>Združevanje podatkov v razrede</strong>',\r\n        17: 'Če ima spremenljivka veliko različnih vrednosti in če želimo podatke predstaviti v frekvenčni tabeli in tabeli relativnih frekvenc, je koristno, da vrednosti združimo v <strong>razrede</strong>.',\r\n        18: 'Pri številskih podatkih pogosto združimo vrednosti v razrede. Običajno v <strong>intervale</strong>.',\r\n        19: 'Posamezna vrednost je lahko le v enem razredu.',\r\n        20: 'Razredi za razvrščanje so skrbno izbrani, da se poudarijo pomembne značilnosti podatkov.',\r\n        21: '<strong>Primer 1.2.1.</strong>',\r\n        22: 'Razrednik določenega razreda spremlja, koliko časa porabijo njegovi učenci za igranje računalniških igric. Zato je učence prosil, naj vodijo evidenco, v tabelo pa je zapisal podatke o tem, koliko časa so v nedeljo preživeli pri igranju računalniških igric. Dodal je podatke o spolu učencev in oceni, ki so jo dobili na zadnjem izpitu iz matematike. Podatki so predstavljeni v naslednji tabeli.',\r\n        23: 'številka <br> učenca',\r\n        24: 'čas <br> igranja',\r\n        25: 'spol',\r\n        26: 'ocena',\r\n        27: 'ž',\r\n        28: 'dobro',\r\n        29: 'm',\r\n        30: 'dobro',\r\n        31: 'ž',\r\n        32: 'zelo dobro',\r\n        33: 'm',\r\n        34: 'dobro',\r\n        35: 'm',\r\n        36: 'zelo dobro',\r\n        37: 'm',\r\n        38: 'nezadostno',\r\n        39: 'm',\r\n        40: 'dobro',\r\n        41: 'm',\r\n        42: 'dobro',\r\n        43: 'ž',\r\n        44: 'odlično',\r\n        45: 'm',\r\n        46: 'dobro',\r\n        47: 'm',\r\n        48: 'zelo dobro',\r\n        49: 'ž',\r\n        50: 'dobro',\r\n        51: 'ž',\r\n        52: 'zadostno',\r\n        53: 'm',\r\n        54: 'dobro',\r\n        55: 'm',\r\n        56: 'dobro',\r\n        57: 'ž',\r\n        58: 'zelo dobro',\r\n        59: 'ž',\r\n        60: 'dobro',\r\n        61: 'm',\r\n        62: 'zadostno',\r\n        64: 'm',\r\n        65: 'odlično',\r\n        66: 'm',\r\n        67: 'zelo dobro',\r\n        68: 'm',\r\n        69: 'zelo dobro',\r\n        70: 'ž',\r\n        71: 'nezadostno',\r\n        72: 'm',\r\n        73: 'zelo dobro',\r\n        74: 'ž',\r\n        75: 'zelo dobro',\r\n        76: '<strong>Primer 1.2.2.</strong>',\r\n        77: 'Naslednje tabele predstavljajo frekvence in relativne frekvence številske spremenljivke <strong>čas igranja</strong> za tabelo iz prejšnjega primera. Ena tabela ne vsebuje podatkov, združenih v razrede, druga pa.',\r\n        78: 'ČAS <br> IGRANJA <br> (min)',\r\n        79: 'FREKVENCA',\r\n        80: 'RELATIVNA <br> FREKVENCA <br> %',\r\n        81: 'SKUPAJ',\r\n        82: 'Frekvenčna tabela in tabela relativnih frekvenc.'\r\n      },\r\n      'frekvencije-i-relativne-frekvencije-primjer': {\r\n        1: 'KATEGORIJA',\r\n        2: 'FREKVENCA',\r\n        3: 'RELATIVNA FREKVENCA (%)',\r\n        4: 'Izberite spremenljivko, da prikažete tabelo frekvenc in relativnih frekvenc.',\r\n        5: 'Frekvenčna tabela in tabela relativnih frekvenc'\r\n      },\r\n      'frekvencije-i-relativne-frekvencije-zadatak': {\r\n        title: 'Frekvence in relativne frekvence',\r\n        1: '<strong>Naloga 1.2.1.</strong>',\r\n        2: 'Za tabelo iz prejšnjega primera združite podatke, ki se nanašajo na spremenljivko <i>čas igranja</i> tako da je vsak interval dolg 30 minut. Ustvarite ustrezno frekvenčno tabelo in tabelo relativnih frekvenc. Odgovorite na naslednja vprašanja:',\r\n        3: 'Kolikšen je odstotek otrok, ki so več kot tri ure igrali računalniške igre?',\r\n        4: 'Kolikšen je odstotek otrok, ki so računalniške igre igrali manj kot dve uri? Ali frekvenčna tabela in tabela relativnih frekvenc združenih podatkov zadostujeta za odgovor na ta vprašanja?',\r\n        5: '<strong>Rešitev</strong>',\r\n        6: 'ČAS IGRANJA (min)',\r\n        7: 'FREKVENCA',\r\n        8: 'RELATIVNA FREKVENCA (%)',\r\n        9: '[0, 30]',\r\n        10: '<30, 60]',\r\n        11: '<60, 90]',\r\n        12: '<90, 120]',\r\n        13: '<120, 150]',\r\n        14: '<150, 180]',\r\n        15: '<180, 210]',\r\n        16: '<210, 240]',\r\n        17: '<240, 270]',\r\n        18: 'skupaj',\r\n        19: '5',\r\n        20: '3',\r\n        21: '7',\r\n        22: '2',\r\n        23: '0',\r\n        24: '1',\r\n        25: '24',\r\n        26: '20,8',\r\n        27: '12,5',\r\n        28: '29,2',\r\n        29: '8,3',\r\n        30: '0',\r\n        31: '4,2',\r\n        32: 'Trije otroci (ali 12,5 %) so igrali računalniške igre več kot tri ure.',\r\n        33: 'Šestnajst otrok (ali 66,7 %) je igralo računalniške igre manj kot dve uri. Tega podatka ni mogoče izpeljati samo iz podatkov, združenih na ta način. Uporabiti moramo tabelo z neurejenimi podatki iz prejšnjega primera.'\r\n      },\r\n      'stupicasti-dijagram-i-histogram': {\r\n        title: 'Stolpčni grafikon in histogram',\r\n        1: '<strong>Stolpčni grafikon </strong> se uporablja za prikaz frekvenc ali relativnih frekvenc kategorij izbrane spremenljivke. Sestavljen je iz stolpcev, dodeljenih kategorijam, katerih višine so sorazmerne s frekvenco ali relativno frekvenco kategorij.',\r\n        2: '<strong>Histogram </strong> se uporablja za prikaz številskih podatkov. Pred izdelavo histograma je treba podatke združiti v intervale in ustvariti frekvenčno tabelo združenih podatkov. V koordinatnem sistemu histogram narišemo tako, da stolpce postavimo nad ustrezne intervale. Višina stolpca je sorazmerna s frekvenco intervala.',\r\n        3: '<strong>Primer 1.3.1.</strong>',\r\n        4: 'Razrednik določenega razreda spremlja, koliko časa porabijo njegovi učenci za igranje računalniških igric. Zato je učence prosil, naj vodijo evidenco, v tabelo pa je zapisal podatke o tem, koliko časa so v nedeljo preživeli pri igranju računalniških igric. Dodal je podatke o spolu učencev in oceni, ki so jo dobili na zadnjem izpitu iz matematike. Podatki so predstavljeni v naslednji tabeli.',\r\n        5: 'ŠTEVILKA<br>UČENCA',\r\n        6: 'ČAS<br>IGRANJA',\r\n        7: 'SPOL',\r\n        8: 'OCENA',\r\n        9: 'ž',\r\n        10: 'dobro',\r\n        11: 'm',\r\n        12: 'dobro',\r\n        13: 'ž',\r\n        14: 'zelo dobro',\r\n        15: 'm',\r\n        16: 'dobro',\r\n        17: 'm',\r\n        18: 'zelo dobro',\r\n        19: 'm',\r\n        20: 'nezadostno',\r\n        21: 'm',\r\n        22: 'dobro',\r\n        23: 'm',\r\n        24: 'dobro',\r\n        25: 'ž',\r\n        26: 'odlično',\r\n        27: 'm',\r\n        28: 'dobro',\r\n        29: 'm',\r\n        30: 'zelo dobro',\r\n        31: 'ž',\r\n        32: 'dobro',\r\n        33: 'ž',\r\n        34: 'zadostno',\r\n        35: 'm',\r\n        36: 'dobro',\r\n        37: 'm',\r\n        38: 'dobro',\r\n        39: 'ž',\r\n        40: 'zelo dobro',\r\n        41: 'ž',\r\n        42: 'dobro',\r\n        43: 'm',\r\n        44: 'zadostno',\r\n        45: 'm',\r\n        46: 'odlično',\r\n        47: 'm',\r\n        48: 'zelo dobro',\r\n        49: 'm',\r\n        50: 'zelo dobro',\r\n        51: 'ž',\r\n        52: 'nezadostno',\r\n        53: 'm',\r\n        54: 'zelo dobro',\r\n        55: 'ž',\r\n        56: 'zelo dobro',\r\n        57: 'Orodje v interakciji lahko uporabimo za risanje stolpčnih grafikonov za opisne spremenljivke iz prejšnje tabele. Narišemo lahko stolpčni grafikon frekvenc ali relativnih frekvenc. Kot vidite, so grafikoni enake oblike, vendar so stolpci različno visoki.',\r\n        58: '<strong>Primer 1.3.2.</strong>',\r\n        59: 'Orodje v interakciji lahko uporabimo za risanje histograma spremenljivke <i>čas igranja </i> iz prejšnjega primera. Izberite najmanjšo in največjo vrednost ter število intervalov, na katere bo nabor razdeljen za prikaz histograma.'\r\n\r\n      },\r\n      'stupcasti-dijagram-i-histogram-primjer': {\r\n        1: 'ENKRATNE PONOVITVE',\r\n        2: 'FREKVENCA',\r\n        3: 'RELATIVNA FREKVENCA (%)',\r\n        4: 'Stolpčni grafikon frekvenc',\r\n        5: 'Frekvenca oseb',\r\n        6: 'Ženske',\r\n        7: 'Moški',\r\n        8: 'Stolpčni grafikon relativnih frekvenc',\r\n        9: 'Relativna frekvenca oseb',\r\n        10: 'Najmanjša in največja zabeležena vrednost igralnega časa: ',\r\n        11: 'Spodnja mejna vrednost za histogram: ',\r\n        12: 'Začetek ranžirne vrste',\r\n        13: 'Zgornja mejna vrednost za histogram: ',\r\n        14: 'Konec ranžirne vrste',\r\n        15: 'Vnesite število segmentov, na katere želite razdeliti nabor:',\r\n        16: 'Število segmentov',\r\n        17: 'Ustvarite tabelo',\r\n        18: 'ČAS IGRANJA (min)',\r\n        19: 'FREKVENCA',\r\n        20: 'RELATIVNA FREKVENCA (%)',\r\n        21: 'Histogram frekvenc',\r\n        22: 'Histogram relativnih frekvenc',\r\n        23: 'Stolpčni grafikon frekvenc',\r\n        24: 'Frekvenca ocen',\r\n        25: 'nezadostno',\r\n        26: 'zadostno',\r\n        27: 'dobro',\r\n        28: 'zelo dobro',\r\n        29: 'odlično',\r\n        30: 'Stolpčni grafikon relativnih frekvenc',\r\n        31: 'Relativna frekvenca ocen',\r\n        32: 'Vpisane vrednosti morajo biti števila',\r\n        33: 'skupaj',\r\n        34: 'Za začetek izberite stolpec spol ali ocena.',\r\n        35: 'Za začetek izberite stolpec čas igranja.',\r\n        36: 'Frekvenca igralnega časa',\r\n        37: 'Relativna frekvenca igralnega časa',\r\n        38: 'Prazen vnos katere koli spremenljivke ni dovoljen.',\r\n        39: 'Izbrane ranžirne vrste ni mogoče razdeliti na izbrano število elementov.'\r\n      },\r\n      'stupicasti-dijagram-i-histogram-zadatak': {\r\n        title: 'Stolpčni grafikon in histogram',\r\n        1: '<strong>Naloga 1.3.1.</strong>',\r\n        2: 'Spodnja tabela prikazuje naslednje podatke o anketiranih: spremenljivka <i>število pregledov</i> prikazuje skupno število pregledov, spremenljivka <i>dopolnilno zdravstveno zavarovanje</i> prikazuje, ali ima zavarovana oseba dopolnilno zdravstveno zavarovanje ali ne (1 - da; 0 - ne), spremenljivka <i>cena</i> pa vsebuje ceno najdražjega zdravstvenega pregleda anketiranca (izraženo v kunah)',\r\n        3: 'ŠTEVILO <br> PREGLEDOV',\r\n        4: 'DOPOLNILNO <br> ZDRAVSTVENO ZAVAROVANJE',\r\n        5: 'CENA',\r\n        6: 'Katera spremenljivka je primerna za predstavitev s strukturnimi stolpci? Izberite to spremenljivko in si oglejte predstavitev podatkov s strukturnimi stolpci.',\r\n        7: 'Izberite spremenljivko <i>cena</i> in tako odprite orodje za razvrščanje podatkov. Vnesite zahtevane parametre in si oglejte ustrezno frekvenčno tabelo in tabelo relativnih frekvenc in histogram ter ugotovite, v kolikšnem odstotku je najdražji zdravstveni pregled stal več kot 200 kun in v kolikšnem odstotku več kot 150 kun.',\r\n        8: '<strong>Rešitev</strong>',\r\n        9: 'Najdražji zdravniški pregled je stal več kot 200 kun v 30 % primerov in več kot 150 kun v 67,5 % primerov.'\r\n      },\r\n      'stupcasti-dijagram-i-histogram-zadatak-interakcija': {\r\n        1: 'ŠTEVILO PREGLEDOV',\r\n        2: 'DOPOLNILNO ZDRAVSTVENO ZAVAROVANJE',\r\n        3: 'CENA',\r\n        4: 'Določene ranžirne vrste',\r\n        5: 'Frekvenca elementov ranžirne vrste',\r\n        6: 'Relativna frekvenca ranžirne vrste',\r\n        7: 'Najmanjše in največje ',\r\n        8: 'Spodnja mejna vrednost za histogram: ',\r\n        9: 'Začetek ranžirne vrste',\r\n        10: 'Zgornja mejna vrednost za histogram: ',\r\n        11: 'Konec ranžirne vrste',\r\n        12: 'Vnesite število segmentov, na katere želite razdeliti nabor:',\r\n        13: 'Število segmentov',\r\n        14: 'Ustvarite tabelo',\r\n        15: 'Stolpčni grafikon frekvenc ',\r\n        16: 'Frekvenca',\r\n        17: 'Relativna frekvenca',\r\n        18: ' številke pregleda',\r\n        19: ' cene pregleda',\r\n        20: ' dopolnilnega zdravstvenega zavarovanja',\r\n        21: 'Začetno število mora biti manjše od končnega',\r\n        22: 'Končno število ranžirne vrste mora biti v izbrani ranžirni vrsti',\r\n        23: 'Začetno število ranžirne vrste mora biti v izbrani ranžirni vrsti',\r\n        24: 'Stolpčni grafikon relativnih frekvenc',\r\n        25: 'Končno število ranžirne vrste mora biti večje od začetnega števila'\r\n      },\r\n      'prosjek': {\r\n        title: 'Aritmetična sredina ali povprečje',\r\n        1: '</strong>Aritmetična sredina ali povprečje</strong> podatkov 𝑥<sub>1</sub>, 𝑥<sub>2</sub> , … , 𝑥<sub>n</sub> je seštevek vseh podatkov, deljen s skupnim številom enot.',\r\n        2: 'Aritmetična sredina ali povprečje je primerno za številske spremenljivke, in je ena od mer srednje vrednosti.',\r\n        3: '<strong>Občutljivost povprečja na osamelce</strong>',\r\n        4: 'Osamelci so podatki, katerih vrednost je veliko večja ali veliko manjša od vrednosti ostalih podatkov. Če se podatkom doda vrednost, ki se bistveno razlikuje od povprečja obstoječih vrednosti, se bo novo povprečje močno spremenilo.',\r\n        5: '<strong>Primer 1.4.1.</strong>',\r\n        6: 'ČAS <br> IGRANJA (min)',\r\n        7: 'SPOL',\r\n        8: 'Če obstoječemu naboru dodamo število 4, bo povprečje znašalo 4,181.',\r\n        9: 'Če obstoječemu naboru dodamo število 50, bo povprečje znašalo 8,36.',\r\n        10: 'Izberite število in ga dodajte obstoječemu naboru. Opazujte, kako se spremeni povprečje.',\r\n        11: 'm',\r\n        12: 'dobro',\r\n        13: 'ž',\r\n        14: 'zelo dobro',\r\n        15: 'm',\r\n        16: 'dobro',\r\n        17: 'm',\r\n        18: 'zelo dobro',\r\n        19: 'm',\r\n        20: 'nezadostno',\r\n        21: 'm',\r\n        22: 'dobro',\r\n        23: 'm',\r\n        24: 'dobro',\r\n        25: 'ž',\r\n        26: 'odlično',\r\n        27: 'm',\r\n        28: 'dobro',\r\n        29: 'm',\r\n        30: 'zelo dobro',\r\n        31: 'ž',\r\n        32: 'dobro',\r\n        33: 'ž',\r\n        34: 'zadostno',\r\n        35: 'm',\r\n        36: 'dobro',\r\n        37: 'm',\r\n        38: 'dobro',\r\n        39: 'ž',\r\n        40: 'zelo dobro',\r\n        41: 'ž',\r\n        42: 'dobro',\r\n        43: 'm',\r\n        44: 'zadostno',\r\n        45: 'm',\r\n        46: 'odlično',\r\n        47: 'm',\r\n        48: 'zelo dobro',\r\n        49: 'm',\r\n        50: 'zelo dobro',\r\n        51: 'ž',\r\n        52: 'nezadostno',\r\n        53: 'm',\r\n        54: 'zelo dobro',\r\n        55: 'ž',\r\n        56: 'zelo dobro',\r\n        57: 'ŠTEVILKA <br> UČENCA',\r\n        58: 'OCENA',\r\n        59: 'ž',\r\n        60: 'dobro',\r\n        61: 'Povprečni čas, ki so ga učenci v nedeljo porabili za igranje igric, znaša 89,96. Dodajte en element in opazujte, kako se spreminjata povprečje in histogram.',\r\n        62: '<strong>Primer 1.4.2.</strong>',\r\n        63: 'Razrednik določenega razreda spremlja, koliko časa porabijo njegovi učenci za igranje računalniških igric. Zato je učence prosil, naj vodijo evidenco, v tabelo pa je zapisal podatke o tem, koliko časa so v nedeljo preživeli pri igranju računalniških igric. Dodal je podatke o spolu učencev in o oceni, ki so jo dobili na zadnjem izpitu iz matematike. Podatki so predstavljeni v naslednji tabeli.',\r\n        64: 'Povprečje podatkovnega nabora 3, 5, 7, 2, 1, 7, 4, 3, 5, 5 je',\r\n\t65: 'Za začetek izberite spremenljivko čas igranja.'\r\n      },\r\n      'prosjek-tablica': {\r\n        1: '1',\r\n        2: '2',\r\n        3: '3',\r\n        4: '4',\r\n        5: '5',\r\n        6: '6',\r\n        7: '7',\r\n        8: '8',\r\n        9: '9',\r\n        10: '10',\r\n        11: '11',\r\n        12: '12',\r\n        13: '13',\r\n        14: '14',\r\n        15: '15',\r\n        16: '16',\r\n        17: '17',\r\n        18: '18',\r\n        19: '19',\r\n        20: '20',\r\n        21: '21',\r\n        22: '22',\r\n        23: '23',\r\n        24: '24'\r\n      },\r\n      'prosjek-interakcija': {\r\n        1: 'Začetna serija števil: ',\r\n        2: 'Vstavite nov element ranžirne vrste: ',\r\n        3: 'Vstavite število',\r\n        4: 'Ustvarite grafikon',\r\n        5: 'Povprečje privzete ranžirne vrste: ',\r\n        6: 'Povprečje ranžirne vrste z novim elementom: ',\r\n        7: 'Začetna porazdelitev serije in povprečje',\r\n        8: 'Dodani element in novo povprečje',\r\n        9: 'Seznam časov igranja:',\r\n        10: 'Čas igranja',\r\n        11: 'Frekvenca elementov ranžirne vrste',\r\n        12: 'Relativna frekvenca ranžirne vrste',\r\n        13: 'Grafikon frekvenc',\r\n        14: 'Novi element ranžirne vrste mora biti število',\r\n        15: 'Potrebna je nova vrednost elementa ranžirne vrste.',\r\n      },\r\n      'prosjek-zadatak': {\r\n        title: 'Aritmetična sredina ali povprečje',\r\n        1: '<strong>Naloga 1.4.1.</strong>',\r\n        2: 'Ko je tržni analitik analiziral cene prehrambnih izdelkov, je opazil, da imajo isti izdelki v različnih nakupovalnih središčih različne cene. Po ogledu enajstih nakupovalnih središč je zabeležil cene izdelka med katerimi so bile razlike največje.',\r\n        3: 'ŠTEVILKA <br> TRGOVINE',\r\n        4: 'CENA',\r\n        5: 'Orodje v interakciji lahko uporabimo za izračun povprečne cene izdelka za izbrana nakupovalna središča. Za koliko se bo povprečje zmanjšalo, če bomo iz nabora izbranih nakupovalnih središč izločili prvo, in za koliko, če bomo izločili enajsto?',\r\n        6: '<strong>Naloga 1.4.2.</strong>',\r\n        7: 'Dana sta naslednja podatkovna nabora:',\r\n        8: '0, 1, 2, 3, −1, −2, −3, 0,5, 0,7, 0,25, −1, −0,45',\r\n        9: '−100, 100, 150, −75, −250, 200, −25',\r\n        10: 'Izračunajte povprečje vsakega od njiju. Kako sta si nabora podobna? Ali daje povprečje dovolj informacij o podatkovnem naboru?',\r\n        11: '<strong>Rešitev</strong>',\r\n        12: 'Povprečna cena vseh trgovin je 52,88. Če izločimo prvo nakupovalno središče, bo povprečna cena znašala 53,62, če izločimo enajsto, pa 48,67.',\r\n        13: 'Povprečje je v obeh primerih 0. Nabora imata enako povprečje, čeprav se bistveno razlikujeta. Zato povprečje ne daje dovolj informacij o podatkovnem naboru.',\r\n        14: 'Cene za izračun povprečja izberite s klikom na določeno ceno.',\r\n        15: 'Posamezno ceno vnesemo v izračun povprečne cene tako, da nanjo kliknemo.'\r\n\r\n      },\r\n      'prosjek-zadatak-interakcija': {\r\n        1: 'ŠTEVILKA TRGOVINE',\r\n        2: 'CENA',\r\n        3: 'Povprečna cena v vseh trgovinah: ',\r\n        4: 'Povprečna cena v izbranih trgovinah: '\r\n      },\r\n      'medijan': {\r\n        title: 'Mediana in modus',\r\n        1: '<strong>Mediana </strong> je ena od mer srednje vrednosti številske spremenljivke, primerna tudi za ordinalne spremenljivke.',\r\n        2: 'Je število, ki podatke, urejene po velikosti, razdeli na dva dela, tako da:',\r\n        3: 'oba dela vsebujeta enako število enot in',\r\n        4: 'noben podatek iz prvega dela ni večji od podatkov iz drugega dela.',\r\n        5: 'Mediana je tista vrednost spremenljivke, od katere je polovica enot manjših, polovica enot pa večjih.',\r\n        6: 'Če želimo dobiti <strong>mediano nabora</strong> podatkov, je treba podatke najprej razvrstiti po velikosti.',\r\n        7: '<strong>Algoritem za izračun mediane je:</strong>',\r\n        8: 'Dan je naslednji podatkovni nabor: 𝑥<sub>1</sub> , 𝑥<sub>2</sub> , … , 𝑥<sub>𝑛</sub>.',\r\n        9: 'Podatki so urejeni po velikosti, od najmanjšega do največjega (ranžirna vrsta).',\r\n        10: 'Če je n liho število, je mediana podatek, ki je na sredini ranžirne vrste.',\r\n        11: 'Če je n sodo število, je mediana povprečje podatkov na sredini ranžirne vrstne (na mestih <div class=\"fraction\" top=\"𝑛\" bottom=\"2\"></div> in <div class=\"fraction\" top=\"𝑛\" bottom=\"2\"></div> + 1). ',\r\n        12: 'Mediana je v primerjavi s povprečjem manj občutljiva za <strong>osamelce</strong>. Osamelci so podatki, katerih vrednost je veliko večja ali veliko manjša od vrednosti drugih podatkov.',\r\n        13: '<strong>Primer 1.5.1.</strong>',\r\n        14: 'Za naslednje podatke:',\r\n\t\t15: '3, 5, 7, 2, 1, 7, 4, 3, 5, 5, 5',\r\n        16: 'Za izračun mediane moramo ta nabor razvrstiti od najmanjšega do največjega števila:',\r\n\t\t17: '1, 2, 3, 3, 4, 5, 5, 5, 5, 7, 7',\r\n        18: 'V naboru je 11 podatkov (liho število). Mediana je podatek na srednjem (šestem) mestu v urejenem podatkovnem naboru. Torej je mediana 5.',\r\n        19: '<strong>Primer 1.5.2.</strong>',\r\n        20: 'Dani so naslednji podatki:',\r\n\t\t21: '3, 5, 7, 2, 1, 7, 4, 3, 5, 5',\r\n        22: 'Za izračun mediane moramo ta nabor razvrstiti od najmanjšega do največjega števila:',\r\n\t\t23: '1, 2, 3, 3, 4, 5, 5, 5, 7, 7',\r\n        24: 'V naboru je 10 podatkov (sodo število). Ker je <div class=\"fraction\" top=\"10\" bottom=\"2\"></div> 5, je mediana povprečje podatkov na petem in šestem mestu v urejenem podatkovnem naboru, torej <div class=\"fraction\" top=\"(4 + 5)\" bottom=\"2\"></div> 4,5.',\r\n        25: '<strong>Primer 1.5.3.</strong>',\r\n        27: 'Povprečje je 4,2, mediana pa 4,5.',\r\n        28: 'Če obstoječemu naboru dodamo število 50, bo povprečje 8,36, mediana pa 5.',\r\n        29: 'Izberite število, dodajte ga v ta nabor in opazujte, kako se mediana in povprečje spreminjata.',\r\n        30: '<strong>Modus</strong> (ali gostiščnica) je prav tako ena od mer srednjih vrednosti, ki je primerna za vse vrste spremenljivk. Je tista vrednost podatka, ki se v naboru podatkov najpogosteje pojavi. Če se vsak podatek pojavi samo enkrat, potem modusa ni. Če se v nekem naboru podatkov zgodi, da se več vrednosti pojavi enako mnogokrat (in hkrati najpogosteje), ima tak nabor več modusov – to so vse vrednosti, ki se pojavijo najpogosteje.',\r\n        31: 'Najpogosteje se pojavi podatek \"5\" (4-krat). Torej je v tem primeru modus enak 5.'\r\n      },\r\n      'median-interaction': {\r\n        1: 'Začetna mediana: ',\r\n        2: 'Začetna ranžirna vrsta števil: ',\r\n        3: 'Vstavite novo število ranžirne vrste: ',\r\n        4: 'Vstavite število',\r\n        5: 'Izračunaj in nariši',\r\n        6: 'Povprečje privzete ranžirne vrste',\r\n        7: 'Povprečje ranžirne vrste z novim številom',\r\n        8: 'Začetna porazdelitev elementov ranžirne vrste',\r\n        9: 'Aritmetična sredina ali povprečje',\r\n        10: 'Mediana',\r\n        11: 'Nova porazdelitev ranžirne vrste',\r\n        12: 'Novo povprečje',\r\n        13: 'Nova mediana',\r\n        14: 'Razvrsti ranžirno vrsto',\r\n        15: 'Izračunaj mediano',\r\n        16: 'Nov element ranžirne vrste mora biti število',\r\n        17: 'Potrebna je vrednost novega elementa ranžirne vrste.',\r\n        18: 'Mediana rezultata:'\r\n      },\r\n      'medijan-zadatak': {\r\n        title: 'Mediana',\r\n        1: '<strong>Naloga 1.5.1.</strong>',\r\n        2: 'Razrednik določenega razreda spremlja, koliko časa porabijo njegovi učenci za igranje računalniških igric. Zato je učence prosil, naj vodijo evidenco, v tabelo pa je zapisal podatke o tem, koliko časa so v nedeljo preživeli pri igranju računalniških igric. Dodal je podatke o spolu učencev in o oceni, ki so jo dobili na zadnjem izpitu iz matematike. Podatki so predstavljeni v naslednji tabeli.',\r\n        3: 'Ali lahko rečemo, da je vsaj 50 % učencev igralo igrice manj časa, kot je povprečni čas igranja v razredu?',\r\n        4: '<strong>Rešitev</solution>',\r\n        5: 'Povprečje je 89,96, medtem ko je mediana 75 in tako nižja od povprečja. Zato je odgovor na zgornje vprašanje pritrdilen.'\r\n      },\r\n      'minimum-maksimum-i-raspon': {\r\n        title: 'Minimum, maksimum in variacijski razmik',\r\n        1: 'Naj bodo 𝑥<sub>1</sub> , 𝑥<sub>2</sub> , … , 𝑥<sub>𝑛</sub> dani podatki.',\r\n        2: '<strong>Minimum</strong> je najmanjše število v podatkovnem naboru in ga označuje 𝑥<sub>𝑚𝑖𝑛</sub>.',\r\n        3: '<strong>Maksimum</strong> pa največje število v podatkovnem naboru in ga označuje 𝑥<sub>𝑚𝑎𝑥</sub>.',\r\n        4: '<strong>Variacijski razmik</strong> je razlika med maksimumom in minimumom:',\r\n        5: 'formula',\r\n        6: 'Variacijski razmik je groba mera razpršenosti podatkov.',\r\n        7: '<strong>Primer 1.6.1.</strong>',\r\n        8: 'Za naslednje podatke:',\r\n        9: '3, 5, 7, 2, 1, 7, 4, 3, 5, 5',\r\n        10: 'lahko izračunamo',\r\n        11: '𝑥𝑚𝑖𝑛 = 1',\r\n        12: '𝑥𝑚𝑎𝑥 = 7',\r\n        13: 'variacijskirazmik = 6',\r\n        14: 'variacijskirazmik'\r\n      },\r\n      'minimum-maksimum-i-raspon-interakcija': {\r\n        1: 'Podatki: ',\r\n        2: 'Urejena ranžirna vrsta: ',\r\n        3: 'Minimum: ',\r\n        4: 'Maksimum: ',\r\n        5: 'Variacijski razmik: ',\r\n        6: 'Razvrsti ranžirno vrsto',\r\n        7: 'Izračunaj minimum, maksimum in variacijski razmik'\r\n      },\r\n      'minimum-maksimum-i-raspon-zadatak': {\r\n        title: 'Minimum, maksimum in variacijski razmik',\r\n        1: '<strong>Naloga 1.6.1.</strong>',\r\n        2: 'Razrednik določenega razreda spremlja, koliko časa porabijo njegovi učenci za igranje računalniških igric. Zato je učence prosil, naj vodijo evidenco, v tabelo pa je zapisal podatke o tem, koliko časa so v nedeljo preživeli pri igranju računalniških igric. Dodal je podatke o spolu učencev in o oceni, ki so jo dobili na zadnjem izpitu iz matematike. Podatki so predstavljeni v naslednji tabeli.',\r\n        3: 'Določite minimum, maksimum in variacijski razmik podatkov spremenljivke čas igranja.',\r\n        4: '<strong>Rešitev</strong>',\r\n        5: 'Minimum je 0, maksimum je 244, variacijski razmik pa 244.'\r\n      },\r\n      'kvartili-i-interkvartilni-raspon': {\r\n        title: 'Kvartili in kvartilni razmik',\r\n        1: '<strong>Kvartilni razmik</strong> je mera razpršenosti podatkov. Definirana je s pomočjo prvega in tretjega <strong>kvartila</strong>.',\r\n        2: '<strong>Prvi in tretji kvartil</strong> sta števili, ki urejen podatkovni nabor razdelita na dva dela, tako da:',\r\n        3: 'en del vsebuje četrtino podatkov, drugi del pa tri četrtine podatkov',\r\n        4: 'noben podatek iz prvega dela ni večji od podatkov iz drugega dela.',\r\n        5: '<strong>Prvi kvartil</strong>, označimo s 𝑄<sub>1</sub>, <strong>tretji kvartil</strong> pa s 𝑄<sub>3</sub>.',\r\n        6: '<strong>Prvi kvartil</strong> deli prvo četrtino urejenega podatkovnega nabora od preostalih treh četrtin. Tako dobimo število, ki je večje ali enako vsaj 25 % podatkom, hkrati pa manjše ali enako vsaj 75 % podatkom.',\r\n        7: '<strong>Tretji kvartil</strong> deli prve tri četrtine urejenega podatkovnega nabora od zadnje četrtine. Tako dobimo število, ki je večje ali enako vsaj 75 % podatkom, hkrati pa manjše ali enako vsaj 25 % podatkom.',\r\n        8: 'Obstaja tudi drugi kvartil, ki mu pogosteje pravimo mediana.',\r\n        9: 'Min',\r\n        10: 'Q<sub>1</sub>',\r\n        11: 'Mediana',\r\n        12: 'Q<sub>3</sub>',\r\n        13: 'Max',\r\n        14: 'Urejeni<br> podatki',\r\n        15: 'Položaj v <br> urejenem naboru',\r\n        16: '<strong>Kvartilni razmik</strong> je razlika med tretjim in prvim kvartilom:',\r\n        17: 'formula',\r\n        18: '<strong>Primer 1.7.1.</strong>',\r\n        19: 'Dan je naslednji nabor 18 podatkov:',\r\n        20: '5, 2, 3, 2, 5, 2, 4, 5, 1, 7, 6, 1, 4, 6, 7, 4, 7, 4',\r\n        21: 'Položaj',\r\n        22: 'kvartilni',\r\n        23: 'razmik',\r\n        24: 'tako',\r\n        25: 'Dan je naslednji podatkovni nabor: x<sub>1</sub>,x<sub>2</sub>,…,x<sub>n</sub>.',\r\n        26: 'Podatki so urejeni po velikosti, od najmanjšega do največjega.',\r\n        27: '<strong>Prvi kvartil<strong>, Q<sub>1</sub>',\r\n        28: 'Če <div class=\"fraction\" top=\"𝑛\" bottom=\"4\"></div> ni naravno število, je podatek na prvem mestu, večjem od <div class=\"fraction\" top=\"𝑛\" bottom=\"4\"></div> prvi kvartil.',\r\n\t\t29: 'Če je <div class=\"fraction\" top=\"𝑛\" bottom=\"4\"></div> naravno število, je prvi kvartil povprečje podatkov na mestih <div class=\"fraction\" top=\"𝑛\" bottom=\"4\"></div> in <div class=\"fraction\" top=\"𝑛\" bottom=\"4\"></div> + 1.',\r\n        30: '<strong>Tretji kvartil<strong>, Q<sub>3</sub>',\r\n        31: 'Če <div class=\"fraction\" top=\"3𝑛\" bottom=\"4\"></div> ni naravno število, je podatek na prvem mestu, večjem od <div class=\"fraction\" top=\"3𝑛\" bottom=\"4\"></div> tretji kvartil.',\r\n        32: 'Če je <div class=\"fraction\" top=\"3𝑛\" bottom=\"4\"></div> naravno število, je tretji kvartil povprečje podatkov na mestih <div class=\"fraction\" top=\"3𝑛\" bottom=\"4\"></div> in <div class=\"fraction\" top=\"3𝑛\" bottom=\"4\"></div> + 1.',\r\n        33: 'Za tiste, ki želijo izvedeti več'\r\n      },\r\n      'kvartili-i-interkvartilni-raspon-interakcija': {\r\n        1: 'Privzeta ranžirna vrsta: ',\r\n        2: 'Ustvari tabelo',\r\n        3: 'Urejeni podatki',\r\n        4: 'Oznaka položaja',\r\n        5: 'Izračunaj kvartile',\r\n        6: ', tako da je Q1: ',\r\n        7: ', tako da je Q3: ',\r\n        8: 'Kvartilni razmik je: ',\r\n        9: 'Mediana je: '\r\n      },\r\n      'kvartili-i-interkvartilni-raspon-zadatak': {\r\n        title: 'Kvartili in kvartilni razmik',\r\n        1: '<strong>Naloga 1.7.1.</strong>',\r\n        2: 'Razrednik določenega razreda spremlja, koliko časa porabijo njegovi učenci za igranje računalniških igric. Zato je učence prosil, naj vodijo evidenco, v tabelo pa je zapisal podatke o tem, koliko časa so v nedeljo preživeli pri igranju računalniških igric. Dodal je podatke o spolu učencev in o oceni, ki so jo dobili na zadnjem izpitu iz matematike. Podatki so predstavljeni v naslednji tabeli.',\r\n        3: 'Izračunajte prvi in tretji kvartil ter kvartilni razmik podatkov spremenljivke <i>čas igranja</i> in odgovorite na naslednja vprašanja:',\r\n        4: 'Ali je res, da je več kot 75 % otrok igralo igrice manj kot dve uri?',\r\n        5: 'Ali je res, da je manj kot 25 % otrok igralo igrice več kot dve uri?',\r\n        6: 'Ali je res, da je več kot 25 % otrok igralo igrice manj kot pol ure?',\r\n        7: '<strong>Rešitev</strong>',\r\n        8: 'Odgovori: ',\r\n        9: 'Tretji kvartil je 129,5 minute. Zato trditev ni resnična.',\r\n        10: 'Tretji kvartil je 129,5 minute. Zato je trditev resnična.',\r\n        11: 'Prvi kvartil je 49 minut. Zato trditev ni resnična.'\r\n      },\r\n      'varijanca-i-standardna-devijacija': {\r\n        title: 'Varianca in standardni odklon',\r\n        1: 'Varianca in standardni odklon sta meri razpršenosti številskih podatkov. Standardni odklon označuje razpršenost podatkov okoli povprečja.',\r\n        2: '<strong>Varianca</strong> je povprečno kvadratno odstopanje nabora podatkov od njihovega povprečja. Če je <i>n</i> število podatkov v <strong>vzorcu</strong>, se njihova varianca označi kot <i>s</i><sup>2</sup>. V nadaljevanju so izračuni narejeni na podlagi te formule za vzorec (<strong>Pozor!</strong> V srednji šoli se navadno za vse primere uporabi formula za <strong>populacijo</strong>, kjer se <i>n-1</i> zamenja s številom vseh enot <i>N</i> in se označi s sigmo 𝜎<sup>2</sup>).',\r\n        3: 'Za podatkovni nabor vzorca 𝑥<sub>1</sub>, 𝑥<sub>2</sub>, … ,𝑥<sub>𝑛</sub> je varianca podana na naslednji način:',\r\n        4: 'formula',\r\n        5: '<strong>Standardni odklon</strong> je kvadratni koren variance. Oznaka za standardni odklon vzorca je <i>s</i>.',\r\n        6: 'formula',\r\n        7: '<strong>Primer 1.8.1.</strong>',\r\n        8: 'Za naslednje podatke:',\r\n        9: '3, 5, 7, 2, 1, 7, 4, 3, 5, 5',\r\n        10: 'je povprečje 4,2. Izračun variance lahko ponazorimo z naslednjo tabelo.',\r\n        11: 'PODATKI',\r\n        12: 'ODKLON OD <br> POVPREČJA',\r\n        13: 'KVADRATNI ODKLON <br> OD POVPREČJA',\r\n        14: 'skupaj',\r\n        15: 'Varianca je <div class=\"fraction\" top=\"35.6\" bottom=\"9\"></div> = 3,96, standardni odklon pa 1,99.',\r\n\t\t16: 'Varianca populacije z N enotami se označi kot 𝜎<sup>2</sup>. Za populacijo z N enotami je varianca podana na naslednji način:',\r\n\t\t17: 'Oznaka za standardni odklon populacije je 𝜎.'\r\n      },\r\n      'varijanca-i-standardna-devijacija-zadatak': {\r\n        title: 'Varianca in standardni odklon',\r\n        1: '<strong>Naloga 1.8.1.</strong>',\r\n        2: 'Dana sta naslednja podatkovna nabora:',\r\n        3: '0, 1, 2, 3, -1, -2, -3, 0,5, 0,7, 0,25, -1, -0,45',\r\n        4: '-100, 100, 150, -75, -250, 200, -25',\r\n        5: 'Izračunajte povprečje in standardni odklon obeh podatkovnih naborov.',\r\n        6: 'Kako sta si nabora podobna? Ali daje povprečje dovolj informacij o podatkovnem naboru? Ali menite, da je standardni odklon pri poročanju o podatkih pomembna informacija?',\r\n        7: '<strong>Naloga 1.8.2.</strong>',\r\n        8: 'Razrednik določenega razreda spremlja, koliko časa porabijo njegovi učenci za igranje računalniških igric. Zato je učence prosil, naj vodijo evidenco, v tabelo pa je zapisal podatke o tem, koliko časa so v nedeljo preživeli pri igranju računalniških igric. Dodal je podatke o spolu učencev in o oceni, ki so jo dobili na zadnjem izpitu iz matematike. Podatki so predstavljeni v naslednji tabeli.',\r\n        9: 'Uporabite preglednico za izračun variance in standardnega odklona za spremenljivko <i>čas igranja</i>.',\r\n        10: '<strong>Rešitev naloge 1.8.1.</strong>',\r\n        11: 'Povprečje prvega nabora je 0, standardni odklon pa 1,65.',\r\n        12: 'Povprečje drugega nabora je 0, standardni odklon pa 158,77.',\r\n        13: 'Povprečja sta enaka, standardna odklona pa se razlikujeta.',\r\n        14: 'Povprečje je 89,96.',\r\n        15: 'ČAS IGRANJA (min)',\r\n        16: 'ODKLON OD POVPREČJA',\r\n        17: 'KVADRATNI ODKLON OD POVPREČJA',\r\n        18: '47',\r\n        19: '177',\r\n        20: '124',\r\n        21: '135',\r\n        22: '69',\r\n        23: '88',\r\n        24: '0',\r\n        25: '69',\r\n        26: '120',\r\n        27: '63',\r\n        28: '57',\r\n        29: '79',\r\n        30: '244',\r\n        31: '99',\r\n        32: '76',\r\n        33: '166',\r\n        34: '193',\r\n        35: '19',\r\n        36: '74',\r\n        37: '51',\r\n        38: '20',\r\n        39: '189',\r\n        40: '<strong>skupaj</strong>',\r\n        41: '-42,96',\r\n        42: '87,04',\r\n        43: '34,04',\r\n        44: '45,04',\r\n        45: '-20,96',\r\n        46: '-1,96',\r\n        47: '-89,96',\r\n        48: '-20,96',\r\n        49: '30,04',\r\n        50: '-89,96',\r\n        51: '-26,96',\r\n        52: '-32,96',\r\n        53: '-10,96',\r\n        54: '154,04',\r\n        55: '-89,96',\r\n        56: '9,04',\r\n        57: '-13,96',\r\n        58: '76,04',\r\n        59: '103,04',\r\n        60: '-70,96',\r\n        61: '-15,96',\r\n        62: '-38,96',\r\n        63: '-69,96',\r\n        64: '99,04',\r\n        65: '1845,56',\r\n        66: '1845,56',\r\n        67: '1158,72',\r\n        68: '2028,60',\r\n        69: '439,32',\r\n        70: '3,84',\r\n        71: '8092,80',\r\n        72: '439,32',\r\n        73: '902,40',\r\n        74: '8092,80',\r\n        75: '726,84',\r\n        76: '1086,36',\r\n        77: '120,12',\r\n        78: '23728,32',\r\n        79: '8092,80',\r\n        80: '81,72',\r\n        81: '194,88',\r\n        82: '5782,08',\r\n        83: '10617,24',\r\n        84: '5035,32',\r\n        85: '254,72',\r\n        86: '1517,88',\r\n        87: '4894,40',\r\n        88: '9808,92',\r\n        89: '102520,96',\r\n        90: 'Varianca je 4457,43, standardni odklon pa 66,76.',\r\n        91: '<strong>Rešitev naloge 1.8.2.</strong>',\r\n      },\r\n      'kutijasti-dijagram': {\r\n        title: 'Graf kvartilov',\r\n        1: '<strong>Graf kvartilov</strong> (angl. box plot) prikazuje odnos med minimumom, maksimumom, prvim in tretjim kvartilom ter mediano podatkov.',\r\n        2: 'Če podatki vsebujejo osamelce (podatki, katerih vrednosti so veliko večje ali veliko manjše od vrednosti drugih podatkov), so le ti tudi prikazani na grafu.',\r\n        3: '<strong>Primer 1.9.1.</strong>',\r\n        4: 'Dan je naslednji nabor 20 podatkov:',\r\n        5: '1, 0, 9, 1,1, 1,1, 0,8, 1,1, 1,2, 0,7, 1, 0,6, 0,9, 1,3, 1,1, 0,7, 1, 1,1, 1, 1,3',\r\n        6: 'Slika prikazuje podatke v grafu kvartilov ter vrednosti minimuma, maksimuma, prvega in tretjega kvartila ter mediane.',\r\n        7: 'Začnite interakcijo, da boste videli graf kvartilov, ki ga dobimo, ko naboru dodamo število 2. Vidite lahko, da je število 2 osamelec in da je prikazan maksimum podatkov brez te vrednosti (1,3).',\r\n        8: '<strong>Primer 1.9.2.</strong>',\r\n      },\r\n      'kutijasti-dijagram-interakcija': {\r\n        1: 'Razvrsti',\r\n        2: 'Nerazvrščeno:',\r\n        3: 'Razvrščeno:',\r\n        4: 'pravilno',\r\n        5: 'mediana',\r\n        6: 'napačno'\r\n      },\r\n      'kutijasti-dijagram-zadatak': {\r\n        title: 'Graf kvartilov',\r\n        1: '<strong>Naloga 1.9.2.</strong>',\r\n        2: 'Spodnja slika prikazuje tri grafe kvartilov. Ali lahko ugotovimo, katera trditev velja za kateri graf:',\r\n        3: 'Vsaj 25 % podatkov je enakih minimumu.',\r\n        4: 'Vsaj 75 % podatkov je manjših od mediane ali enakih mediani.',\r\n        5: 'Vsaj 25 % podatkov je enakih maksimumu.',\r\n        6: 'Mediana in tretji kvartil sta enaka.',\r\n        7: '<strong>Rešitev</strong>',\r\n        8: 'Izjava:',\r\n        13: 'velja za graf 1',\r\n        14: 'velja za graf 3',\r\n        15: 'velja za graf 2',\r\n        16: 'velja za graf 3.'\r\n      },\r\n      'dijagram-rasprsenosti-i-standardna-devijacija': {\r\n        title: 'Razsevni diagram',\r\n        1: 'Če so za enote zbrani podatki o dveh številskih spremenljivkah, je pare vrednosti koristno prikazati z <strong>razsevnim diagramom</strong>. Takšen diagram je primeren za ugotavljanje povezanosti med spremenljivkama.',\r\n        2: '<strong>Razsevni diagram</strong> je sestavljen iz parov vrednosti, prikazanih s točkami v koordinatnem sistemu, kjer je na vodoravni osi prikazana prva spremenljivka, na navpični pa druga.',\r\n        3: '<strong>Primer 1.10.1.</strong>',\r\n        4: 'Dani so naslednji podatki:',\r\n        5: 'Naslednja slika prikazuje njihov razsevni diagram.',\r\n        6: 'NASLEDNJE POGLAVJE:',\r\n        7: '2. Osnove verjetnosti',\r\n        8: 'Če kliknete gumb \"Padlo je sodo število\", se prikaže nova množica izidov in nova množica ugodnih izidov z dodatnimi informacijami, da je pri metanju kock padlo sodo število.'\r\n      },\r\n      'dijagram-rasprsenosti-i-standardna-devijacija-zadatak': {\r\n        title: 'Razsevni diagram',\r\n        1: '<strong>Naloga 1.10.1.</strong>',\r\n        2: 'Razrednik določenega razreda spremlja, koliko časa porabijo njegovi učenci za igranje računalniških igric. Zato je učence prosil, naj vodijo evidenco, v tabelo pa je zapisal podatke o tem, koliko časa so v nedeljo in ponedeljek preživeli pri igranju računalniških igric. Podatki so predstavljeni v naslednji tabeli.',\r\n        3: 'Naslednja slika prikazuje razsevni diagram spremenljivke čas, porabljen za igranje igric v nedeljo in ponedeljek. Ali opazite kakšno povezanost spremenljivk?',\r\n        4: '<strong>Rešitev</strong>',\r\n        5: 'Obstaja povezanost spremenljivk v smislu rasti. Na podlagi tega diagrama je mogoče sklepati, da tisti otroci, ki igrajo igrice veliko časa ob nedeljah, jih igrajo veliko časa tudi ob ponedeljkih.'\r\n      }\r\n    },\r\n    osnove_vjerojatnosti: {\r\n      chapterNumber: '&mdash; 2. poglavje &mdash;',\r\n      title: 'Osnove verjetnosti',\r\n      'vjerojatnost': {\r\n        title: 'Verjetnost',\r\n        1: '<strong>Poskus</strong> je realizacija neke množice skupaj nastopajočih dejstev (kompleksa pogojev).',\r\n\t\t2: '<strong>Dogodek</strong> je vsak pojav, ki se pri poskusu lahko zgodi ali pa tudi ne. Je podmnožica množice vseh možnih izidov poskusa. <strong>Izid</strong> je vsak dogodek, ki se lahko zgodi v danem poskusu. Ugodni izidi so tisti, ki se zgodijo v korist opazovanega dogodka, neugodni pa tisti, pri katerih se opazovani dogodek ne zgodi. <strong>Nemogoč dogodek (N)</strong> je dogodek, ki se nikoli ne zgodi. Ustreza mu prazna množica izidov. <strong>Gotov dogodek (G)</strong> je dogodek, ki se vedno zgodi. Ustreza mu univerzalna množica oziroma množica vseh izidov.',\r\n\t\t3: '<strong>Verjetnost dogodka</strong> je število, ki izraža stopnjo prepričanja, da se bo dogodek zgodil. <strong>Množica vseh možnih izidov poskusa</strong> je enota, označena z &#937;.',\r\n\t\t4: '<strong>Primer 2.1.1.</strong>',\r\n        5: 'Ko vržemo kovanec, lahko pade cifra (označeno z 𝑝) ali grb (označeno z 𝑔). Iz tega sledi, da je množica vseh izidov enega meta kovanca množica z dvema elementoma.',\r\n        6: 'Ω = {𝑝, 𝑔}',\r\n        7: 'Poskus je sestavljen iz dveh zaporednih metov kovanca. Vsakič pade bodisi 𝑝 bodisi 𝑔. Vsak možen izid poskusa lahko predstavimo z urejenim parom, v katerem je prvi element rezultat prvega meta, drugi element pa rezultat drugega meta. Zato so izidi poskusa urejeni pari (𝑝, 𝑝), (𝑝, 𝑔), (𝑔, 𝑝) in (𝑔, 𝑔), medtem ko je množica izidov štiričlanski nabor',\r\n        8: 'Ω = {(𝑝, 𝑝), (𝑝, 𝑔), (𝑔, 𝑝), (𝑔, 𝑔)}',\r\n        9: 'Pri metanju kocke s ploskvami, oštevilčenimi od 1 do 6, je lahko izid katera koli od teh števil. Iz tega sledi, da je množica izidov enega meta kocke naslednja:',\r\n        10: 'Ω = {1, 2, 3, 4, 5, 6}.',\r\n        11: 'Vemo, da se bo med izvajanjem poskusa zgodil element nabora &#937;. V tem kontekstu pravimo, da smo gotovi, da bi se zgodil vsaj eden od možnih dogodkov množice &#937;, še pogosteje pa pravimo, da je verjetnost, da se bo &#937; zgodil enaka 1. Tako s številom izražamo stopnjo prepričanja o pojavu &#937;.',\r\n        12: 'Dogodek A je del nabora &#937;, zato je stopnja prepričanja o pojavu A izražena z odstotkom, ki je nižji od ali enak 100 %.',\r\n        13: 'Ker je odstotek število z imenovalcem 100, je stopnja prepričanja o pojavu Ω izražena s številom 1, stopnja prepričanja o pojavu A pa s številom iz intervala [0, 1].',\r\n        14: '<strong>Verjetnost</strong> (ali verjetnostna mera) je predpis, ki vsakemu dogodku A priredi število, ki ga označimo s P(A) in mu pravimo verjetnost dogodka A, v skladu s spodnjimi načeli: ',\r\n        15: '0 ≤ P(A) ≤ 1 za vsak dogodek A;',\r\n        16: 'Če sta dogodka A in B nezdružljiva, mora biti',\r\n        17: 'formula',\r\n        18: 'Verjetnost nemogočega dogodka je 0 in verjetnost gotovega dogodka je 1: P(N) = 0, P(G) = 1.',\r\n        19: '<strong>Primer 2.1.2.</strong>',\r\n        20: '<strong>Klasična definicija verjetnosti</strong>',\r\n        21: 'Če ima poskus končno število izidov, ki so vsi enako možni, je verjetnost dogodka količnik števila ugodnih izidov in števila vseh možnih izidov tega poskusa.',\r\n        22: 'Število ugodnih izidov je označeno s k(A), medtem ko je število vseh možnih izidov označeno s k(&#937;).',\r\n        23: 'Zato se verjetnost dogodka A izračuna na naslednji način:',\r\n        24: 'formula',\r\n        25: 'Na primer množica izidov metanja kovanca je Ω = {𝑝, 𝑔}. Če je kovanec, ki ga mečemo, pošten, ni nobenega razloga, da bi dali prednost eni od njegovih strani. Zato je verjetnost, da bomo vrgli cifro, enaka verjetnosti, da bomo vrgli grb:',\r\n        26: 'formula',\r\n        27: '<strong>Primer 2.1.3.</strong>',\r\n        28: '<strong>Statistična definicija verjetnosti</strong>',\r\n        29: 'Ni potrebo, da je množica izidov Ω končna, niti da so vsi izidi enako verjetni. V tem primeru ni mogoče uporabiti klasičnega pristopa k računanju verjetnosti dogodka 𝐴 ⊆ Ω. Ena od metod za izračun verjetnosti dogodka A temelji na neodvisnem ponavljanju poskusa.',\r\n        30: 'Po vsaki ponovitvi poskusa preštejemo, kolikokrat se je do tedaj zgodil dogodek A. To število se imenuje <strong>frekvenca dogodka</strong> A.',\r\n        31: 'Poleg frekvence dogodka A izračunamo po vsaki ponovitvi poskusa količnik frekvence dogodka A in skupnega števila ponovitev poskusa. To število se imenuje <strong>relativna frekvenca dogodka</strong> A.',\r\n        32: 'Ko se zaradi povečanja števila izvedb poskusa relativne frekvence dogodkov ustalijo pri določenem številu, se to število vzame kot verjetnost P(A).',\r\n        33: 'Če se na primer poveča število metov poštenega kovanca, se bodo relativne frekvence kovancev, ki pristanejo z grbom navzgor, bližale <div class=\"fraction\" top=\"1\" bottom=\"2\"></div>. Če kovanec vržemo 40-krat, bi lahko zaporedje teh relativnih frekvenc predstavili z naslednjim linijskim grafom:',\r\n        34: 'Vendar bi bil kovanec lahko nepošten. Kaj se zgodi, če vržemo kovanec, za katerega je verjetnost, da bo pristal z grbom navzgor, dvakrat večja, kot da bo pristal s cifro navzgor? Ta poskus izvedite večkrat in si oglejte spreminjanje relativnih frekvenc izida grba z večanjem števila poskusov.',\r\n        35: 'Navodila za interakcijo:',\r\n        36: 'Vprašanje št. 1. -  Kliknite \"Izračunaj verjetnost\", da se bo prikazala rešitev.',\r\n        37: 'Vprašanji št. 2. in 3. - Od ponujenih parov izberite dva in kliknite \"Izračunaj verjetnost\". Če je bila izbira pravilna, se bo prikazala rešitev.',\r\n        38: 'Vprašanje št. 4. - Kliknite \"Izračunaj verjetnost\", da se bo prikazala rešitev.'\r\n      },\r\n      'vjerojatnost-interakcija': {\r\n        1: 'Kolikšna je verjetnost, da bo pri prvem metu padel grb?',\r\n        2: 'Izračunaj verjetnost',\r\n        3: 'Ponastavi označene dogodke',\r\n        4: 'Kolikšna je verjetnost, da bo pri drugem metu padel grb?',\r\n        5: 'Napačno izbrani dogodki, poskusite znova.',\r\n        6: 'Kolikšna je verjetnost, da bo pri obeh metih padel grb?',\r\n        7: 'Preverite verjetnost drugih dvodelnih delov Ω. Določite tudi verjetnost nekaterih tridelnih delov Ω.',\r\n        8: 'Relativne frekvence pristajanja kovancev z grbom navzgor',\r\n        9: 'Število metov kovanca',\r\n        10: 'V redu'\r\n      },\r\n      'vjerojatnost-interakcija-2': {\r\n        1: 'Vrzi kovanec',\r\n        2: 'Število metov mora biti pozitivno celo število, večje od 0.',\r\n        3: 'Kovanec',\r\n        4: 'Število metov',\r\n        5: 'Število grbov',\r\n        6: 'Število cifer',\r\n        7: 'Navaden kovanec',\r\n        8: 'Verjetnost, da pade grb, je dvakrat večja, kot da pade cifra.',\r\n        9: 'Verjetnost, da pade cifra, je dvakrat večja, kot da pade grb.',\r\n      },\r\n      'vjerojatnost-zadatak': {\r\n        title: 'Verjetnost',\r\n        1: '<strong>Naloga 2.1.1.</strong>',\r\n        2: 'Brata, oba hazarderja, sta popolnoma drugačna - prvi je pošten, drugi pa goljufa.',\r\n        3: 'Pošteni hazarder igra s pošteno kocko. Kolikšna je verjetnost, da bo dobil sodo število, ko bo vrgel kocko enkrat?',\r\n        4: 'Njegov brat se je odločil, da bo goljufal, in je izdelal kocko, pri kateri se določena števila pojavijo pogosteje kot druga. Postavite se na njegovo mesto in izberite števila, ki bi jim radi dali prednost. Z interaktivnim orodjem ugotovite po statistični definiciji verjetnosti, kolikšna je verjetnost, da bo pri metu takšne kocke padlo sodo število.',\r\n        5: '<strong>Rešitev</strong>',\r\n        6: 'Množica izidov metanja kocke je ',\r\n        7: 'Dogodek \"padlo je sodo število\" (označen z A) je naslednja podmnožica množice Ω:',\r\n        8: 'Ker je kocka poštena, z uporabo klasične definicije verjetnosti izhaja, da je verjetnost, da bo pošteni igralec pri metu kocke dobil sodo število',\r\n        9: 'V naslednjo tabelo vpišite za vsako število na kocki, kolikšna je verjetnost, da bo padla prav ta. Upoštevajte, da, kot je navedeno v besedilu naloge, sodim številom dodelite večje verjetnosti in da je vsota šestih verjetnosti 1. Na primer:',\r\n        10: 'Izid',\r\n        11: 'Verjetnost'\r\n      },\r\n      'vjerojatnost-zadatak-interakcija': {\r\n        1: 'Izid',\r\n        2: 'Verjetnost',\r\n        3: 'Verjetnost, da bo padlo sodo število',\r\n        4: 'Verjetnost, da bo padlo liho število',\r\n        5: 'Vrzi kocko',\r\n        6: 'Kocka',\r\n        7: 'Neveljavno število!',\r\n        8: 'Verjetnosti niso bile dobro izbrane (vsota mora biti 1).',\r\n        9: 'Vnesite število metov kocke:',\r\n        10: 'Število metov',\r\n        11: 'Verjetnost, da bo padlo sodo število (%)',\r\n        12: 'Izračunaj verjetnost'\r\n      },\r\n      'uvjetna-vjerojatnost': {\r\n        title: 'Pogojna verjetnost',\r\n        1: 'Opazujemo dogodek A v poskusu, ki je realizacija določenega kompleksa pogojev. Verjetnost dogodka A označimo s P(A). Kompleksu pogojev pridružimo dogodek B in v tem novem poskusu se verjetnost dogodka ujema s P(A) ali pa ne. Novo verjetnost imenujemo pogojna verjetnost in označimo P(A|B).',\r\n        2: 'Naj bo A pri pogoju B dogodek, katerega verjetnost nas zanima. Če vemo, da se je pri izvedbi poskusa zgodil dogodek B, za katerega je P(B)>0, se množici ugodnih izidov in vseh izidov spremenita. Množica ugodnih izidov postane A ∩ B, množica vseh izidov pa B.',\r\n        3: '<strong>Primer 2.2.1.</strong>',\r\n        4: 'V igri na srečo je cilj, da s kocko vržemo praštevilo.',\r\n        5: 'Množica izidov metanja kocke je &Omega; = {1, 2, 3, 4, 5, 6}, množica ugodnih izidov pa je množica vseh praštevil iz &Omega;, {2, 3, 5}.',\r\n        6: 'Vendar se z dodatno informacijo, da je padlo sodo število, množica ugodnih in vseh izidov spremeni.',\r\n        7: 'Če v poskusu opazujemo dogodek A in vemo, da se je zgodil dogodek B, za katerega P(B)>0, potem verjetnosti dogodka A rečemo <strong>pogojna verjetnost dogodka</strong> A pod pogojem B in jo izračunamo na naslednji način:',\r\n        8: '<strong>Primer 2.2.2.</strong>',\r\n        9: 'V poskusu, v katerem pošten kovanec vržemo dvakrat zapored, je množica izidov &omega; = {(p,p), (p,g), (g,p), (g,g)} in vsi izidi so enako verjetni.',\r\n        10: 'Verjetnost, da bo kovanec padel na isto stran v obeh metih, pri čemer je ta dogodek označen z A = {(p, p), (g, g)}, se izračuna po klasični definiciji verjetnosti in znaša <div class=\"fraction\" top=\"1\" bottom=\"2\"></div>.',\r\n        11: 'Če pa je znano, da je pri prvem ali drugem metu padla cifra, vemo, da se je zgodil dogodek:',\r\n        12: 'B = {(𝑝, 𝑝), (𝑝, 𝑔), (𝑔, 𝑝)}, 𝑃(𝐵) = 3/4',\r\n        13: 'S to dodatno informacijo je verjetnost, da bo kovanec padel na isto stran v obeh metih, tj. pogojna verjetnost dogodka A pri pogoju B',\r\n        14: '1 𝑃(𝐴 ∩ 𝐵) 4 1 𝑃(𝐴|𝐵) = = = . 𝑃(𝐵) 3 3 4',\r\n\t\t15: ''\r\n      },\r\n      'uvjetna-vjerojatnost-interakcija': {\r\n        1: '(Množica vseh izidov):',\r\n        2: 'Množica ugodnih izidov:',\r\n        3: 'Padlo je sodo število',\r\n        4: 'Uresničen dogodek',\r\n        5: 'Nova množica ugodnih izidov',\r\n        6: '3. Slučajna spremenljivka'\r\n      },\r\n      'uvjetna-vjerojatnost-zadatak': {\r\n        title: 'Pogojna verjetnost',\r\n        1: '<strong>Naloga 2.2.1.</strong>',\r\n        2: 'Z interaktivnim orodjem izračunajte verjetnost, da pri metu kocke, ki ni nujno poštena, pade šestica, če veste, da se je zgodil izbrani dogodek B. Verjetnosti izidov metanja kocke in dogodek B izberite sami.',\r\n        3: 'Navodilo: Vsota verjetnosti pri metu kocke mora biti enaka 1.'\r\n      },\r\n      'uvjetna-vjerojatnost-zadatak-interakcija': {\r\n        1: 'Izid',\r\n        2: 'Verjetnost',\r\n        3: 'Vstavi število',\r\n        4: 'Verjetnost, da bo padla šestica s pogojem B',\r\n        5: 'Vsota vseh elementov mora biti enaka 1. Ponovite vnos!',\r\n        6: 'Vpisane številke morajo biti pozitivne.',\r\n        7: 'Vnos besedila ni dovoljen',\r\n        8: 'Elementi dogodka B se izbirajo s klikom na želene izide v prvi vrstici tabele. Vnesite tudi verjetnosti za vse izide.',\r\n        9: 'Izpolniti je treba vsa polja',\r\n        10: 'Iz prve vrstice tabele je treba izbrati vsaj en izid.'\r\n      }\r\n    },\r\n    statisticko_zakljucivanje: {\r\n      chapterNumber: '&mdash; 5. poglavje &mdash;',\r\n      title: 'Statistično sklepanje',\r\n      'populacija_i_uzorak': {\r\n        title: 'Populacija in vzorec',\r\n        1: 'Pri statističnem sklepanju podatke, ki so nam na voljo, obravnavamo kot vrednosti, zbrane v delu <strong>populacije</strong>; ta del populacije imenujemo <strong>vzorec</strong>. Primer za to so predvolilne ankete, za katere se izbere del volilnih upravičencev, potem pa se skuša na podlagi njihovih odgovorov sklepati o izidu volitev.',\r\n        2: 'Z zbiranjem <a href=\"../opisivanje-podataka/podaci\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">podatkov</a> o neki značilnosti (spremenljivka 𝑋) populacije na vzorcu dobimo vrednosti 𝑥<sub>1</sub>, 𝑥<sub>2</sub>, ... , 𝑥<sub>𝑛</sub>, pri čemer je n <strong>velikost vzorca</strong>.',\r\n        3: 'Statistični sklepi, ki temeljijo na vzorcu, imajo določeno stopnjo negotovosti, ker: ',\r\n        4: 'vzorec ne zajema vseh enot populacije (na primer predvolilne ankete, katerih namen je napovedati izid volitev, se izvajajo samo na delu volilnih upravičencev),',\r\n        5: 'podatki vsebujejo komponento slučajnosti (na primer izida meta kovanca ni mogoče predvideti).',\r\n\t\t6: 'Vzorec obravnavamo kot realizacijo 𝑛 <a href=\"../slucajna-varijabla/slucajna-varijabla\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">slučajnih spremenljivk</a> 𝑋<sub>1</sub>, 𝑋<sub>2</sub>, ... , 𝑋<sub>𝑛</sub>, imenovanih <strong>slučajni vzorec</strong>.',\r\n        7: 'Slučajni vzorec je <strong>enostaven</strong>, če velja naslednje:',\r\n        8: '𝑋<sub>1</sub>, 𝑋<sub>2</sub>, ... , 𝑋<sub>𝑛</sub> so enako porazdeljene kot slučajna spremenljivka X (značilnost populacije),',\r\n        9: '𝑋<sub>1</sub>, 𝑋<sub>2</sub>, ... , 𝑋<sub>𝑛</sub> so medsebojno neodvisne.',\r\n        10: 'Predvolilne ankete ne smemo izvesti samo med upokojenci, ampak mora biti vzorec <strong>reprezentativen</strong>, tj. tak, da  predstavlja tipične značilnosti prebivalstva, pomembne za anketo.',\r\n        11: 'Vzorec je torej sestavljen iz realizacij neodvisnih slučajnih spremenljivk, ki so enako porazdeljene kot spremenljivka X na celotni populaciji. Zato pravimo, da so vrednosti 𝑥<sub>1</sub>, 𝑥<sub>2</sub>, ... , 𝑥<sub>𝑛</sub> <strong>vzorec za spremenljivko</strong> 𝑋.',\r\n        12: 'Na podlagi vrednosti iz vzorca so podani sklepi o porazdelitvi <a href=\"../slucajna-varijabla/slucajna-varijabla\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">slučajne spremenljivke</a> 𝑋. Porazdelitev spremenljivke 𝑋 je lahko popolnoma neznana ali pa je lahko znan le njen tip, medtem ko so njeni parametri neznani (na primer 𝑋 ima <a href=\"../distribucije/normalna-distribucija\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">normalno porazdelitev</a> z neznano pričakovano vrednostjo in standardnim odklonom).',\r\n        13: '<strong>Primer 5.1.1.</strong>',\r\n        14: 'Na Hrvaškem so leta 2014 izvedli raziskovanje o potrošnji gospodinjstev ter o socialno-ekonomskih in demografskih značilnostih gospodinjstev. Anketiranih je bilo 2029 slučajno izbranih gospodinjstev, zbrani pa so bili podatki za naslednje tri spremenljivke:',\r\n        15: 'skupni letni izdatki gospodinjstva, ',\r\n        16: 'vrsta stanovanjske enote (hiša ali stanovanje), ',\r\n        17: 'število članov gospodinjstva.',\r\n        18: 'Populacija v tem raziskovanju so vsa gospodinjstva na Hrvaškem, vzorec pa anketirana gospodinjstva. Velikost vzorca je 2029. Imamo tri vrste spremenljivk:',\r\n        19: 'Spremenljivka skupni letni izdatki gospodinjstva je zvezna slučajna spremenljivka. Ker ni utemeljenega razloga za domnevo o tipu porazdelitve, menimo, da je popolnoma neznan.',\r\n        20: 'Spremenljivka, ki predstavlja tip stanovanjske enote, ima lahko le dve vrednosti. Če sta vrednosti označeni z 0 (hiša) in 1 (stanovanje), je to <a href=\"../distribucije/bernoulijeva-distribucija\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">Bernoullijeva slučajna spremenljivka</a> z neznanim parametrom 𝑝',\r\n        21: 'Torej je tip porazdelitve znan, parameter p pa ni znan.',\r\n        22: 'Spremenljivka število članov gospodinjstva je diskretna slučajna spremenljivka z možnimi vrednostmi 1, 2.... Verjetnosti teh vrednosti niso znane.'\r\n      },\r\n      'populacija_i_uzorak_zadatak_1': {\r\n        title: 'Populacija in vzorec - naloga',\r\n        1: 'V poskusu dvakrat vržemo kovanec. Poskus ponovimo 200-krat. Opazujemo, kolikokrat padeta dve cifri. Kaj je v tem primeru populacija in kaj je vzorec? Katero spremenljivko opazujemo in kaj lahko rečemo o njeni porazdelitvi?',\r\n        2: '<strong>Rešitev</strong>',\r\n        3: 'Poskus dvakratnega meta kovanca lahko ponovimo kolikorkrat želimo, zato je populacija vseh dvojnih metov neskončna. Vzorec je 200 dvojnih metov kovanca. Poskusi so medsebojno neodvisni in porazdelitev možnih izidov je vedno enaka, saj ves čas mečemo isti kovanec. Zato je to <strong>enostaven slučajni vzorec</strong>.',\r\n        4: 'Opazovana spremenljivka je število cifer v dveh metih. Spremenljivka ima lahko tri vrednosti: 0, 1 in 2. Verjetnost 𝑝, da pade cifra v enem metu, ni znana, znano pa je, da je porazdelitev spremenljivke število cifer v dveh metih naslednja: ',\r\n        5: '<strong>Naloga 5.1.1.</strong>'\r\n      },\r\n      'procjena_proporcije_vjerojatnosti': {\r\n        title: 'Ocena deleža',\r\n        1: 'Naj ima spremenljivka X na vzorcu vrednosti 𝑥<sub>1</sub>, 𝑥<sub>2</sub>, ... , 𝑥<sub>𝑛</sub>. Če spremenljivka lahko zavzame le dve vrednosti 0 in 1, ima spremenljivka 𝑋 <a href=\"../distribucije/bernoulijeva-distribucija\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">Bernoullijevo porazdelitev:</a>',\r\n        2: 'pri čemer 𝑝 ni znan. Parameter 𝑝 je verjetnost vrednosti 1, to je deleža vrednosti 1 v celotni populaciji. Neznani parameter 𝑝 lahko <strong>ocenimo</strong> z <a href=\"../opisivanje-podataka/frekvencije-i-relativne-frekvencije\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">relativno frekvenco</a> (𝑝&#770;) vrednosti 1 na vzorcu (f<sub>1</sub> je frekvenca vrednosti 1): ',\r\n\t\t3: 'Isto načelo lahko uporabimo, ko ima spremenljivka 𝑋 več kot dve možne vrednosti. Verjetnost vsake vrednosti se nato oceni z relativno frekvenco te vrednosti na vzorcu. Če ima na primer spremenljivka 𝑋 verjetnostno shemo',\r\n        4: 'je ocena za 𝑝<sub>i</sub> relativna frekvenca vrednosti na vzorcu (i=1, 2, 3, 4). Ocenjena verjetnostna shema spremenljivke 𝑋 se imenuje <stong>empirična porazdelitev</strong>.',\r\n        5: '<strong>Primer 5.2.1.</strong>',\r\n        6: 'Vržemo kovanec, za katerega ni znano, ali je pošten ali ne. Če je \"cifra\" označena z 1 in \"grb\" z 0, dobimo spremenljivko z Bernoullijevo porazdelitvijo,',\r\n        7: 'kjer je 𝑝 neznana verjetnost, da bo padla cifra.',\r\n        8: 'Ocena (𝑝&#770;) z večjim številom metov je praviloma bližje dejanski vrednosti, kar zagotavlja <a href=\"../slucajna-varijabla/ocekivanje/dodatni-zadaci\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">zakon velikih števil</a>.'\r\n      },\r\n      'procjena_proporcije_vjerojatnosti_interakcija': {\r\n        1: 'Populacijski parameter p:',\r\n        2: 'Število metov:',\r\n        3: 'Vrzi',\r\n        4: 'Ocena',\r\n        5: 'Velikost vzorca n = ',\r\n        6: 'Ocena deleža/verjetnosti',\r\n        7: 'Cifra',\r\n        8: 'Grb',\r\n        9: 'Parametri niso bili dobro izbrani.',\r\n        10: 'Verjetnost mora biti v intervalu [0, 1]',\r\n        11: 'Vstavi števila',\r\n        12: 'Število metov mora biti večje od 0'\r\n      },\r\n      'procjena_proporcije_vjerojatnosti_zadatak_1': {\r\n        title: 'Ocena deleža/verjetnosti - naloga',\r\n        1: 'Na Hrvaškem od 2029 anketiranih v 1635 gospodinjstvih živi v stanovanju ali hiši v zasebni lasti brez stanovanjskega posojila, 160 v stanovanju ali hiši v zasebni lasti s stanovanjskim posojilom, 77 v najetem stanovanju ali hiši in 156 v brezplačno najetem stanovanju ali hiši.',\r\n        2: 'Na podlagi teh podatkov ocenite porazdelitev spremenljivke, s katero lahko opišete bivališča celotne populacije.',\r\n        3: '<strong>Rešitev</strong>',\r\n        4: 'Možne vrednosti spremenljivke X, ki predstavlja vrsto stanovanja, so:',\r\n        5: 'stanovanje ali hiša v zasebni lasti brez stanovanjskega posojila',\r\n        6: 'stanovanje ali hiša v zasebni lasti s stanovanjskim posojilom',\r\n        7: 'najeto stanovanje ali hiša',\r\n        8: 'brezplačno najeto stanovanje ali hiša.',\r\n        9: 'Ocena porazdelitve (empirična porazdelitev) je',\r\n        10: '<stong>Naloga 5.2.1.</strong>'\r\n      },\r\n      'procjena_ocekivanja_i_varijance': {\r\n        title: 'Ocena pričakovane vrednosti in variance',\r\n        1: 'Naj ima spremenljivka X na vzorcu vrednosti 𝑥<sub>1</sub>, 𝑥<sub>2</sub>, ... , 𝑥<sub>𝑛</sub>. Pričakovano vrednost 𝜇 = 𝐸(𝑋) ocenimo z <a href=\"../opisivanje-podataka/prosjek\" class=\"topic-link\">aritmetično sredino</a> vrednosti na vzorcu',\r\n        2: 'Varianco 𝜎<sup>2</sup> = 𝑉𝑎𝑟(𝑋) ocenimo z <a href=\"../opisivanje-podataka/varijanca-i-standardna-devijacija\" class=\"topic-link\" target=\"_blank\" rel=\"noopener noreferrer\">vzorčno varianco</a> vrednosti na vzorcu',\r\n        3: 'Ocena za <strong>standardni odklon</strong> 𝜎 je <a href=\"../opisivanje-podataka/varijanca-i-standardna-devijacija\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">vzorčni standardni odklon</a> 𝑠<sub>𝑛</sub>.',\r\n        4: '<strong>Primer 5.3.1.</strong>',\r\n        5: 'Na voljo so podatki o izmerjeni višini 100 moških iz populacije. Oceniti je treba pričakovano vrednost in varianco višine v obravnavani populaciji.',\r\n        6: 'Z naslednjim orodjem je mogoče izračunati ocene za različno velike podvzorce, naključno izbrane iz izvirnega vzorca velikosti 100. Opazujte, kaj se zgodi z ocenami pričakovane vrednosti in variance na takih manjših vzorcih.'\r\n      },\r\n      'procjena_ocekivanja_i_varijance_interakcija': {\r\n        1: 'Histogram podatkov: ',\r\n        2: 'Velikost vzorca: ',\r\n        3: 'Ocena pričakovane vrednosti <span class=\"math-symbol\">𝜇<sup>^</sup></span>= 𝑥̅',\r\n        4: 'Ocena variance <span class=\"math-symbol\">𝜎<sup>^</sup></span>',\r\n        5: 'Velikost podvzorca mora biti celo število od 0 do 100!',\r\n        6: 'Vzemi podvzorec',\r\n        7: 'Podatki: ',\r\n      },\r\n      'pouzdani_interval_za_ocekivanje': {\r\n        title: 'Interval zaupanja za pričakovano vrednost',\r\n        1: 'Namesto da parameter ocenimo z eno vrednostjo, lahko ocenimo interval, ki z določenim zaupanjem vsebuje pravo vrednost parametra. Tak interval se imenuje interval zaupanja.',\r\n        2: 'Če je slučajna spremenljivka X porazdeljena normalno z neznano pričakovano vrednostjo 𝜇 in neznano varianco, se interval zaupanja za pričakovano vrednost 𝜇 izračuna po formuli',\r\n        3: ' ',\r\n        4: 'V zgornji formuli je 𝛾 <strong>stopnja zaupanja</strong>, običajno 0,95 ali 0,99. Število 𝑡<sub>𝑛−1,𝛾</sub> se določi tako, da je:',\r\n        5: 'za slučajno spremenljivko 𝑇<sub>𝑛−1</sub>, s Studentovo t-porazdelitvijo s stopinjami prostosti 𝑛−1. Grafično to pomeni določitev intervala, simetričnega glede na 0, nad katerim verjetnostna gostota Studentove t-porazdelitve zapira območje s ploščino 𝛾.',\r\n\t\t6: ' ',\r\n        7: '<strong>Primer 5.4.1.</strong>',\r\n        8: 'Interaktivno orodje uporabite za simulacijo izračuna 100 intervalov zaupanja za vzorce iz normalne porazdelitve, ki vsebujejo (ne vsebujejo) populacijske vrednosti 𝜇.'\r\n      },\r\n      'pouzdani_interval_za_ocekivanje_interakcija': {\r\n        1: 'Pričakovana vrednost 𝜇:',\r\n        2: 'Varianca 𝜎<sup>2</sup>:',\r\n        3: 'Stopnja zaupanja 𝛾:',\r\n        4: 'Velikost vzorca 𝑛:',\r\n        5: 'Vpiši številko',\r\n        6: 'Ustvari 100 vzorcev',\r\n        7: 'Stopnja zaupanja mora biti manjša od 1. Znova vnesite podatke!',\r\n        8: 'Vpisana vrednost mora biti število!',\r\n        9: 'siva - število zanesljivih intervalov, ki vsebujejo realno vrednost 𝜇',\r\n        10: 'rdeča - število zanesljivih intervalov, ki ne vsebujejo realne vrednosti 𝜇'\r\n      },\r\n      'pouzdani_interval_za_ocekivanje_zadatak_1': {\r\n        title: 'Interval zaupanja za pričakovano vrednost - naloga',\r\n        1: 'Gospodinjstva na Hrvaškem porabijo za oblačila in obutev letno povprečno 5494 kun s standardnim odklonom 197,78 kun. Podatki temeljijo na 2029 anketiranih gospodinjstvih.',\r\n        2: 'S kalkulatorjem izračunajte 95-odstotni interval zaupanja za pričakovane izdatke za oblačila in obutev.',\r\n        3: 'Dobljeni interval primerjajte z intervali, ki bi jih dobili, če (druge vrednosti so nespremenjene):',\r\n        4: 'a) bi bil standardni odklon 100',\r\n        5: 'a) bi bila velikost vzorca 1000',\r\n        6: 'c) bi bila stopnja zaupanja 0,99.',\r\n        7: 'Kako se interval zaupanja spremeni s spreminjanjem standardnega odklona/velikosti vzorca/stopnje zaupanja, če druge vrednosti ostanejo nespremenjene?',\r\n        8: '<strong>Rešitev</strong>',\r\n        9: 'Za manjši standardni odklon je interval ožji - če je razpršenost manjša, lahko z ožjim intervalom podamo enako zanesljivo oceno. Za manjšo velikost vzorca je interval širši. Pri večji stopnji zaupanja je interval širši.',\r\n        10: 'Povprečje<span class=\"math-symbol\"><i>x&#772;</i></span><sub><i>n</i></sub>:',\r\n        11: 'Standardni odklon vzorca <span class=\"math-symbol\"><i>s&#772;</i></span><sub><i>n</i></sub>:',\r\n        12: 'Stopnja zaupanja 𝛾',\r\n        13: 'Velikost vzorca 𝑛',\r\n        14: '<strong>Naloga 5.4.1.</strong>'\r\n      },\r\n      'pouzdan-interval-za-procjenu-i-vjerojatnost': {\r\n        title: 'Interval zaupanja za delež',\r\n        1: 'Pogosto slišimo izjave, da je npr. \"80 % uporabnikov opazilo izboljšanje lepote las/beline zob/čistoče perila\". V takih izjavah je mogoče skritih veliko dvoumnosti. Velikost vzorca na primer redko poznamo in 80 % se lahko nanaša na štiri od petih uporabnikov.',\r\n        2: 'Namesto da bi ocenili neznan delež p značilnosti v populaciji z enim številom, ga je bolje oceniti z <strong>intervalom zaupanja za delež</strong>',\r\n        3: 'formula',\r\n        4: 'pri čemer je 𝑝&#770; vzorčna ocena paranetra p, 𝑛 je velikost vzorca, <i>z</i><sub>𝛾</sub> se določi tako, da velja ',\r\n        5: 'formula',\r\n        6: 'za slučajno spremenljivko Z, ki ima standardizirano <a href=\"../distribucije/normalna-distribucija\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">normalno porazdelitev</a>. Grafično to pomeni določitev intervala, simetričnega glede na 0, nad katerim verjetnostna gostota standardizirane normalne porazdelitve zapre območje s ploščino 𝛾.',\r\n        7: 'Če izračunamo večje število intervalov zaupanja, bodo ti vsebovali populacijsko vrednost deleža 𝑝 v približno 100𝛾 % primerov. Opisani interval zaupanja je uporaben le, če je vzorec dovolj velik. Če nimamo dovolj velikega vzorca, je interval zaupanja tako širok, da ni uporaben.',\r\n        8: '<strong>Primer 5.5.1.</strong>',\r\n        9: 'V poskusu metanja kovancev želimo z intervalom zaupanja oceniti verjetnost, da pade cifra. Orodje v interakciji lahko uporabimo, da opazujemo, kako se intervali zaupanja s povečanjem velikosti vzorca praviloma krajšajo.',\r\n        10: '<strong>Primer 5.5.2.</strong>',\r\n        11: 'Na Hrvaškem živi 26,4 % gospodinjstev v stanovanjih. Podatki temeljijo na 2029 anketiranih gospodinjstvih. S kalkulatorjem na desni lahko izračunamo 95-odstotni interval zaupanja za delež gospodinjstev, ki živijo v stanovanjih.'\r\n      },\r\n      'pouzdan-interval-za-procjenu-i-vjerojatnost-interakcija': {\r\n        1: 'Verjetnost, da pade cifra 𝑝: ',\r\n        2: 'Stopnja zaupanja 𝛾: ',\r\n        3: 'Število metov 𝑛: ',\r\n        4: 'Vrzi',\r\n        5: 'Stopnja zaupanja mora biti manjša od 1. Znova vnesite podatke!',\r\n        6: 'Vpišite število',\r\n        7: 'Vpisane vrednosti morajo biti pozitivne',\r\n        8: 'Vpisane vrednosti morajo biti števila',\r\n        9: 'Verjetnost mora biti v območju [0, 1]'\r\n      },\r\n      'pouzdan-interval-za-procjenu-i-vjerojatnost-interakcija-2': {\r\n        1: 'Relativna frekvenca <i class=\"math-symbol\">p̂</i>:',\r\n        2: 'Stopnja zaupanja ',\r\n        3: 'Velikost vzorca ',\r\n        4: 'Izračunaj',\r\n        5: 'Interval zaupanja',\r\n        6: 'Vpisane vrednosti morajo biti pozitivne',\r\n        7: 'Vpisane vrednosti morajo biti števila',\r\n        8: 'Vpisati je treba vse vrednosti',\r\n        9: 'Relativna frekvenca mora biti med 0 in 1.',\r\n        10: 'Stopnja zaupanja mora biti med 0 in 1.'\r\n      },\r\n      'pouzdan-interval-za-procjenu-i-vjerojatnost-zadatak': {\r\n        title: 'Interval zaupanja za delež/verjetnost',\r\n        1: '<strong>Naloga 5.5.1.</strong>',\r\n        2: 'Predpostavimo, da na volitvah sodelujeta le dva kandidata, A in B. Cilj ankete je napovedati zmagovalca. Od 1000 anketiranih državljanov jih je 577 izjavilo, da bodo glasovali za kandidata A. Z uporabo kalkulatorja za interval zaupanja izračunajte 95-odstotni interval zaupanja za delež glasov za kandidata A.',\r\n        3: '<strong>Rešitev</strong>',\r\n        4: 'Ocena deleža glasov za kandidata A je 0,577 (ali 57,5 %), interval zaupanja pa [0,5464, 0,6076] (ali [54,64 %, 60,76 %]). ',\r\n        5: 'Intervali zaupanja so pogosto predstavljeni v obliki 0,577±0,0306, to je 57,7 %±3,06 %. Ko govorimo o rezultatih javnomnenjske ankete v medijih, pogosto slišimo opombo, ki pravi, da \"statistična napaka znaša ±3 %\". To je dejansko polovica dolžine intervala zaupanja in običajno se domneva, da je stopnja zaupanja 0,95.'\r\n      },\r\n      'testiranje-statistickih-hipoteza': {\r\n        title: 'Preizkušanje statističnih domnev',\r\n        1: 'Predpostavimo, da igramo igro s kovancem, v kateri zmagamo, če vržemo cifro. Radi bi vedeli, ali je kovanec pošten. Ta kovanec vržemo desetkrat. V desetih metih je dvakrat padla cifra in osemkrat grb. Če bi bil kovanec pošten, bi pričakovali 5 cifer in 5 grbov. Ali je odstopanje, ki smo ga dobili, le slučajno (slaba sreča) ali lahko sumimo, da je kovanec nepošten?',\r\n        2: 'Odgovor je mogoče poiskati s statističnim sklepanjem, kjer postavimo dve <strong>statistični domnevi</strong>. Ena domneva se imenuje <strong>ničelna domneva</strong> in se označi s <i>H<sub>0</sub></i>, druga pa <strong>alternativna domneva</strong> in se označi s <i>H<sub>1</sub></i>. V tem primeru sta domnevi',\r\n        3: '<i>H<sub>0</sub></i>: kovanec je pošten',\r\n        4: '<i>H<sub>1</sub></i>: kovanec ni pošten in cifra pade redkeje kot grb.',\r\n        5: 'Z metanjem kovanca dobimo vzorec iz Bernoullijeve porazdelitve s parametrom <i>p</i>, ki predstavlja verjetnost, da pade cifra. Domnevi lahko izrazimo kot izjavi o neznanem parametru',\r\n        6: '<i>H<sub>0</sub></i>: p = 0,5',\r\n        7: '<i>H<sub>1</sub></i>: p < 0,5',\r\n        8: '<strong>Primer 5.6.1.</strong>',\r\n        9: 'Interaktivno orodje uporabite za ponovitev poskusa desetih metov poštenega kovanca. Preverite, kolikokrat se je poskus končal z največ dvema ciframa.',\r\n        10: 'Kolikšna je verjetnost, da boste v 10 metih poštenega kovanca, dobili največ dve cifri? To verjetnost je mogoče izračunati. Število cifer v 10 metih poštenega kovanca ima <a href=\"../distribucije/binomna-distribucija\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\">binomsko porazdelitev</a> s parametroma 10 in 0,5, zato je verjetnost, da pade cifra največ dvakrat, 0,0547. To je verjetnost, da cifra pade največ dvakrat pod pogojem, da ničelna domneva velja. Ta verjetnost kaže, kako gotova je <i>H<sub>0</sub></i>.',\r\n        11: 'Ali lahko zaradi le dveh padlih cifer v desetih metih kovanca zavrnemo ničelno domnevo <i>H<sub>0</sub></i>, da je kovanec pošten? Do povsem zanesljivega odgovora ne moremo priti, ker se kaj takega lahko zgodi tudi pri metanju poštenega kovanca. Vnaprej lahko določimo, kolikšno verjetnost napačne zavrnitve ničelne domenve še dopuščamo. Ta verjetnost se imenuje <strong>stopnja značilnosti</strong>, in je običajno nastavljeno na 0,05.',\r\n        12: 'V tem primeru je verjetnost največ dveh cifer višja od običajne stopnje značilnosti, 0,0547 > 0,05. Če je kovanec pošten, opažen rezultat poskusa niti ni tako neverjeten, zato ni razloga za zavrnitev ničelne domneve.',\r\n        13: 'Koliko cifer bi zadostovalo za zavrnitev ničelne domneve? Predpostavimo, da je cifra padla pri enem metu od desetih. Verjetnost največ ene cifre je 0,0107. V približno enem od 100 poskusov s poštenim kovancem bi cifra padla največ enkrat. To je tako neverjetno, da bi lahko pri stopnji značilnosti 0,05 rekli, da kovanec ni pošten in da cifra pade redkeje kot grb.',\r\n        14: 'Ta primer ponazarja le enega od mnogih statističnih testov, ki jih je mogoče uporabiti za različne probleme in vrste domnev.'\r\n      },\r\n      'testiranje-statistickih-hipoteza-interakcija': {\r\n        1: 'Število ponovitev N: ',\r\n        2: 'Ponovite 10 metov N-krat',\r\n        3: 'Število poskusov 10 metov: ',\r\n        4: 'Število iger z dvema ciframa ali manj: ',\r\n        5: 'Relativna frekvenca: ',\r\n        6: 'vrednosti',\r\n        7: 'Vpisane vrednosti morajo biti pozitivne in nad 0',\r\n        8: 'Vpisane vrednosti morajo biti števila',\r\n        9: 'Pričakovana vrednost mora biti pozitivno število',\r\n        10: 'Vpisati je treba vse vrednosti'\r\n      },\r\n      'testiranje-statistickih-hipoteza-zadatak': {\r\n        title: 'Preizkušanje statističnih domnev - naloga',\r\n        1: '<strong>Naloga 5.6.1.</strong>',\r\n        2: 'Na vzorcu 50 oseb je bil opravljen test, ali lahko prepoznajo razliko med dragim in poceni vinom. Vsakemu poskuševalcu so dali neoznačene kozarce dragega in poceni vina in jih prosili, naj uganejo vrsto vina. Po pokušini jih je 34 pravilno opredelilo vrsto vina. Ali lahko pri stopnji značilnosti 0,05 rečemo, da ljudje prepoznajo vrsto vina glede na njegov okus?',\r\n        3: '<strong>Rešitev</strong>',\r\n        4: 'Gre za vzorec iz Bernoullijeve porazdelitve, pri kateri naj vrednost 1 pomeni, da je oseba vino pravilno prepoznala. Verjetnost vrednosti 1 označimo s p. Domnevi lahko zapišemo na naslednji način: ',\r\n        5: '<i>H<sub>0</sub></i>: p=0,5 (vrsto vina ugane slučajno)',\r\n        6: '<i>H<sub>1</sub></i>: p>0,5 (vrsto vina prepozna)',\r\n        7: 'Če poskuševalci vrsto vina slučajno ugibajo, potem jih vsaj 34 pravilno ugane z verjetnostjo 0,0078. Zato lahko s stopnjo značilnosti 0,05 zavrnemo ničelno domnevo. Ljudje torej prepoznajo razliko v vrstah vina.'\r\n      },\r\n      'jednostavna-linearna-regresija': {\r\n        title: 'Enostavna linearna regresija',\r\n        1: 'Ko proučujemo povezanost dveh številskih spremenljivk X in Y, vzamemo vzorec podatkovnih parov:',\r\n        2: 'formula',\r\n        3: 'Takšne podatkovne pare lahko narišemo v koordinatnem sistemu, s čimer dobimo <a href=\"../opisivanje-podataka/dijagram-rasprsenosti-i-standardna-devijacija\" class=\"topic-link\" target=\"_blank\" rel=\"noopener noreferrer\">razsevni diagram</a>.',\r\n        4: '<strong>Regresijske metode</strong> se lahko uporabijo za opis povezave med spremenljivkama X in Y. Če so točke, prikazane v razsevnem diagramu, razpršene okoli premice, je smiselno opazovati linearno povezavo med X in Y; zato govorimo o <strong>linearni regresiji</strong>. To pomeni, da je treba najti premico ',\r\n        5: 'y = ax + b',\r\n        6: 'za parametra <strong><i>a</i></strong> in <strong><i>b</i></strong>, tako da premica opisuje povezanost med spremenljivkama. Parameter <strong><i>a</i></strong> je <strong>naklon</strong> premice. <strong><i>a</i></strong> > 0 pomeni, da je razmerje med X in Y naraščajoče, <strong><i>a</i></strong> < 0 pa, da je padajoče.',\r\n        7: 'Parametra <strong><i>a</i></strong> in <strong><i>b</i></strong> sta neznana in ju moramo oceniti na podlagi podatkov. Določiti parametra <strong>a</strong> in <strong>b</strong> pomeni določiti premico, ki najbolje opisuje povezavo med spremenljivkama. To lahko storite z <strong>metodo najmanjših kvadratov</strong>, tako da zmanjšate vsoto kvadratov navpičnih odklonov vseh točk od premice. Navpične razdalje točk od premice so prikazane na naslednji sliki.',\r\n        8: '<strong>Primer 5.7.1.</strong>',\r\n        9: 'Z naslednjim orodjem lahko izberemo enega od danih naborov podatkovnih parov in poskusimo določiti premico, ki najbolje opisuje podatke.'\r\n      },\r\n      'jednostavna-linearna-regresija-interakcija': {\r\n        1: 'Podatki 1',\r\n        2: 'Podatki 2',\r\n        3: 'Podatki 3',\r\n        4: 'Prikaži oceno regresijske premice',\r\n        5: '<strong>Opis: </strong>Spremenljivka X vsebuje mesečne bruto indekse obsega industrijske proizvodnje v obdobju od 2011 do 2013, spremenljivka Y pa mesečne podatke o številu delovno aktivnih v istem obdobju.',\r\n        6: '<strong>Opis: </strong>Proizvajalec je predstavil nov izdelek in ga razdelil v trgovine po različnih cenah. Čez nekaj časa smo zbrali podatke o številu prodanih izdelkov glede na njihove cene. Opaziti je, da višja cena kaže na manjše število prodanih izdelkov, to pomeni, da je razmerje med spremenljivkama padajoče. ',\r\n        7: '<strong>Opis: </strong>Simulirani podatki so razpršeni po premici z enim osamelcem. Opaziti je, da samo en osamelec pomembno vpliva na položaj regresijske premice.',\r\n      }\r\n    },\r\n    slucajna_varijabla: {\r\n      chapterNumber: '&mdash; Poglavje 3 &mdash;',\r\n      title: 'Slučajna spremenljivka',\r\n      slucajna_varijabla: {\r\n        title: 'Slučajna spremenljivka',\r\n        1: '<strong>Slučajna spremenljivka</strong> je funkcija, ki izidom poskusa (elementom množice Ω) priredi realna števila. Običajno jo označimo z veliko črko, npr. X.',\r\n        2: 'Množica vseh vrednosti, ki jih lahko zavzame slučajna spremenljivka X, se imenuje zaloga vrednosti slučajne spremenljivke in je označena z Z<i>(X)</i>.',\r\n        3: 'Pogosto nas zanima verjetnost, da slučajna spremenljivka 𝑋 zavzame vrednost iz množice 𝐴 ⊆ R. Dogodek, ki nas zanima, je {𝜔 ∈ Ω: 𝑋 (𝜔) ∈ 𝐴} ⊆ Ω, označen okrajšano z (𝑋 ∈ 𝐴).',\r\n        4: '<strong>Primer 3.1.1.</strong>',\r\n        5: 'Ko dvakrat zapored vržemo kovanec, nas zanima, kolikokrat bo padla cifra. Določimo funkcijo 𝑋, ki vsakemu izidu iz množice izidov poskusa',\r\n        6: 'priredi število cifer v urejenem paru, ki predstavlja ta izid:',\r\n        7: 'Izid poskusa',\r\n        8: 'Vrednost <i>X</i>',\r\n        9: '2',\r\n        10: '1',\r\n        11: '1',\r\n        12: '0',\r\n        13: 'Zaloga vrednosti slučajne spremenljivke X je množica:',\r\n        14: 'Analogno določimo še eno slučajno spremenljivko, označeno z <i>Y</i>, ki vsakemu izidu tega poskusa priredi število cifer. Zaloga vrednosti te slučajne spremenljivke je množica Z(𝑌) = {0, 1, 2}.',\r\n        15: 'Opazimo, da na istem Ω lahko določimo več slučajnih spremenljivk.'\r\n      },\r\n      slucajna_varijabla_zadatak_1: {\r\n        title: 'Slučajna spremenljivka - naloga',\r\n        1: 'Poskus je sestavljen iz dveh zaporednih metov kocke. Določite zalogo vrednosti slučajne spremenljivke, ki izidom tega poskusa priredi vsoto vrženih pik.',\r\n        2: '<strong>Rešitev</strong>',\r\n        3: 'Pri dveh zaporednih metih kocke je mogoče doseči naslednje izide:',\r\n        4: 'Zgornja slika prikazuje množico vseh možnih izidov poskusa. Lahko jo zapišemo v naslednji obliki:',\r\n        5: 'pri čemer vsak izid predstavimo z urejenim parom vrženih pik.',\r\n        6: 'Slučajno spremenljivko, ki izidom poskusa priredi vsoto vrženih pik, določimo na naslednji način:',\r\n        7: 'Zaloga vrednosti slučajne spremenljivke 𝑋 je množica  <i>Z(X)</i> = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.',\r\n        8: '<strong>Naloga 3.1.1.</strong>',\r\n        9: '<strong>Naloga 3.2.1.</strong>'\r\n      },\r\n      diskretna_slucajna_varijabla: {\r\n        title: 'Diskretna slučajna spremenljivka',\r\n        1: '<strong>Slučajna spremenljivka X je diskretna</strong>, če je njena zaloga vrednosti: ',\r\n        2: 'končna {𝑥<sub>1</sub>, 𝑥<sub>2</sub>, ... , 𝑥<sub>𝑛</sub>} ali',\r\n        3: 'števna {𝑥<sub>1</sub>, 𝑥<sub>2</sub>, ... , 𝑥<sub>𝑛</sub>, ... }',\r\n        4: ' ',\r\n        5: 'Če so verjetnosti 𝑃(𝑋 = 𝑥<sub>𝑖</sub>) znane za vse možne vrednosti 𝑥<sub>𝑖</sub> iz Z(𝑋), pravimo, da je <strong>porazdelitev diskretne slučajne spremenljivke</strong> 𝑋 znana in jo pregledno prikažemo v <strong>verjetnostni shemi</strong>:',\r\n        6: 'kjer 𝑝<sub>𝑖</sub> označuje 𝑃(𝑋 = 𝑥<sub>𝑖</sub>), 𝑖 = 1,2...',\r\n        7: 'Z uporabo verjetnostne sheme lahko izračunamo verjetnost, da slučajna spremenljivka X zavzame vrednost iz množice 𝐴 ⊆ Z (𝑋).',\r\n        8: 'Ta verjetnost je enaka vsoti verjetnosti 𝑝<sub>𝑖</sub> za vse 𝑥<sub>𝑖</sub> iz 𝐴:',\r\n        9: '<strong>Primer 3.2.1.</strong>',\r\n        10: 'Ko dvakrat zapored vržemo pošten kovanec, je množica vseh možnih izidov Ω = {(𝑝, 𝑝), (𝑝, 𝑔), (𝑔, 𝑝), (𝑔, 𝑔)} in vsi izidi so enako verjetni:',\r\n        11: 'Slučajna spremenljivka 𝑋, ki vsakemu izidu poskusa priredi število padlih cifer, je diskretna in ima naslednjo zalogo vrednosti:',\r\n        12: 'Verjetnosti posameznih elementov zaloge vrednosti Z<i>(X)</i> so:',\r\n        13: 'Zato je porazdelitev slučajne spremenljivke 𝑋 podana z verjetnostno shemo',\r\n        14: 'Verjetnost, da bo vsaj enkrat padla cifra, je',\r\n        15: 'Poleg verjetnostne sheme je porazdelitev lahko prikazana tudi grafično:',\r\n        16: 'Vendar pa kovanec, ki ga mečemo, ni nujno pošten. Lahko se zgodi, da grb pada dvakrat pogosteje kot cifra. To pomeni, da posamezni izidi dveh zaporednih metov niso enako verjetni:',\r\n        17: 'V tem primeru je porazdelitev slučajne spremenljivke X, ki priredi število padlih cifer izidom tega poskusa, podana z verjetnostno shemo',\r\n        18: 'Zdaj je verjetnost, da bo padla vsaj ena cifra, enaka',\r\n        19: 'Grafični prikaz porazdelitve je na naslednji sliki:',\r\n        20: 'Z interaktivnim orodjem raziščimo, kako se spreminjata porazdelitev X in verjetnost P(X ≥ 1), ko se spreminja verjetnost, da pade cifra:'\r\n      },\r\n      diskretna_slucajna_varijabla_interakcija: {\r\n        1: 'Verjetnost, da pade cifra: ',\r\n        2: 'Verjetnost ni bila dobro izbrana',\r\n        3: 'Izračunaj verjetnost P(X>=1)',\r\n        4: 'Izračunaj verjetnost',\r\n        5: 'Verjetnosti',\r\n        6: '0 cifer',\r\n        7: '1 cifra',\r\n        8: 'Vrednost verjetnosti mora biti število',\r\n        9: '2 cifri',\r\n        10: 'verjetnost',\r\n        11: 'Prosimo, vpišite vrednost verjetnosti'\r\n      },\r\n      diskretna_slucajna_varijabla_zadatak_1: {\r\n        title: 'Diskretna slučajna spremenljivka - naloga',\r\n        1: 'Poskus je sestavljen iz dveh zaporednih metov kocke, ki ni nujno poštena. Določite porazdelitev slučajne spremenljivke, ki izidom poskusa priredi vsoto vrženih pik. Z interaktivnim orodjem izračunajte verjetnost, da je vsota pik manjša od pet.',\r\n        2: '<strong>Rešitev</strong>',\r\n        3: 'Kocka ni nujno poštena. Slučajna spremenljivka, ki izidom poskusa priredi vsoto metanih števil, je označena z 𝑋. Verjetnost, da je vsota števil, ki so padla, manjša od pet, je',\r\n        4: 'pri čemer so 𝑝<sub>2</sub>, 𝑝<sub>3</sub>, 𝑝<sub>4</sub>, 𝑝<sub>5</sub> verjetnosti iz porazdelitvene tabele slučajne spremenljivke 𝑋.'\r\n      },\r\n      diskretna_slucajna_varijabla_zadatak_interakcija: {\r\n        1: 'Izid meta kocke',\r\n        2: 'Verjetnost izida',\r\n        3: 'Verjetnosti niso bile dobro izbrane (vsota mora biti 1)',\r\n        4: 'Porazdelitev X',\r\n        5: 'Izračunaj verjetnost',\r\n        6: 'Verjetnosti',\r\n        7: 'Izračunaj verjetnost',\r\n        8: 'V naslednjo tabelo vnesite verjetnosti števila pik, na kocki. S klikom na gumb \"Porazdelitev X\" se prikaže tabela porazdelitve slučajne spremenljivke X, ki pomeni vsoto pik, vrženih v dveh zaporednih metih, medtem ko se s klikom na gumb \"Izračunaj verjetnost\" prikaže verjetnost, da je vsota pik element poljubne podmnožice zaloge vrednosti slučajne spremenljivke X, pri čemer p<sub>i</sub> označuje P(X=i).',\r\n        9: 'Podmnožico, na kateri bo izračunana verjetnost, oblikujete tako, da kliknete na verjetnost v drugi vrstici tabele.',\r\n        10: 'V tabeli je treba izbrati nekaj verjetnosti!'\r\n      },\r\n      neprekidna_slucajna_varijabla: {\r\n        title: 'Zvezna slučajna spremenljivka',\r\n        1: '<strong>Zvezna slučajna spremenljivka</strong> ima zalogo vrednosti Z(𝑋), ki ni diskretna. ',\r\n        2: 'Z(𝑋) je lahko interval ali množica vseh realnih števil.',\r\n        3: '<strong>Porazdelitev</strong> zvezne slučajne spremenljivke 𝑋 je podana z nenegativno funkcijo 𝑓,<strong>verjetnostno gostoto</strong>, za katero je ploščina območja med grafom te funkcije in osjo x enaka 1.',\r\n        4: 'Verjetnost, da zvezna slučajna spremenljivka X zavzame vrednost iz množice 𝐴 ⊆ <i>Z(X)</i> je enaka ploščini pod grafom funkcije gostote 𝑓 nad množico 𝐴, kot je predstavljeno v naslednji sliki:',\r\n        5: '<strong>Primer 3.3.1.</strong>',\r\n        6: 'Slučajna spremenljivka 𝑋, katere zaloga vrednosti je interval (𝑎, 𝑏), −∞ <𝑎 <𝑏 <∞ ima na intervalu (𝑎, 𝑏) konstantno verjetnostno gostoto',\r\n        7: 'je zvezno enakomerno porazdeljena na intervalu (a,b). Na primer za 𝑎 = -1 in 𝑏 = 1 se ta slučajna spremenljivka lahko uporabi za opis merske napake nekega merilnega instrumenta. Graf verjetnostne gostote za a = -1 in b = 1 je predstavljen na naslednji sliki:',\r\n        8: 'Za a = -1, b = 1, c = -1, d = 0 je P(X ∈ (-1, 0)) enaka ploščini pravokotnika z dolžino stranic 1 in <div class=\"fraction\" top=\"1\" bottom=\"2\"></div> :',\r\n        9: 'Analogno za a = -1, b = 1, c = <div class=\"fraction\" top=\"1\" bottom=\"2\"></div>, d = 1 velja naslednje:',\r\n        10: 'Z interaktivnim orodjem poskusite izračunati verjetnost P(<i>c < X < d</i>) za zgoraj omenjeno porazdelitev za različne vrednosti 𝑎 in 𝑏.'\r\n      },\r\n      neprekidna_slucajna_varijabla_interakcija: {\r\n        1: 'Začetna vrednost',\r\n        2: 'Končna vrednost',\r\n        3: 'Nariši graf verjetnostne gostote',\r\n        4: 'Določi verjetnost P(c < X < d)',\r\n        5: 'Parametri niso dobro izbrani. Število a mora biti manjše od b!',\r\n        6: 'Začetek drugega intervala',\r\n        7: 'Konec drugega intervala',\r\n        8: 'Parametri niso dobro izbrani. Število c mora biti manjše od d!',\r\n        9: 'Vrednosti morajo biti številke',\r\n        10: 'Vrednosti podintervala morajo biti v razponu intervala.',\r\n        11: 'Vpisati je treba vse vrednosti'\r\n      },\r\n      neprekidna_slucajna_varijabla_zadatak_1: {\r\n        title: 'Zvezna slučajna spremenljivka - naloga',\r\n        1: 'Slučajna spremenljivka, podana z verjetnostno gostoto',\r\n        2: 'se lahko uporablja za opis časa med dvema zaporednima pojavitvama opazovanega dogodka, na primer prihodoma tramvaja na tramvajsko postajo. Število <i>λ</i> je parameter te porazdelitve. Pri <i>λ</i> = 1 z interaktivnim orodjem izračunajte verjetnost, da bo med dvema prihodoma tramvaja na postajo minilo',\r\n        3: '<strong>Rešitev</strong>',\r\n        4: 'Graf verjetnostne gostote pri <i>λ</i> = 1 je predstavljen na naslednji sliki:',\r\n        5: 'Iskane verjetnosti so:',\r\n        6: 'a) 𝑃(0<𝑋<1)=0,6321',\r\n        7: 'Verjetnost, da bo med dvema zaporednima prihodoma tramvaja na tramvajsko postajo minilo manj kot 1 minuta, je 0,6321.',\r\n        8: 'b) 𝑃(1<𝑋<2)=0,2325',\r\n        9: 'Verjetnost, da bo med dvema zaporednima prihodoma tramvaja na tramvajsko postajo minilo od 1 do 2 minuti, je 0,2325.',\r\n        10: 'c) 𝑃(𝑋 > 2) = 0,1353',\r\n        11: 'Verjetnost, da bo med dvema zaporednima prihodoma tramvaja na tramvajsko postajo minilo več kot 2 minuti, je 0,1353.',\r\n        12: 'Grafični prikaz verjetnostne gostote in iskanih verjetnosti:',\r\n        13: 'manj kot 1 minuta,',\r\n        14: '1 do 2 minuti,',\r\n        15: 'več kot 2 minuti,',\r\n        16: 'Spremenite vrednosti parametra <i>λ</i> in analizirajte rezultate.',\r\n        17: '<strong>Naloga 3.3.1.</strong>',\r\n        18: 'Verjetnost za element med 0 in 1',\r\n        19: 'Verjetnost za element med 1 in 2',\r\n        20: 'Verjetnost za element, večji od 2'\r\n      },\r\n      neprekidna_slucajna_varijabla_zadatak_interakcija: {\r\n        1: 'Vpišite število',\r\n        2: 'Nariši graf verjetnostne gostote',\r\n        3: 'Določi verjetnost P(c < X < d)',\r\n        4: 'Graf verjetnostne gostote',\r\n        5: 'Vrednosti morajo biti številke',\r\n        6: 'Vrednosti c in d ne smeta biti enaki.',\r\n        7: 'Vrednost d mora biti večja od c.',\r\n        8: 'Vpisati je treba vse vrednosti.'\r\n      },\r\n      funkcija_distribucije: {\r\n        title: 'Porazdelitvena funkcija',\r\n        1: '<strong>Porazdelitvena funkcija</strong> 𝐹 slučajne spremenljivke 𝑋 vsakemu realnemu številu 𝑥 priredi verjetnost dogodka (𝑋 ≤ 𝑥): ',\r\n        2: 'Za diskretno slučajno spremenljivko 𝑋 se vrednost porazdelitvene funkcije izračuna z uporabo <a href=\"../slucajna-varijabla/diskretna-slucajna-varijabla\" class=\"topic-link\" target=\"_blank\" rel=\"noopener noreferrer\">verjetnostne sheme</a>. Za poljuben 𝑥 je vrednost 𝐹(𝑥) vsota verjetnosti 𝑝<sub>𝑖</sub> za tiste 𝑥<sub>𝑖</sub> ∈ Z(𝑋), ki so manjše ali enake 𝑥:',\r\n        3: '<strong>Primer 3.4.1.</strong>',\r\n        4: 'Porazdelitev diskretne slučajne spremenljivke 𝑋, ki pomeni število padlih cifer pri dveh zaporednih metih poštenega kovanca, je podana z:',\r\n        5: 'Vrednosti porazdelitvene funkcije F za vrednosti slučajne spremenljivke 𝑋 so:',\r\n        6: 'Porazdelitvena funkcija je podana z:',\r\n        7: 'njen graf pa je prikazan na naslednji sliki: ',\r\n        8: 'Opazimo, da ima porazdelitvena funkcija diskretne slučajne spremenljivke v vsakem x<sub>i</sub>∈Z(X) skok v višini p<sub>i</sub>=P(X=x<sub>i</sub>) in da je funkcija naraščajoča in omejena (navzdol z vrednostjo 0 in nazgor z vrednostjo 1).',\r\n        9: '<strong>Primer 3.4.2.</strong>',\r\n        10: 'Zvezno enakomerno porazdeljena slučajna spremenljivka 𝑋, z zalogo vrednosti na intervalu (-1, 1) je podana z verjetnostno gostoto',\r\n        11: 'Določimo vrednost njene porazdelitvene funkcije F v točki 𝑥 = <div class=\"fraction\" top=\"1\" bottom=\"2\"></div> z grafoma verjetnostne gostote in porazdelitvene funkcije:',\r\n        12: 'Zgornja verjetnostna gostota je poseben primer verjetnostne gostote zvezno enakomerne porazdeljene slučajne spremenljivke:',\r\n        13: 'Pri nekaterih drugih <i>a</i> in <i>b</i> opazujmo graf verjetnostne gostote, graf porazdelitvene funkcije in verjetnost P(X≤x).',\r\n        14: 'Kaj pa, če kovanec ni pošten? Poglejmo, kako se porazdelitvena funkcija spreminja, ko se spreminja verjetnost, da pade cifra:',\r\n        15: 'Za zvezno slučajno spremenljivko 𝑋 se vrednost porazdelitvene funkcije izračuna z uporabo <a href=\"../slucajna-varijabla/neprekidna-slucajna-varijabla\" class=\"topic-link\" target=\"_blank\" rel=\"noopener noreferrer\">verjetnostne gostote</a>. Za poljuben 𝑥 je <i>F(</i>𝑥<i>)</i> enak ploščini pod grafom verjetnostne gostote nad intervalom (-∞, 𝑥].'\r\n      },\r\n      funkcija_distribucije_dodatni_zadaci: {\r\n        title: 'Več o tem: kako izračunati verjetnost P(X∈A)?',\r\n        1: 'Verjetnost realizacije slučajne spremenljivke X iz intervala (a, b) je mogoče izračunati z uporabo vrednosti porazdelitvene funkcije v točkah a in b:',\r\n        2: 'P X∈(a, b)=P a<X≤b=P X≤b-P X≤a=F b-F (a).',\r\n        3: 'Na podoben način se izračunajo tudi verjetnosti, da se X uresniči iz intervalov (a, b), [a, b] in (a, b).',\r\n        4: 'Pri zvezni slučajni spremenljivki (povezava na temo) s tabelo porazdelitve',\r\n        5: 'X~(x1 x2 ... p1 p2 ... xn…  pn…)',\r\n        6: 'je vsaka od teh verjetnosti vsota verjetnosti pi=P(X = xi) za vse xi iz opazovanega intervala.',\r\n        7: 'Pri zvezni slučajni spremenljivki (povezava na temo) je vsaka od teh verjetnosti enaka površini pod grafikonom gostote nad intervalom A verjetnosti P(a<X≤b),',\r\n        8: 'P (a≤X<b), P (a≤X≤b) in P (a<X≤b) so enake, ker je pri zvezni slučajni spremenljivki P X=x = 0 za vsako število X.'\r\n      },\r\n      funkcija_distribucije_interakcija: {\r\n        1: 'Verjetnost, da pade cifra:',\r\n        2: 'Porazdelitev X',\r\n        3: 'Porazdelitvena funkcija X',\r\n        4: 'Graf porazdelitvene funkcije',\r\n        5: 'Graf zvezne slučajne spremenljivke',\r\n        6: 'Verjetnost mora biti število',\r\n        7: 'Verjetnost mora biti v območju [0, 1]',\r\n        8: 'Treba je vnesti verjetnost.'\r\n      },\r\n      funkcija_distribucije_interakcija_2: {\r\n        1: 'Graf funkcije gostote',\r\n        2: 'Graf porazdelitvene funkcije',\r\n        3: 'Vrednost x ni v intervalu med a in b',\r\n        4: 'Vpisane vrednosti morajo biti števila',\r\n        5: 'Verjetnost P(X ≤ ',\r\n        6: 'Prosimo, vpišite vse vrednosti'\r\n      },\r\n      ocekivanje: {\r\n        title: 'Pričakovana vrednost',\r\n        1: '<strong>Pričakovana vrednost</strong> ali matematično upanje slučajne spremenljivke 𝑋 je število, ki prikazuje sredino verjetnostne porazdelitve te slučajne spremenljivke. Označujemo jo z 𝐸(𝑋) ali 𝜇 .',\r\n        2: 'Pričakovana vrednost slučajne spremenljivke se izračuna na naslednji način:',\r\n        3: 'Za <a href=\"../slucajna-varijabla/diskretna-slucajna-varijabla\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\" target=\"_blank\" rel=\"noopener noreferrer\">diskretno slučajno spremenljivko</a> 𝑋 z verjetnostno shemo',\r\n        4: 'je pričakovana vrednost vsota zmnožkov vsake vrednosti 𝑥<sub>𝑖</sub> s pripadajočo verjetnostjo 𝑝<sub>𝑖</sub> :',\r\n        5: 'Pričakovano vrednost za <a href=\"../slucajna-varijabla/neprekidna-slucajna-varijabla\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"topic-link\" target=\"_blank\" rel=\"noopener noreferrer\">zvezno slučajno spremenljivko</a> 𝑋 z verjetnostno gostoto 𝑓 izračunamo z uporabo predznačene ploščine med osjo 𝑥 in grafom funkcije 𝑥𝑓(𝑥).',\r\n        6: '<strong>Primer 3.5.1.</strong>',\r\n        7: 'Porazdelitev slučajne spremenljivke, ki izidom meta poštene kocke priredi število padlih pik, je podana z:',\r\n        8: 'Pričakovana vrednost te slučajne spremenljivke je:',\r\n        9: 'Naslednja slika prikazuje grafikon porazdelitve in položaj pričakovane vrednosti te slučajne spremenljivke:',\r\n        10: 'Ker so vse verjetnosti med seboj enake, je pričakovana vrednost povprečje vrednosti, ki jih slučajna spremenljivka lahko zavzame. ',\r\n        11: 'Vendar ni nujno, da je tako. Če kocka ni poštena, pričakovana vrednost ne bo nujno povprečje števil iz zaloge vrednosti. Opazujmo, kako se pričakovana vrednost spreminja zaradi sprememb v porazdelitvi.',\r\n        12: '<strong>Primer 3.5.2.</strong>',\r\n        13: 'Zvezno enakomerno porazdeljena slučajna spremenljivka 𝑋 z zalogo vrednosti na intervalu (-1, 1) je podana z verjetnostno gostoto',\r\n        14: 'Ker je funkcija 𝑥𝑓(𝑥), uporabljena za izračun pričakovane vrednosti, liha in zaloga vrednosti simetrična čez izhodišče, je pričakovana vrednost slučajne spremenljivke X enaka 0.',\r\n        15: 'To je razvidno iz spodnjih grafov.',\r\n        16: 'Z interaktivnim orodjem opazujmo območje med osjo x in grafom funkcije 𝑥𝑓(𝑥) ter graf verjetnostne gostote',\r\n        17: 'z označeno pričakovano vrednostjo na osi x.',\r\n        18: '<strong>Primer 3.5.3.</strong>',\r\n        19: 'Naj bo (𝑋𝑛, 𝑛 ∈ 𝑁) nabor slučajnih spremenljivk, ki opisujejo izide zaporednih metov pravične kocke. Slučajna spremenljivka 𝑋𝑛 dobi vrednost 1, če število 6 pade v 𝑛-tem metu. V nasprotnem primeru dobi vrednost 0. Porazdelitev 𝑋𝑛 je podana v tabeli',\r\n        20: 'Opaziti je, da povprečje 𝑋𝑛 ustreza relativni frekvenci enot. Poleg tega opazimo, da je pričakovana vrednost relativne frekvence enot 1/6.',\r\n        21: 'V skladu s šibkim zakonom velikih števil lahko s povečanjem števila metov kocke verjetnost odstopanja relativne frekvence enot od 1/6 postane poljubno majhna.'\r\n      },\r\n      ocekivanje_interakcija: {\r\n        1: 'Nariši grafe',\r\n        2: 'Graf funkcije xf(x)',\r\n        3: 'Graf funkcije f(x)',\r\n        4: 'Vpisati je treba vse vrednosti.',\r\n        5: 'Vpisane vrednosti morajo biti številke.',\r\n        6: 'Število a mora biti manjše od števila b.'\r\n      },\r\n      ocekivanje_interakcija_2: {\r\n        1: 'Nariši porazdelitev in označi pričakovano vrednost',\r\n        2: 'Pričakovana vrednost',\r\n        3: 'Verjetnosti niso bile dobro izbrane (vsota mora biti 1)'\r\n      },\r\n      ocekivanje_dodatni_zadaci: {\r\n        title: 'Za tiste, ki bi radi izvedeli več',\r\n        1: 'Naj bo (𝑋<sub>𝑛</sub>, 𝑛 ∈ 𝑁) zaporedje neodvisnih, enako porazdeljenih slučajnih spremenljivk s pričakovano vrednostjo 𝜇. Takšno zaporedje lahko opisuje izide ponovitev poskusa.',\r\n        2: 'Šibki zakon velikih števil obravnava limitno obnašanje zaporedja delnih povprečij (<span class=\"overline\">𝑋</span><sub>𝑛</sub>, 𝑛 ∈ 𝑁), kjer',\r\n        3: 'V skladu s šibkim zakonom velikih števil lahko verjetnost odstopanja povprečja <span class=\"overline\">𝑋</span><sub>𝑛</sub> od pričakovane vrednosti 𝜇 poljubno zmanjšamo z izbiro dovolj velikega števila ponovitev poskusov, to je števila 𝑛.',\r\n        4: '<strong>Za tiste, ki bi radi izvedeli več - primer 1</strong>',\r\n        5: 'Naj bo (<i>X<sub>n</sub></i>, <i>n∈N</i>) zaporedje slučajnih spremenljivk, ki opisujejo izide zaporednih metov poštene kocke. Slučajna spremenljivka X<sub>𝑛</sub> dobi vrednost 1, če v n-tem metu pade šestica. V nasprotnem primeru dobi vrednost 0. Porazdelitev <i>X<sub>n</sub></i> je podana z verjetnostno shemo',\r\n        6: 'Opazimo, da povprečje <span class=\"overline\">X</span><sub>n</sub> ustreza relativni frekvenci šestic. Poleg tega opazimo, da je pričakovana vrednost relativne frekvence šestic <div class=\"fraction\" top=\"1\" bottom=\"6\"></div>.',\r\n        7: 'V skladu s šibkim zakonom velikih števil lahko s povečanjem števila metov kocke verjetnost odstopanja relativne frekvence šestic od <div class=\"fraction\" top=\"1\" bottom=\"6\"></div> poljubno zmanjšate.',\r\n        8: '<strong>Za tiste, ki bi radi izvedeli več - primer 2</strong>',\r\n        9: 'Naj bo (<i>X<sub>n</sub>, n∈N</i>) zaporedje slučajnih spremenljivk, ki opisujejo izide zaporednih metov kovanca. Slučajna spremenljivka <i>X<sub>n</sub></i> dobi vrednost 1, če pade grb v n-tem metu. Če pade cifra, dobi vrednost 0. Če je verjetnost, da pade grb enaka <i>p</i>, sledi, da je porazdelitev <i>X<sub>n</sub></i> podana z verjetnostno shemo',\r\n        10: 'Opazimo, da povprečje <span class=\"overline\">X</span><sub>n</sub> ustreza relativni frekvenci grbov. Poleg tega opazimo, da je pričakovana vrednost relativne frekvence grbov enaka 𝑝, 𝐸(<span class=\"overline\">𝑋</span><sub>𝑛</sub>) = 𝑝.',\r\n        11: 'V skladu s šibkim zakonom velikih števil lahko s povečanjem števila metov kovanca verjetnost odstopanja relativne frekvence grbov od pričakovane vrednosti 𝑝 poljubno zmanjšate.',\r\n        12: '<strong>Položaj pričakovane vrednosti</strong>',\r\n        13: 'Če se vprašamo, ali obstaja realno število, ki je nekako \"najbližje\" slučajni spremenljivki, potem je v primerno izbranem načinu merjenja razdalje to ravno pričakovana vrednost slučajne spremenljivke. Razdalja med slučajno spremenljivko <i>X</i> in številom <i>a</i> se izmeri kot pričakovana vrednost kvadratnega odklona.',\r\n        14: 'Če to opazujemo kot funkcijo z neodvisno spremenljivko <i>a</i>,',\r\n        15: 'sledi, da doseže svoj minimum pri <i>a = E(X)</i>. Zato <i>E(X)</i> minimizira pričakovano vrednost kvadratnega odklona od slučajne spremenljivke <i>X</i>.',\r\n        16: '<strong>Šibki zakon velikih števil</strong>',\r\n        17: 'Za tiste, ki bi radi izvedeli več',\r\n        18: 'Za tiste, ki bi radi izvedeli več - primer'\r\n\r\n      },\r\n      ocekivanje_dodatni_zadaci_interakcije: {\r\n        1: 'Število metov: ',\r\n        2: 'Vpiši število',\r\n        3: 'Vrzi kocko',\r\n        4: 'Število metov mora biti večje od 0!',\r\n        5: 'Verjetnost, da pade grb',\r\n        6: 'Število metov',\r\n        7: 'Vrzi kovanec',\r\n        8: 'Verjetnost mora biti med 0 in 1.',\r\n        9: 'Število metov ne sme biti nabor.',\r\n        10: 'Število metov mora biti celo število.',\r\n        11: 'Treba je vpisati število metov.',\r\n        12: 'Treba je vpisati vse vrednosti.'\r\n      },\r\n      varijanca_i_standardna_devijacija: {\r\n        title: 'Varianca in standardni odklon slučajne spremenljivke',\r\n        1: '<strong>Varianca</strong> ali disperzija slučajne spremenljivke 𝑋 je nenegativno število, ki prikazuje <strong>razpršenost</strong> porazdelitve slučajne spremenljivke 𝑋 glede na njeno pričakovano vrednost 𝐸(𝑋).',\r\n        2: 'Označujemo jo z 𝑉𝑎𝑟(𝑋) ali 𝜎<sup> 2</sup> .',\r\n        3: 'Natančneje, 𝑉𝑎𝑟(𝑋) je pričakovana vrednost kvadratnega odklona slučajne spremenljivke 𝑋 od njene pričakovane vrednosti:',\r\n        4: 'Kvadratni koren variance 𝑉𝑎𝑟(𝑋) se imenuje <strong>standardni odklon</strong> slučajne spremenljivke 𝑋 in je označen s 𝜎.',\r\n        5: '<strong>Primer 3.6.1.</strong>',\r\n        6: 'Zvezno enakomerno porazdeljena slučajna spremenljivka 𝑋, ima verjetnostno gostoto',\r\n        7: 'Z interaktivnim orodjem opazujmo pričakovano vrednost in varianco te slučajne spremenljivke za različne vrednosti parametrov a in b:',\r\n        8: 'Slučajne spremenljivke s porazdelitvijo na enako dolgih intervalih imajo enake variance.',\r\n        9: 'Če primerjamo varianco slučajne spremenljivke s porazdelitvijo na krajšem intervalu in slučajne spremenljivke s porazdelitvijo na daljšem intervalu, je varianca slučajne spremenljivke s porazdelitvijo na daljšem intervalu večja.'\r\n      },\r\n      varijanca_i_standardna_devijacija_interakcija: {\r\n        1: 'Izračunaj pričakovano vrednost in varianco',\r\n        2: 'Nariši graf funkcije gostote',\r\n        3: 'Pričakovana vrednost: ',\r\n        4: 'Varianca: ',\r\n        5: 'Originalni graf funkcije gostote',\r\n        6: 'Pričakovana vrednost',\r\n        7: 'Pričakovana vrednost minus standardni odklon',\r\n        8: 'Število b mora biti večje od števila a',\r\n        9: 'Pričakovana vrednost plus standardni odklon',\r\n        10: '4. Porazdelitve',\r\n        11: 'Vpisati je treba vse vrednosti.'\r\n      },\r\n      varijanca_i_standardna_devijacija_zadatak: {\r\n        1: 'Z interaktivnim orodjem preverite, kako se z vrednostjo parametra λ>0 spreminjata pričakovana vrednost in varianca slučajne spremenljivke X z verjetnostno gostoto.',\r\n        2: '<strong>Rešitev</strong>',\r\n        3: 'S povečanjem vrednosti parametra λ se pričakovana vrednost in varianca zmanjšata.',\r\n        4: '<strong>Naloga 3.6.1.</strong>'\r\n      },\r\n      varijanca_i_standardna_devijacija_zadatak_interakcija: {\r\n        1: 'Izračunajte pričakovano vrednost in varianco',\r\n        2: 'Nariši graf funkcije gostote',\r\n        3: 'Pričakovana vrednost: ',\r\n        4: 'Varianca: ',\r\n        5: 'Originalni graf funkcije gostote',\r\n        6: 'Pričakovana vrednost minus standardni odklon',\r\n        7: 'Pričakovana vrednost plus standardni odklon',\r\n        8: 'Pričakovana vrednost'\r\n      }\r\n    },\r\n    distribucije: {\r\n      chapterNumber: '&mdash; 4. poglavje &mdash;',\r\n      title: 'Porazdelitve',\r\n      bernoulijeva_distribucija: {\r\n        title: 'Bernoullijeva porazdelitev',\r\n        1: 'Slučajna spremenljivka 𝑋, ki opisuje poskus s samo <strong>dvema možnima izidoma</strong>:',\r\n        2: '<strong>neuspeh</strong> (označen z 0), ki se zgodi z verjetnostjo (1 − 𝑝),',\r\n        3: '<strong>uspeh</strong> (označen z 1), ki se zgodi z verjetnostjo 𝑝,',\r\n        4: 'ima Bernoullijevo porazdelitev s parametrom 𝑝 ∈ (0, 1) in verjetnostno shemo',\r\n        5: '<strong>Pričakovana vrednost</strong> in <strong>varianca</strong> slučajne spremenljivke z Bernoullijevo porazdelitvijo s parametrom 𝑝 sta',\r\n        6: '<strong>Primer 4.1.1.</strong>',\r\n        7: 'Ko vržemo kovanec, lahko pade cifra ali grb. Če je kovanec pošten, sta ta dva izida enako verjetna. Če rečemo, da je izid grb uspeh, ki ga označimo z 1, izid cifra pa neuspeh, ki ga označimo z 0, opišemo izid meta kovanca s slučajno spremenljivko 𝑋 z Bernoullijevo porazdelitvijo s parametrom 𝑝 = <div class=\"fraction\" top=\"1\" bottom=\"2\"></div> in verjetnostno shemo',\r\n        8: 'Pričakovana vrednost in varianca sta',\r\n        9: 'Naslednja slika prikazuje graf Bernoullijeve porazdelitve s poudarjeno pričakovano vrednostjo:',\r\n        10: 'Če mečemo kovanec, ki je nepošten, izida cifra in grb nista enako verjetna.',\r\n        11: 'Z interaktivnim orodjem opazujte, kako sprememba verjetnosti uspeha <i>p</i> vpliva na Bernoullijevo porazdelitev, ki opisuje izid meta kovanca, in tudi na pričakovano vrednost.'\r\n      },\r\n      bernoulijeva_distribucija_interakcija: {\r\n        1: 'Verjetnost',\r\n        2: 'Grafikon porazdelitve',\r\n        3: 'Pričakovana vrednost',\r\n        4: 'Varianca',\r\n        5: 'Verjetnost mora biti znotraj intervala [0, 1]!',\r\n        6: 'Verjetnost mora biti število!'\r\n      },\r\n      bernoulijeva_distribucija_zadatak_1: {\r\n        title: 'Bernoullijeva porazdelitev - naloga',\r\n        1: 'a) V igri Človek, ne jezi se igralci mečejo pošteno kocko, uspeh pa je, če pade šestica. Če pade 1, 2, 3, 4 ali 5, se šteje za neuspeh. Določite porazdelitev, pričakovano vrednost in varianco slučajne spremenljivke, uporabljene za opis metanja poštene kocke v tem kontekstu. Porazdelitev in položaj pričakovane vrednosti predstavite grafično z interaktivnim orodjem.',\r\n        2: 'b) Z interaktivnim orodjem opazujte, kako se spreminjata porazdelitev in pričakovana vrednost, ko mečemo kocko, ki ni poštena; na primer, ko se spremeni verjetnost, da bo padla šestica.',\r\n        3: '<strong>Rešitev</strong>',\r\n        4: 'a) Ker je kocka poštena, je verjetnost uspeha (meta šestice) <div class=\"fraction\" top=\"1\" bottom=\"6\"></div>, zato je izid meta kocke v tem primeru opisan z Bernoullijevo slučajno spremenljivko 𝑋 s parametrom 𝑝 = <div class=\"fraction\" top=\"1\" bottom=\"6\"></div> in verjetnostno shemo',\r\n        5: 'Pričakovana vrednost in varianca sta',\r\n        6: 'b) Uporabnik z interaktivnim orodjem nariše grafikone porazdelitve z označenimi pričakovanimi vrednostmi za različne vrednosti parametra 𝑝.',\r\n        7: '<strong>Naloga 4.1.1.</strong>'\r\n      },\r\n      bernoulijeva_distribucija_zadatak_interakcija: {\r\n        1: 'Verjetnost',\r\n        2: 'Grafikon porazdelitve',\r\n        3: 'Pričakovana vrednost',\r\n        4: 'Varianca',\r\n        5: 'Verjetnost mora biti znotraj intervala [0, 1]!'\r\n      },\r\n      binomna_distribucija: {\r\n        title: 'Binomska porazdelitev',\r\n        1: 'Slučajna spremenljivka 𝑋, ki šteje uspehe v 𝑛 neodvisnih realizacijah istega poskusa z le dvema možnima izidoma (uspeh in neuspeh), pri čemer je verjetnost uspeha v vsaki izvedbi poskusa 𝑝, ima <strong>binomsko porazdelitev</strong>s parametroma 𝑛 ∈ 𝑁 in 𝑝 ∈ (0, 1), označeno z 𝑋~ℬ(𝑛, 𝑝).',\r\n        2: 'Zaloga vrednosti binomsko porazdeljene slučajne spremenljivke X ~ ℬ(𝑛, 𝑝) je Z(𝑋) = {0, 1, 2, ... , 𝑛}, posamezne verjetnosti pa izračunamo po Bernoullijevem obrazcu:',\r\n        3: '<strong>Pričakovana vrednost</strong> in <strong>varianca</strong> sta',\r\n        4: '<strong>Primer 4.2.1.</strong>',\r\n        5: 'Predpostavimo, da kovanec vržemo 20-krat. Če je kovanec, ki ga mečemo, pošten, je število grbov v teh 20 metih opisano s slučajno spremenljivko X z binomsko porazdelitvijo s parametroma n = 20 in p = <div class=\"fraction\" top=\"1\" bottom=\"2\"></div>. Pričakovana vrednost in varianca spremenljivke sta:',\r\n        6: 'Naslednja slika prikazuje grafikon porazdelitve z označeno pričakovano vrednostjo: ',\r\n        7: 'Z interaktivnim orodjem lahko izračunamo nekaj zanimivih verjetnosti, na primer naslednje:',\r\n        8: 'Verjetnost, da bo natanko 10-krat padel grb, je P(X=10) = 0,1762.',\r\n        9: 'Verjetnost, da bo manj kot 10-krat padel  grb, je P(X<10) = 0,4119.',\r\n        10: 'Verjetnost, da bo vsaj 10-krat padel grb, je P(X≥10) = 0,5881.'\r\n      },\r\n      binomna_distribucija_interakcija: {\r\n        1: 'Grafikon porazdelitve',\r\n        2: 'Pričakovana vrednost',\r\n        3: 'Varianca',\r\n        4: 'Izračunaj zahtevane verjetnosti',\r\n        5: 'Vpisane vrednosti morajo biti števila',\r\n        6: 'Verjetnost mora biti v območju [0, 1]',\r\n        7: 'Število metov mora biti pozitivno število',\r\n        8: 'Za izbrana parametra n in p binomske porazdelitve in vrednost x iz njene slike določite verjetnosti P(X=x), P(X<=x) in P(X>x).',\r\n        9: 'P(X<=x)',\r\n        10: 'P(X>x)',\r\n        11: 'Vpisati je treba vrednost verjetnosti.',\r\n        12: 'Vpisati je treba vse vrednosti.',\r\n        13: 'Vpišite vrednosti med 0 in '\r\n      },\r\n      binomna_distribucija_zadatak_1: {\r\n        title: 'Binomska porazdelitev - naloga',\r\n        1: 'Z interaktivnim orodjem izračunajte verjetnost, da bo v 50 metih kocke padla šestica več kot petkrat. Ali je bolj verjetno, da bo šestica padla vsaj petkrat ali da bo padla največ desetkrat?',\r\n        2: '<strong>Rešitev</strong>',\r\n        3: ' ',\r\n\t\t4: '𝑋 predstavlja število metov šestice v 50 metih poštene kocke:',\r\n        5: 'Iskane verjetnosti so',\r\n        6: 'Zato je bolj verjetno, da bo šestica padla vsaj petkrat, kot da bo padla največ desetkrat.',\r\n        7: '<strong>Naloga 4.2.1.</strong>',\r\n        8: 'Za izbrana parametra n (število metov kocke) in p (verjetnost, da bo padla šestica) binomske porazdelitve določimo verjetnosti P(X>5), P(X>=5) in P(X<=10).'\r\n      },\r\n      uniformna_distribucija: {\r\n        title: 'Enakomerna porazdelitev',\r\n        1: 'Slučajna spremenljivka 𝑋 z verjetnostno gostoto',\r\n        2: 'ima <strong>enakomerno porazdelitev</strong> na intervalu (𝑎, 𝑏) in je označena z 𝑿~𝓤(𝒂, 𝒃). Realni števili 𝑎 in 𝑏, −∞ < 𝑎 < 𝑏 < ∞, sta parametra te porazdelitve.',\r\n        3: 'Funkcija gostote enakomerne porazdelitve odraža dejstvo, da so enako dolgi podintervali (𝑎,𝑏) enako verjetni.',\r\n        4: 'Verjetnost realizacije slučajne spremenljivke 𝑋~𝒰(𝑎, 𝑏) iz intervala (𝑐, 𝑑), 𝑎 ≤ 𝑐 < 𝑑 ≤ 𝑏, je enaka površini pod grafom funkcije gostote nad intervalom (𝑐, 𝑑):',\r\n        5: 'Pričakovana vrednost in varianca 𝒰(𝑎, 𝑏) porazdelitve sta',\r\n        6: 'O tej porazdelitvi smo podrobno razpravljali v poglavju o zveznih slučajnih spremenljivkah (povezava do teme).',\r\n        7: '<strong>Primer 4.3.1.</strong>',\r\n        8: 'Opazujmo grafe funkcij gostote enakomernih porazdelitev z različnimi intervali, z označenimi pričakovanimi vrednostmi.',\r\n        9: 'Porazdelitev 𝒰(5, 10) je na primer podana s funkcijo gostote',\r\n        10: 'Poleg tega je porazdelitev 𝒰(−1,1) podana s funkcijo gostote'\r\n      },\r\n      uniformna_distribucija_zadatak_1: {\r\n        title: 'Enakomerna porazdelitev - naloga',\r\n        1: 'Specifikacija natančnega merilnega instrumenta za maso kaže, da izmerjena masa odstopa od dejanske mase za manj kot 1 𝜇𝑔 in da je porazdelitev napake enakomerna. Z interaktivnim orodjem izračunajte naslednje:',\r\n        2: 'a) verjetnost, da je izmerjena masa manjša od dejanske',\r\n        3: 'b) verjetnost, da je izmerjena masa večja od dejanske.',\r\n        4: '<strong>Rešitev</strong>',\r\n        5: 'Napako pri merjenju mase opisuje slučajna spremenljivka 𝑋 z enakomerno porazdelitvijo v intervalu (-1, 1). Funkcija gostote porazdelitve 𝒰 (−1, 1) je',\r\n        6: ', kar je grafično predstavljeno v prejšnjem primeru.',\r\n        7: 'a) Če sta dejanska in izmerjena masa enaki, je napaka enaka nič. Zato je verjetnost, da je izmerjena masa manjša od dejanske, 𝑃(𝑋 <0), enaka površini pod grafom funkcije gostote porazdelitve 𝒰(−1, 1) nad intervalom (−1, 0).',\r\n        8: 'Opaziti je, da gre za površino pravokotnika z dolžino stranic 1 in 1/2; zato je verjetnost 𝑃(𝑋 < 0) = 1/2.',\r\n        9: 'b) Verjetnost, da je izmerjena masa večja od dejanske, je enaka površini pod graf funkcije gostote porazdelitve (−1, 1) nad intervalom (0, 1) in znaša 𝑃(𝑋 > 0) = 1/2.'\r\n      },\r\n      normalna_distribucija: {\r\n        title: 'Normalna porazdelitev',\r\n        1: 'Slučajna spremenljivka X z verjetnostno gostoto',\r\n        2: 'ima <strong>normalno porazdelitev</strong> s parametroma 𝜇 ∈ 𝑅 in 𝜎 > 0 in je označena z X ~ 𝒩 (𝜇, 𝜎).',\r\n        3: '<strong>Pričakovana vrednost</strong> in <strong>varianca</strong> slučajne spremenljivke X sta:',\r\n        4: 'Zato je 𝜎 > 0 standardni odklon slučajne spremenljivke s porazdelitvijo 𝒩(𝜇, 𝜎).',\r\n        5: 'Normalna porazdelitev s pričakovano vrednostjo 𝜇 = 0 in standardnim odklonom 𝜎 = 1 se imenuje standardizirana normalna porazdelitev.',\r\n        6: '<strong>Primer 4.3.1.</strong>',\r\n        7: 'Opazujmo grafe verjetnostnih gostot normalno porazdeljenih slučajnih spremenljivk z različnimi parametri 𝜇 in 𝜎.',\r\n        8: 'Izberimo standardni odklon 𝜎 = 1 in za pričakovano vrednost 𝜇 vzemimo vrednosti −1, 0, 1, 2. Opazimo, da verjetnostna gostota doseže največjo vrednost pri pričakovani vrednosti 𝜇.',\r\n        9: 'Izberimo pričakovano vrednost 𝜇 = 0 in za standardni odklon 𝜎 vzemimo vrednosti 0,3; 0,5; 1 in 5. Opazimo, da povečevanje standardnega odklona povzroči širjenje grafa verjetnostne gostote normalne porazdelitve in graf postaja vse bolj sploščen.',\r\n        10: 'Na grafu verjetnostne gostote 𝒩(𝜇,𝜎) bomo označili pričakovano vrednost 𝜇 in meje intervalov (𝜇−𝜎, 𝜇+𝜎), (𝜇−2𝜎, 𝜇+2𝜎), (𝜇−3𝜎, 𝜇+3𝜎)',\r\n        11: 'Z interaktivnim orodjem lahko izračunamo, da za poljubna 𝜇 in 𝜎 velja naslednje',\r\n        12: 'Iz tega sledi, da slučajna spremenljivka X~𝒩 (𝜇, 𝜎) odstopa od pričakovane vrednosti za več kot en standardni odklon z verjetnostjo 31,73 %, verjetnost, da odstopa od pričakovane vrednosti za več kot dva standardna odklona, je 4,55 %, verjetnost, da odstopa od pričakovane vrednosti za več kot tri standardne odklone, pa je 0,27 %.'\r\n      },\r\n      normalna_distribucija_interakcija: {\r\n        1: 'Pričakovana vrednost',\r\n        2: 'Začetna vrednost',\r\n        3: 'Standardni odklon',\r\n        4: 'Končna vrednost',\r\n        5: 'Graf verjetnostne gostote',\r\n        6: 'P(c < Z < d)',\r\n        7: 'Končni vrednosti intervalov c in d nista dobro izbrani!',\r\n        8: 'Pričakovana vrednost',\r\n        9: 'Varianca',\r\n        10: 'Vrednosti morajo biti števila',\r\n        11: 'Vpisan je napačni odklon',\r\n        12: '5. Statistično sklepanje',\r\n        13: 'Vpisati je treba vse vrednosti.',\r\n        14: 'Vrednosti c in d morata biti znotraj intervala',\r\n        15: ' s pogojem c < d.'\r\n      },\r\n      normalna_distribucija_zadatak_1: {\r\n        title: 'Normalna porazdelitev - naloga',\r\n        1: 'Standardizirani test inteligence je umerjen na podlagi predpostavke, da je inteligenčni kvocient v populaciji normalno porazdeljena lastnost s pričakovano vrednostjo 𝜇 = 100 in standardnim odklonom 𝜎 = 15. Z interaktivnim orodjem izračunajte naslednje:',\r\n        2: 'a) verjetnost, da je inteligenčni kvocient slučajno izbrane osebe iz populacije večji od pričakovane vrednosti,',\r\n        3: 'b) verjetnost, da je inteligenčni kvocient slučajno izbrane osebe iz populacije med 85 in 115.',\r\n        4: '<strong>Rešitev</strong>',\r\n        5: 'Inteligenčni kvocient v populaciji je opisan s slučajno spremenljivko X~𝒩(100, 15).',\r\n        6: 'a) Ker je 𝐸(X) = 100, iščemo verjetnost 𝑃(X > 100). Ta verjetnost je enaka ploščini pod grafom verjetnostne gostote slučajne spremenljivke s porazdelitvijo 𝒩(100, 15) nad intervalom (100, ∞) in znaša <div class=\"fraction\" top=\"1\" bottom=\"2\"></div>.',\r\n        7: 'b) Iskana verjetnost 𝑃(85 < X <115) je enaka ploščini pod grafom verjetnostne gostote slučajne spremenljivke s porazdelitvijo 𝒩(100, 15) nad intervalom (85, 115) in znaša 0,6827.',\r\n        8: '<strong>Naloga 4.3.1.</strong>'\r\n      },\r\n      normalna_distribucija_zadatak_interakcija: {\r\n        1: 'Pričakovana vrednost',\r\n        2: 'Začetna vrednost',\r\n        3: 'Standardni odklon',\r\n        4: 'Končna vrednost',\r\n        5: 'Graf funkcije gostote',\r\n        6: 'P(c < Z < d)',\r\n        7: 'Končni vrednosti intervalov c in d nista dobro izbrani!',\r\n        8: 'Odstopanje mora biti večje od 1!'\r\n      },\r\n      distribucija: {\r\n        title: 'Porazdelitev',\r\n        1: 'Če so 𝑍1, ... , 𝑍𝑛 neodvisne standardne normalne slučajne spremenljivke, je vsota njihovih kvadratov',\r\n        2: 'slučajna spremenljivka z <strong>𝝌𝟐 porazdelitvijo</strong> s parametrom 𝑛 ∈ 𝑁 in je označena z 𝑌~𝜒2(𝑛).',\r\n        3: 'Parameter 𝑛 se imenuje <strong>število stopenj prostosti</strong> porazdelitve 𝜒2.',\r\n        4: '<strong>Pričakovana vrednost</strong> in <strong>varianca</strong> porazdelitve 𝜒2(𝑛) sta:',\r\n        5: '<strong>Primer 4.5.1.</strong>',\r\n        6: 'Grafi funkcije gostote porazdelitev 𝜒2(3), 𝜒2(5) in 𝜒2(7) z označeno pričakovano vrednostjo so predstavljeni na naslednjih slikah.',\r\n        7: 'Z interaktivnim orodjem preučite 𝜒2(𝑛) porazdelitve za druge vrednosti parametra.'\r\n      },\r\n      studentova_t_distribucija: {\r\n        title: 'Studentova t-porazdelitev',\r\n        1: 'Če sta 𝑍~𝒩(0, 1) in 𝑌~𝜒2(𝑛), ima slučajna spremenljivka',\r\n        2: '<strong>Studentovo t-porazdelitev</strong> z 𝑛 stopnjami prostosti in je označena s 𝑇 ~𝑡(𝑛).',\r\n        3: '<strong>Pričakovana vrednost</strong> in <strong>varianca</strong> porazdelitve 𝑡(𝑛) sta:',\r\n        4: '<strong>Primer 4.6.1.</strong>',\r\n        5: 'Grafi funkcije gostote porazdelitev 𝑡(3), 𝑡(5) in 𝑡(7) z označeno pričakovano vrednostjo so predstavljeni na naslednji sliki.',\r\n        6: 'Z interaktivnim orodjem proučite 𝑡(𝑛) porazdelitve za druge vrednosti parametra 𝑛.'\r\n      }\r\n    }\r\n  }\r\n}\r\n\r\nexport default messages\r\n","import Vue from 'vue'\r\n\r\nVue.mixin({\r\n  methods: {\r\n    generateRandomNumber (minValue, maxValue) {\r\n      let randomNumber = Math.random() * (maxValue - minValue) + minValue\r\n      return Math.floor(randomNumber)\r\n    },\r\n    qnorm (p) {\r\n      p = parseFloat(p)\r\n      var split = 0.42\r\n\r\n      var a0 = 2.50662823884\r\n      var a1 = -18.61500062529\r\n      var a2 = 41.39119773534\r\n      var a3 = -25.44106049637\r\n      var b1 = -8.47351093090\r\n      var b2 = 23.08336743743\r\n      var b3 = -21.06224101826\r\n      var b4 = 3.13082909833\r\n      var c0 = -2.78718931138\r\n      var c1 = -2.29796479134\r\n      var c2 = 4.85014127135\r\n      var c3 = 2.32121276858\r\n      var d1 = 3.54388924762\r\n      var d2 = 1.63706781897\r\n\r\n      var q = p - 0.5\r\n\r\n      var r, ppnd\r\n\r\n      if (Math.abs(q) <= split) {\r\n        r = q * q\r\n        ppnd = q * (((a3 * r + a2) * r + a1) * r + a0) / ((((b4 * r + b3) * r + b2) * r + b1) * r + 1)\r\n      } else {\r\n        r = p\r\n        if (q > 0) r = 1 - p\r\n        if (r > 0) {\r\n          r = Math.sqrt(-Math.log(r))\r\n          ppnd = (((c3 * r + c2) * r + c1) * r + c0) / ((d2 * r + d1) * r + 1)\r\n          if (q < 0) ppnd = -ppnd\r\n        } else {\r\n          ppnd = 0\r\n        }\r\n      }\r\n\r\n      return ppnd\r\n    },\r\n    lessonFooterLogic () {\r\n      window.onscroll = () => {\r\n        const elem = document.querySelector('.footer')\r\n        if (elem) {\r\n          if ((window.innerHeight + window.pageYOffset) >= document.body.offsetHeight) {\r\n            elem.style.opacity = 1\r\n          }\r\n        }\r\n      }\r\n    },\r\n    factorial (n) {\r\n      if (n < 0) {\r\n        return undefined\r\n      } else if (n == 0) {\r\n        return 1\r\n      } else {\r\n        return n * this.factorial(n - 1)\r\n      }\r\n    },\r\n    combinations (n, k) {\r\n      // check if k > n\r\n      if (k > n) {\r\n        return 0\r\n      }\r\n      // grab n! and k!\r\n      var nFact = this.factorial(n)\r\n      var kFact = this.factorial(k)\r\n\r\n      // compute (n-k)! for later\r\n      var nkFact = this.factorial(n - k)\r\n\r\n      // set numerator & denominator\r\n      var numerator = nFact\r\n      var denominator = kFact * nkFact\r\n\r\n      var ans = numerator / denominator\r\n      return ans\r\n    },\r\n    binomialProbability (trials, successes, prob_of_success) {\r\n      return this.combinations(trials, successes) * Math.pow(prob_of_success, successes) * Math.pow(1 - prob_of_success, trials - successes)\r\n    },\r\n    cumulativeBinomialProbability (trials, successes, prob_of_success) {\r\n      let cumulative = 0\r\n\r\n      for (let i = 0; i <= successes; ++i) {\r\n        cumulative = cumulative + this.binomialProbability(trials, i, prob_of_success)\r\n      }\r\n\r\n      return cumulative\r\n    },\r\n    is_touch_device () {\r\n      const prefixes = ' -webkit- -moz- -o- -ms- '.split(' ')\r\n      let mq = function (query) {\r\n        return window.matchMedia(query).matches\r\n      }\r\n\r\n      if (('ontouchstart' in window) || window.DocumentTouch && document instanceof DocumentTouch) {\r\n        return true\r\n      }\r\n\r\n      // include the 'heartz' as a way to have a non matching MQ to help terminate the join\r\n      // https://git.io/vznFH\r\n      let query = ['(', prefixes.join('touch-enabled),('), 'heartz', ')'].join('')\r\n      return mq(query)\r\n    },\r\n    compressArray (original) {\r\n      const occurances = []\r\n      const copy = original.slice(0)\r\n\r\n      for (let i = 0; i < original.length; i++) {\r\n        let myCount = 0\r\n        for (let w = 0; w < copy.length; w++) {\r\n          if (original[i] == copy[w]) {\r\n            myCount++\r\n            delete copy[w]\r\n          }\r\n        }\r\n\r\n        if (myCount > 0) {\r\n          occurances.push(myCount)\r\n        }\r\n      }\r\n      return occurances\r\n    },\r\n    updateChapterLessonsProgress (chapterIndex, lessonIndex) {\r\n      let lessonsProgress = JSON.parse(window.localStorage.getItem('lessonsProgress'))\r\n      lessonsProgress[chapterIndex].isOpened[lessonIndex] = true\r\n      window.localStorage.setItem('lessonsProgress', JSON.stringify(lessonsProgress))\r\n    },\r\n    getChapterLessonsProgress (chapterIndex) {\r\n      let lessonsProgress = JSON.parse(window.localStorage.getItem('lessonsProgress'))\r\n      return lessonsProgress[chapterIndex]\r\n    },\r\n    alignWithExample () {\r\n\r\n      this.examples = this.$el.querySelectorAll('.example')\r\n\r\n      if(window.innerWidth < 768) {\r\n        this.interactions = this.$el.querySelectorAll('.interaction')\r\n\r\n        for (let i = 0; i < this.interactions.length; i++) {\r\n          this.interactions[i].style.marginTop = `54px`\r\n        }\r\n\r\n        if (this.interactions != this.examples) {\r\n          for (let i = 0; i < this.interactions.length; i++) {\r\n            this.interactions[i].style.marginTop = `54px`\r\n          }\r\n        }\r\n      } else {\r\n        for (let i = 0; i < this.examples.length; i++) {\r\n          // element.offsetTop - element.scrollTop + element.clientTop\r\n          // let offset = this.examples[i].offsetTop - this.examples[i].scrollTop + this.examples[i].clientTop\r\n          this.$set(this.examplesOffsets, i, this.examples[i].offsetTop)\r\n        }\r\n\r\n        this.interactions = this.$el.querySelectorAll('.interaction')\r\n\r\n        if (this.interactions != this.examples) {\r\n          for (let i = 0; i < this.interactions.length; i++) {\r\n            this.interactions[i].style.marginTop = `${this.examplesOffsets[0] - 44 - 40}px`\r\n          }\r\n        }\r\n\r\n        for (let i = 0; i < this.interactions.length; i++) {\r\n          this.interactions[i].style.marginTop = `${this.examplesOffsets[i] - 44 - 40}px`\r\n        }\r\n      }\r\n    },\r\n    alignWithOffset (exampleOffset) {\r\n      this.examples = this.$el.querySelectorAll('.example')\r\n\r\n      for (let i = 0; i < this.examples.length; i++) {\r\n        if (i !== exampleOffset) {\r\n          this.$set(this.examplesOffsets, i - 1, this.examples[i].offsetTop)\r\n        }\r\n      }\r\n      this.interactions = this.$el.querySelectorAll('.interaction')\r\n\r\n      for (let i = 0; i < this.interactions.length; i++) {\r\n        this.interactions[i].style.top = `${this.examplesOffsets[i] - 44 - 40}px`\r\n      }\r\n    },\r\n    updateFormulaScroll() {\r\n      setTimeout(() => {\r\n        this.$nextTick(() => {\r\n          for(var ref in this.$refs) {\r\n            this.$refs[ref].update()\r\n          }\r\n          // this.$refs.ps1.update()\r\n          // this.$refs.ps2.update()\r\n        });\r\n      }, 1000);\r\n    }\r\n  }\r\n})\r\n","/* eslint-disable */\r\nimport '@babel/polyfill'\r\nimport Vue from 'vue'\r\nimport VueI18n from 'vue-i18n'\r\nimport VueObserveVisibility from 'vue-observe-visibility'\r\n\r\nimport App from './App.vue'\r\nimport messages from './translations'\r\nimport router from './router'\r\nimport store from './store'\r\nimport PerfectScrollbar from 'vue2-perfect-scrollbar'\r\nimport 'vue2-perfect-scrollbar/dist/vue2-perfect-scrollbar.css'\r\nimport Meta from 'vue-meta'\r\n\r\nimport './utils'\r\nimport './scss/main.scss'\r\n\r\nrequire('intersection-observer')\r\n\r\nVue.config.productionTip = false\r\n\r\nVue.use(require('vue-chartist'))\r\nVue.use(VueI18n)\r\nVue.use(VueObserveVisibility)\r\nVue.use(PerfectScrollbar)\r\nVue.use(Meta)\r\n\r\nVue.use(require('vue-scrollto'))\r\n\r\nimport ChartDataLabels from 'chartjs-plugin-datalabels'\r\nChart.plugins.unregister(ChartDataLabels)\r\n\r\nexport const eventBus = new Vue();\r\n\r\n// Create VueI18n instance with options\r\nconst i18n = new VueI18n({\r\n  locale: window.localStorage.getItem('lang'), // set locale\r\n  messages // set locale messages\r\n})\r\n\r\nnew Vue({\r\n  router,\r\n  store,\r\n  i18n,\r\n  watch:{\r\n    '$route' (){\r\n       this.$store.commit('closeSidebar')\r\n    }\r\n  },\r\n  render: h => h(App)\r\n}).$mount('#app')\r\n","module.exports = __webpack_public_path__ + \"img/pink_background_with_illustration@2x.425deed0.svg\";","module.exports = __webpack_public_path__ + \"img/Group2_homepage.653496ba.svg\";","module.exports = __webpack_public_path__ + \"img/eurostat_logo@2x.246ded9c.svg\";","module.exports = __webpack_public_path__ + \"img/Group_homepage.5b3b8ffe.svg\";","module.exports = __webpack_public_path__ + \"img/purple_background_with_illustration@2x.cfc08061.svg\";","import mod from \"-!../../node_modules/mini-css-extract-plugin/dist/loader.js??ref--8-oneOf-1-0!../../node_modules/css-loader/index.js??ref--8-oneOf-1-1!../../node_modules/vue-loader/lib/loaders/stylePostLoader.js!../../node_modules/postcss-loader/src/index.js??ref--8-oneOf-1-2!../../node_modules/sass-loader/lib/loader.js??ref--8-oneOf-1-3!../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Loader.vue?vue&type=style&index=0&lang=scss&\"; export default mod; export * from \"-!../../node_modules/mini-css-extract-plugin/dist/loader.js??ref--8-oneOf-1-0!../../node_modules/css-loader/index.js??ref--8-oneOf-1-1!../../node_modules/vue-loader/lib/loaders/stylePostLoader.js!../../node_modules/postcss-loader/src/index.js??ref--8-oneOf-1-2!../../node_modules/sass-loader/lib/loader.js??ref--8-oneOf-1-3!../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Loader.vue?vue&type=style&index=0&lang=scss&\"","module.exports = __webpack_public_path__ + \"img/Group_homepage_mobile.ddbae56b.svg\";","import Vue from 'vue'\r\nimport Vuex from 'vuex'\r\n\r\nVue.use(Vuex)\r\n\r\nexport default new Vuex.Store({\r\n  state: {\r\n    isSidebarOpen: false,\r\n    isLoading: false\r\n  },\r\n  mutations: {\r\n    toggleSidebar (state, nexState) {\r\n      state.isSidebarOpen = nexState\r\n    },\r\n    toggleLoader (state, nexState) {\r\n      state.isLoading = nexState\r\n    },\r\n    closeSidebar (state) {\r\n      return state.isSidebarOpen = false\r\n    }\r\n  },\r\n  actions: {\r\n\r\n  }\r\n})\r\n","module.exports = __webpack_public_path__ + \"img/Group_homepage2_mobile.f75e59ac.svg\";","module.exports = __webpack_public_path__ + \"img/dzs_logo@2x.1edae14f.svg\";","import mod from \"-!../../node_modules/mini-css-extract-plugin/dist/loader.js??ref--8-oneOf-1-0!../../node_modules/css-loader/index.js??ref--8-oneOf-1-1!../../node_modules/vue-loader/lib/loaders/stylePostLoader.js!../../node_modules/postcss-loader/src/index.js??ref--8-oneOf-1-2!../../node_modules/sass-loader/lib/loader.js??ref--8-oneOf-1-3!../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../node_modules/vue-loader/lib/index.js??vue-loader-options!./HomepageNavigation.vue?vue&type=style&index=0&id=74863973&lang=scss&scoped=true&\"; export default mod; export * from \"-!../../node_modules/mini-css-extract-plugin/dist/loader.js??ref--8-oneOf-1-0!../../node_modules/css-loader/index.js??ref--8-oneOf-1-1!../../node_modules/vue-loader/lib/loaders/stylePostLoader.js!../../node_modules/postcss-loader/src/index.js??ref--8-oneOf-1-2!../../node_modules/sass-loader/lib/loader.js??ref--8-oneOf-1-3!../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../node_modules/vue-loader/lib/index.js??vue-loader-options!./HomepageNavigation.vue?vue&type=style&index=0&id=74863973&lang=scss&scoped=true&\"","import mod from \"-!../../node_modules/mini-css-extract-plugin/dist/loader.js??ref--8-oneOf-1-0!../../node_modules/css-loader/index.js??ref--8-oneOf-1-1!../../node_modules/vue-loader/lib/loaders/stylePostLoader.js!../../node_modules/postcss-loader/src/index.js??ref--8-oneOf-1-2!../../node_modules/sass-loader/lib/loader.js??ref--8-oneOf-1-3!../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Home.vue?vue&type=style&index=0&id=da914d72&lang=scss&scoped=true&\"; export default mod; export * from \"-!../../node_modules/mini-css-extract-plugin/dist/loader.js??ref--8-oneOf-1-0!../../node_modules/css-loader/index.js??ref--8-oneOf-1-1!../../node_modules/vue-loader/lib/loaders/stylePostLoader.js!../../node_modules/postcss-loader/src/index.js??ref--8-oneOf-1-2!../../node_modules/sass-loader/lib/loader.js??ref--8-oneOf-1-3!../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Home.vue?vue&type=style&index=0&id=da914d72&lang=scss&scoped=true&\"","module.exports = __webpack_public_path__ + \"img/logo_stedi_nav_bar_en.34661b55.svg\";","module.exports = __webpack_public_path__ + \"img/logo_stedi_nav_bar@2x.0a6c4187.svg\";","module.exports = __webpack_public_path__ + \"img/green_background_and_illustration@2x.f830e10b.svg\";","import mod from \"-!../../node_modules/mini-css-extract-plugin/dist/loader.js??ref--6-oneOf-1-0!../../node_modules/css-loader/index.js??ref--6-oneOf-1-1!../../node_modules/vue-loader/lib/loaders/stylePostLoader.js!../../node_modules/postcss-loader/src/index.js??ref--6-oneOf-1-2!../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Cookies.vue?vue&type=style&index=0&lang=css&\"; export default mod; export * from \"-!../../node_modules/mini-css-extract-plugin/dist/loader.js??ref--6-oneOf-1-0!../../node_modules/css-loader/index.js??ref--6-oneOf-1-1!../../node_modules/vue-loader/lib/loaders/stylePostLoader.js!../../node_modules/postcss-loader/src/index.js??ref--6-oneOf-1-2!../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Cookies.vue?vue&type=style&index=0&lang=css&\""],"sourceRoot":""}