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data set containing n values: \\\\(x = {x_1, x_2, x_3, ..., x_n} \\\\). Then the mean of this data set is given as:\\n    $$\\\\mu = \\\\frac{x_1+x_2+ ...+x_n}{n}= \\\\frac{\\\\sum x_i}{n}$$\\n  \")]),_c('h3',{ref:\"ia\"},[_vm._v(\"\\n    Median\\n  \")]),_c('p',[_vm._v(\"\\n    The median of a set is the value at the middle of a sorted data set. Half of the values are greater than the median and other half of the values\\n    are smaller than median.\\n    The median is found by ordering the set from lowest to highest and locating the value in the exact middle.\\n  \")]),_c('h3',{ref:\"meth\"},[_vm._v(\"\\n    Standard Deviation\\n  \")]),_c('p',[_vm._v(\"\\n    Standard deviation is a measure of the spread in the data from the mean value. Standard deviation is typically represented by the symbol \\\\(\\\\sigma\\\\).\\n    A low standard deviation means that the values in the set lie within a narrow window around the mean (i.e., the values are close to the mean). Conversely,\\n    a high standard deviation means that the values spread over a wide window around the mean.\\n    Mathematically, the standard deviation is given as:\\n  \")]),_vm._v(\"\\n  $$\\\\sigma = \\\\sqrt{\\\\frac{(x_1-\\\\mu)^2+(x_2-\\\\mu)^2+ ...+(x_n-\\\\mu)^2}{n}}= \\\\sqrt{\\\\frac{\\\\sum (x_i-\\\\mu)^2}{n}}$$\\n  \"),_c('h3',{ref:\"pg\"},[_vm._v(\"\\n    MagicGraph | Mean & Standard Deviation\\n  \")]),_c('p',[_vm._v(\" In this MagicGraph, You will learn about the mean and the standard deviation of a dataset.\")]),_vm._m(0),_c('p',[_vm._v(\" You can repeat the above steps any number of times to learn different scenarios. \")]),_c('br'),_c('v-responsive',[_c('v-layout',{attrs:{\"justify-center\":\"\"}},[_c('div',{staticClass:\"edliy-box-about\",attrs:{\"id\":\"jxgbox1\"}})])],1)],1)\n}\nvar staticRenderFns = [function (){var _vm=this,_c=_vm._self._c;return _c('ul',{staticStyle:{\"list-style-type\":\"square\"}},[_c('li',[_c('h5',[_vm._v(\"Getting Started\")]),_vm._v(\" You are to choose from a pack of 10 dogs. You're supposed to choose 5 dogs. To select, click on the dogs that you would like to choose.  \")]),_c('br'),_c('li',[_c('h5',[_vm._v(\"To Explore\")]),_vm._v(\"\\n      Select different combinations of dogs to see how the mean and standard deviation change.\\n    \")]),_c('br')])\n}]\n\nexport { render, staticRenderFns }","const Boxes = {\r\n  box1: function () {\r\n\t JXG.Options.board.minimizeReflow = 'none';\r\n  var brd1 = JXG.JSXGraph.initBoard('jxgbox1',{boundingbox: [-18, 25, 12, -5],keepaspectratio: true, axis:true, ticks:true, grid:true, showCopyright:false, showNavigation:false, pan:{enabled:false}, zoom:{enabled:false}, showReload:true});\r\n\t var resize = function () {\r\n\t   brd1.resizeContainer(brd1.containerObj.clientWidth, brd1.containerObj.clientHeight, true);\r\n\t   brd1.fullUpdate();};\r\n\twindow.onresize = resize;\r\n    brd1.options.layer['image'] =14;\r\n\tbrd1.create('text', [-12, 24., '<b> Statistics: Mean & Standard Deviation <b>'],{CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(18*brd1.canvasWidth/500.)}, fixed:true});\r\n\tvar a=0.25;\r\n\t//\r\n\tvar plus1=brd1.create('image', ['/assets/bulldog.svg', [-14., 20.-a],[1.6, 1.7]], {opacity:1, fixed:true});\r\n\tplus1.setLabel('Bulldog')\r\n\tplus1.label.setAttribute({visible:false, offset:[0, -15], CssStyle:'fontFamily:Oswald', fontSize:12});\r\n\tplus1.on('over', function () {this.label.setAttribute({visible:true});});\r\n\tplus1.on('out', function () {this.label.setAttribute({visible:false});});\r\n\t//\r\n\tvar plus2=brd1.create('image', ['/assets/dachshund.svg', [-12., 20.-a-0.1],[1.75, 1.75]], {opacity:1, fixed:true});\r\n\tplus2.setLabel('Corgi')\r\n\tplus2.label.setAttribute({visible:false, offset:[0, -15], CssStyle:'fontFamily:Oswald', fontSize:12});\r\n\tplus2.on('over', function () {this.label.setAttribute({visible:true});});\r\n\tplus2.on('out', function () {this.label.setAttribute({visible:false});});\r\n\t//\r\n\tvar plus3=brd1.create('image', ['/assets/mastiff.svg', [-10, 20-a-0.1],[3, 3.2]], {opacity:1, fixed:true});\r\n\tplus3.setLabel('Mastiff')\r\n\tplus3.label.setAttribute({visible:false, offset:[0, -15], CssStyle:'fontFamily:Oswald', fontSize:12});\r\n\tplus3.on('over', function () {this.label.setAttribute({visible:true});});\r\n\tplus3.on('out', function () {this.label.setAttribute({visible:false});});\r\n    //\r\n\tvar plus4=brd1.create('image', ['/assets/pointer.svg', [-7.5, 20-a-0.1],[2.5, 2.5]], {opacity:1, fixed:true});\r\n\tplus4.setLabel('Pointer')\r\n\tplus4.label.setAttribute({visible:false, offset:[0, -15], CssStyle:'fontFamily:Oswald', fontSize:12});\r\n\tplus4.on('over', function () {this.label.setAttribute({visible:true});});\r\n\tplus4.on('out', function () {this.label.setAttribute({visible:false});});\r\n    //\r\n\tvar plus5=brd1.create('image', ['/assets/doberman.svg', [-5, 20.15-a],[2.5, 2.5]], {opacity:1, fixed:true});\r\n\tplus5.setLabel('Doberman')\r\n\tplus5.label.setAttribute({visible:false, offset:[0, -15], CssStyle:'fontFamily:Oswald', fontSize:12});\r\n\tplus5.on('over', function () {this.label.setAttribute({visible:true});});\r\n\tplus5.on('out', function () {this.label.setAttribute({visible:false});});\r\n    //\r\n\tvar plus6=brd1.create('image', ['/assets/greyhound.svg', [-2.5, 20-a-0.1],[2.85, 2.85]], {opacity:1, fixed:true});\r\n\tplus6.setLabel('Greyhound')\r\n\tplus6.label.setAttribute({visible:false, offset:[0, -15], CssStyle:'fontFamily:Oswald', fontSize:12});\r\n\tplus6.on('over', function () {this.label.setAttribute({visible:true});});\r\n\tplus6.on('out', function () {this.label.setAttribute({visible:false});});\r\n    //\r\n\tvar plus7=brd1.create('image', ['/assets/dalmatian.svg', [0, 20-0.2-a],[2.35, 2.6]], {opacity:1, fixed:true});\r\n\tplus7.setLabel('Dalmatian')\r\n\tplus7.label.setAttribute({visible:false, offset:[0, -15], CssStyle:'fontFamily:Oswald', fontSize:12});\r\n\tplus7.on('over', function () {this.label.setAttribute({visible:true});});\r\n\tplus7.on('out', function () {this.label.setAttribute({visible:false});});\r\n    //\r\n\tvar plus8=brd1.create('image', ['/assets/shar-pei.svg', [2.5, 20-a-0.1],[2.25, 2.25]], {opacity:1, fixed:true});\r\n\tplus8.setLabel('Shar-Pei')\r\n\tplus8.label.setAttribute({visible:false, offset:[0, -15], CssStyle:'fontFamily:Oswald', fontSize:12});\r\n\tplus8.on('over', function () {this.label.setAttribute({visible:true});});\r\n\tplus8.on('out', function () {this.label.setAttribute({visible:false});});\r\n    //\r\n\tvar plus9 = brd1.create('image', ['/assets/rottweiler.svg', [5, 20-a-0.1],[2.5, 2.5]], {opacity:1, fixed:true});\r\n\tplus9.setLabel('Rottweiler')\r\n\tplus9.label.setAttribute({visible:false, offset:[0, -15], CssStyle:'fontFamily:Oswald', fontSize:12});\r\n\tplus9.on('over', function () {this.label.setAttribute({visible:true});});\r\n\tplus9.on('out', function () {this.label.setAttribute({visible:false});});\r\n    //\r\n\tvar plus10 =brd1.create('image', ['/assets/chihuahua.svg', [7.5, 20.25-a],[1.15, 1.]], {opacity:1, fixed:true});\r\n\tplus10.setLabel('Chihuahua')\r\n\tplus10.label.setAttribute({visible:false, offset:[0, -15], CssStyle:'fontFamily:Oswald', fontSize:12});\r\n\tplus10.on('over', function () {this.label.setAttribute({visible:true});});\r\n\tplus10.on('out', function () {this.label.setAttribute({visible:false});});\r\n\t//\r\n\tvar v =[0,0,0,0,0];\r\n\tvar i=0;\r\n\tplus1.on('down', function(){if(i<=4){plus1.moveTo([-14+2.75*i+0.5,-a]); v[i]=14/12; i+=1;}else{return;}});\r\n\tplus2.on('down', function(){if(i<=4){plus2.moveTo([-14+2.75*i+0.5,-a-0.1]); v[i]=12/12; i+=1;}else{return;}});\r\n\tplus3.on('down', function(){if(i<=4){plus3.moveTo([-14+2.75*i,-a-0.1]); v[i]=30/12; i+=1;}else{return;}});\r\n\tplus4.on('down', function(){if(i<=4){plus4.moveTo([-14+2.75*i,-a-0.1]); v[i]=24/12; i+=1;}else{return;}});\r\n\tplus5.on('down', function(){if(i<=4){plus5.moveTo([-14+2.75*i,0.15-a]);v[i]=28/12;  i+=1;}else{return;}});\r\n\tplus6.on('down', function(){if(i<=4){plus6.moveTo([-14+2.75*i,-a]); v[i]=27/12; i+=1;}else{return;}});\r\n\tplus7.on('down', function(){if(i<=4){plus7.moveTo([-14+2.75*i,-0.1-a]); v[i]=22/12; i+=1;}else{return;}});\r\n\tplus8.on('down', function(){if(i<=4){plus8.moveTo([-14+2.75*i,-a]);v[i]=20/12;  i+=1;}else{return;}});\r\n\tplus9.on('down', function(){if(i<=4){plus9.moveTo([-14+2.75*i,-a]); v[i]=2; i+=1;}else{return;}});\r\n\tplus10.on('down',function(){if(i<=4){plus10.moveTo([-14+2.75*i+0.5,0.25-a]);v[i]=11/12;  i+=1;}else{return;}});\r\n///////////////////////////////////////////////////////////\r\n\tvar mu = function(){return (v[0]+v[1]+v[2]+v[3]+v[4])/(i+0.00001)};\r\n\tvar sig = function(){\r\n\t\tif(i==1){return Math.sqrt((v[0]-mu())*(v[0]-mu()))}\r\n\t\telse if(i==2){return Math.sqrt(((v[0]-mu())*(v[0]-mu())+(v[1]-mu())*(v[1]-mu()))/2)}\r\n\t\telse if(i==3){return Math.sqrt(((v[0]-mu())*(v[0]-mu())+(v[1]-mu())*(v[1]-mu())+ (v[2]-mu())*(v[2]-mu()))/3)}\r\n\t\telse if(i==4){return Math.sqrt(((v[0]-mu())*(v[0]-mu())+(v[1]-mu())*(v[1]-mu())+(v[2]-mu())*(v[2]-mu())+ (v[3]-mu())*(v[3]-mu()))/4)}\r\n\t\telse if(i==5){return Math.sqrt(((v[0]-mu())*(v[0]-mu())+(v[1]-mu())*(v[1]-mu())+(v[2]-mu())*(v[2]-mu())+(v[3]-mu())*(v[3]-mu())+(v[4]-mu())*(v[4]-mu()))/5)}\r\n\t\telse{return 0;}\r\n\t};\r\n\tbrd1.create('text', [-17.7, -1.5, 'Heights(ft.)'],{CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(14*brd1.canvasWidth/500.)}, fixed:true});\r\n\tbrd1.create('text', [-13.625, -1.5, function(){return ''+ (v[0]).toFixed(2)}],{ fixed:true, CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(14*brd1.canvasWidth/500.)}});\r\n\tbrd1.create('text', [-10.875, -1.5, function(){return ''+ (v[1]).toFixed(2)}],{ fixed:true, CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(14*brd1.canvasWidth/500.)}});\r\n\tbrd1.create('text', [-8.125, -1.5, function(){return ''+ (v[2]).toFixed(2)}],{ fixed:true,CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(14*brd1.canvasWidth/500.)}});\r\n\tbrd1.create('text', [-5.375, -1.5, function(){return ''+ (v[3]).toFixed(2)}],{ fixed:true, CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(14*brd1.canvasWidth/500.)}});\r\n\tbrd1.create('text', [-2.625, -1.5, function(){return ''+ (v[4]).toFixed(2)}],{ fixed:true, CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(14*brd1.canvasWidth/500.)}});\r\n\tbrd1.create('text', [-13.5, 7.5, 'Mean &mu; (ft.)'],{CssStyle:'fontFamily:Oswald', color:'red', fontSize:function(){return Math.round(14*brd1.canvasWidth/500.)}, fixed:true});\r\n\tbrd1.create('text', [-5, 7.5, function(){return ''+ (mu()).toFixed(2)}],{fixed:true, CssStyle:'fontFamily:Oswald', color:'red', fontSize:function(){return Math.round(14*brd1.canvasWidth/500.)}});\r\n\tbrd1.create('text', [-13.5, 6., 'Standard Deviation &sigma; (ft.)'],{CssStyle:'fontFamily:Oswald',color:'blue', fontSize:function(){return Math.round(14*brd1.canvasWidth/500.)}, fixed:true});\r\n\tbrd1.create('text', [-5, 6., function(){return ''+ (JXG.Math.Statistics.sd(v)).toFixed(2)}],{ fixed:true, CssStyle:'fontFamily:Oswald', color:'blue', fontSize:function(){return Math.round(14*brd1.canvasWidth/500.)}});\r\n\tbrd1.create('text', [-13.5, 4.5, 'Median (ft.)'],{CssStyle:'fontFamily:Oswald',color:'green', fontSize:function(){return Math.round(14*brd1.canvasWidth/500.)}, fixed:true});\r\n\tbrd1.create('text', [-5, 4.5, function(){return ''+ (JXG.Math.Statistics.median(v)).toFixed(2)}],{ fixed:true, CssStyle:'fontFamily:Oswald', color:'green', fontSize:function(){return Math.round(14*brd1.canvasWidth/500.)}});\r\n\tvar func =brd1.create('functiongraph',[function(x){return (2.5/(sig()+0.01)/Math.sqrt(2*Math.PI))*Math.exp(-0.5*(x+mu())*(x+mu())/(sig()+0.01)/(sig()+0.01))}, 0, -4],{strokeColor:'red', strokeWidth:2});\r\n\tvar t = brd1.create('transform', [-Math.PI/2], {type: 'rotate'});\r\n\tt.bindTo(func);\r\n\tbrd1.create('line',[[0, function(){return mu()}],[function(){return 2/sig()/Math.sqrt(2*Math.PI)}, function(){return mu()}]], {strokeWidth:1, dash:1});\r\n\tvar mean =brd1.create('image', ['/assets/random.svg', [6, function(){return mu()}],[1.25, 1.25]], {opacity:1, fixed:true});\r\n\tmean.setLabel('Mean')\r\n\tvar std =brd1.create('image', ['/assets/random.svg', [2, function(){return mu()+sig()}],[1.25, 1.25]], {opacity:1, rotate:90, fixed:true});\r\n\tstd.setLabel('Spread')\r\n\tmean.label.setAttribute({offset:[0, 50], CssStyle:'fontFamily:Oswald', fontSize:12});\r\n\tstd.label.setAttribute({offset:[0, 50], CssStyle:'fontFamily:Oswald', fontSize:12});\r\n\tvar reload = brd1.create('image', ['/assets/reloading.svg', [5,8],[3.25, 3.25]], {opacity:1, fixed:true});\r\n\treload.on('down', function(){v=[0,0,0,0,0]; i=0; plus1.moveTo([-14., 20.-a]); plus2.moveTo([-12., 20.-a-0.1]); plus3.moveTo([-10, 20.-a-0.1]); plus4.moveTo([-7.5, 20.-a-0.1]);plus5.moveTo([-5., 20.15-a]);plus6.moveTo([-2.5, 20.-a-0.1]); plus7.moveTo([0., 20.-a-0.2]);plus8.moveTo([2.5, 20.-a-0.1]); plus9.moveTo([5, 20.-a-0.1]);plus10.moveTo([7.5, 20.25-a])});\r\n\r\n    },\r\n}\r\nexport default Boxes;\r\n","<template>\r\n  <div>\r\n    <h3 ref=\"ia\">\n      Mean\n    </h3>\r\n    <p>\n      In statistics, mean and standard deviation are used to described the values in a set.\r\n      The mean value of a data set represents the average of all the values in the set.\r\n      It is calculated as the sum of all the values in the set divided by the size of the set.\r\n      Consider a data set containing n values: \\(x = {x_1, x_2, x_3, ..., x_n} \\). Then the mean of this data set is given as:\r\n      $$\\mu = \\frac{x_1+x_2+ ...+x_n}{n}= \\frac{\\sum x_i}{n}$$\r\n    </p>\r\n    <h3 ref=\"ia\">\n      Median\n    </h3>\r\n    <p>\n      The median of a set is the value at the middle of a sorted data set. Half of the values are greater than the median and other half of the values\r\n      are smaller than median.\r\n      The median is found by ordering the set from lowest to highest and locating the value in the exact middle.\r\n    </p>\r\n    <h3 ref=\"meth\">\n      Standard Deviation\n    </h3>\r\n    <p>\n      Standard deviation is a measure of the spread in the data from the mean value. Standard deviation is typically represented by the symbol \\(\\sigma\\).\r\n      A low standard deviation means that the values in the set lie within a narrow window around the mean (i.e., the values are close to the mean). Conversely,\r\n      a high standard deviation means that the values spread over a wide window around the mean.\r\n      Mathematically, the standard deviation is given as:\n    </p>\r\n    $$\\sigma = \\sqrt{\\frac{(x_1-\\mu)^2+(x_2-\\mu)^2+ ...+(x_n-\\mu)^2}{n}}= \\sqrt{\\frac{\\sum (x_i-\\mu)^2}{n}}$$\r\n    <h3 ref=\"pg\">\n      MagicGraph | Mean & Standard Deviation\n    </h3>\r\n    <p> In this MagicGraph, You will learn about the mean and the standard deviation of a dataset.</p>\r\n    <ul style=\"list-style-type: square;\">\r\n      <li><h5>Getting Started</h5> You are to choose from a pack of 10 dogs. You're supposed to choose 5 dogs. To select, click on the dogs that you would like to choose.  </li> <br>\r\n      <li>\n        <h5>To Explore</h5>\r\n        Select different combinations of dogs to see how the mean and standard deviation change.\r\n      </li> <br>\r\n    </ul>\r\n    <p> You can repeat the above steps any number of times to learn different scenarios. </p>\r\n    <br>\r\n    <v-responsive>\r\n      <v-layout justify-center>\r\n        <div id=\"jxgbox1\" class=\"edliy-box-about\" />\r\n      </v-layout>\r\n    </v-responsive>\r\n  </div>\r\n</template>\r\n<script>\r\nimport Boxes from './Boxes.js'\r\nexport default {\r\n  name: 'Resistors',\r\n  created: function () {\r\n    this.$store.commit('navigation/resetState');\r\n    let title = 'Mean and Standard Deviation';\r\n    this.$store.commit('navigation/changeTitle', title);\r\n    this.$store.commit('navigation/changeMenu', title);\r\n    let newTopics = [\r\n      {title: 'Mean', img:'/assets/number-1.svg', action: () => this.goto('ia')},\r\n      {title: 'Standard Deviation', img:'/assets/number-2.svg', action: () => this.goto('meth')},\r\n      {title: 'MagicGraph',img:'/assets/touch.svg', action: () => this.goto('pg')},\r\n    ];\r\n    this.$store.commit('navigation/replaceTopics', newTopics);\r\n    let newshowhome = false;\r\n    this.$store.commit('navigation/toggleshowhome', newshowhome);\r\n    let newMath =true;\r\n    this.$store.commit('navigation/replaceMath', newMath);\r\n    let newLeftArrow =true;\r\n    this.$store.commit('navigation/replaceLeftArrow', newLeftArrow);\r\n    let newModule=true;\r\n    this.$store.commit('navigation/replaceModule', newModule);\r\n  },\r\n  mounted () {\r\n    MathJax.Hub.Queue([\"Typeset\", MathJax.Hub]);\r\n    Boxes.box1();\r\n  },\r\n  metaInfo() {\r\n  return{ title: 'Mean, Median and Standard Deviation',\r\n          titleTemplate: '%s - Learn interactively',\r\n          meta: [ {name: 'viewport', content: 'width=device-width, initial-scale=1'},\r\n                  {name: 'description', content: 'Learn interactively about mean, median and standard deviation.'}\r\n                ]\r\n        }\r\n   },\r\n}\r\n</script>\r\n<style lang=\"scss\">\r\n@import 'src/styles/edliy-box.scss';\r\n@import 'src/styles/subtopic-menu.scss';\r\n@import 'src/styles/edliy-box-about.scss';\r\n@import 'src/styles/screen-sizes.scss';\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!./Lesson.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!./Lesson.vue?vue&type=script&lang=js&\"","import { render, staticRenderFns } from \"./Lesson.vue?vue&type=template&id=4efedb10&\"\nimport script from \"./Lesson.vue?vue&type=script&lang=js&\"\nexport * from \"./Lesson.vue?vue&type=script&lang=js&\"\nimport style0 from \"./Lesson.vue?vue&type=style&index=0&id=4efedb10&prod&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\nexport default component.exports"],"sourceRoot":""}