{"id":432,"date":"2023-07-29T23:03:07","date_gmt":"2023-07-29T23:03:07","guid":{"rendered":"https:\/\/statorials.org\/de\/ausreisser-rechner\/"},"modified":"2023-07-29T23:03:07","modified_gmt":"2023-07-29T23:03:07","slug":"ausreisser-rechner","status":"publish","type":"post","link":"https:\/\/statorials.org\/de\/ausreisser-rechner\/","title":{"rendered":"Ausrei\u00dferrechner"},"content":{"rendered":"<p><script src=\"https:\/\/unpkg.com\/d3@4.6.0\"><\/script><script src=\"https:\/\/unpkg.com\/d3fc@12.1.0\"><\/script><script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/d3-legend\/2.18.0\/d3-legend.min.js\"><\/script><script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjs\/5.1.1\/math.js\"><\/script><script src=\"https:\/\/cdn.jsdelivr.net\/npm\/jstat@latest\/dist\/jstat.min.js\"><\/script><\/p>\n<style>\n@import url('https:\/\/fonts.googleapis.com\/css?family=Droid+Serif|Raleway');<\/p>\n<p>#chart {\n  width: 100%;\n  height: 500px;\n}<\/p>\n<p>.point path {\n  opacity: 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black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\npadding-left: 100px;\n}<\/p>\n<p>#calcTitle {\ntext-align: center;\nfont-size: 20px;\nmargin-bottom: 0px;\nfont-family: 'Raleway', serif;\n}<\/p>\n<p>#hr_top {\nwidth: 30%;\nmargin-bottom: 0px;\nborder: none;\nheight: 2px;\ncolor: black;\nbackground-color: black;\n}<\/p>\n<p>#hr_bottom {\nwidth: 30%;\nmargin-top: 15px;\nborder: none;\nheight: 2px;\ncolor: black;\nbackground-color: black;\n}<\/p>\n<p>#words label, input {\n    display: inline-block;\n    vertical-align: baseline;\n    width: 350px;\n}<\/p>\n<p>    #button {\n      border: 1px solid;\n      border-radius: 10px;\n      margin-top: 20px;<\/p>\n<p>      cursor: pointer;\n      outline: none;\n      background-color: white;\n      color: black;\n      font-family: 'Work Sans', sans-serif;\n      border: 1px solid grey;\n      \/* Green *\/\n    }<\/p>\n<p>    #button:hover {\n      background-color: #f6f6f6;\n      border: 1px solid black;\n    }<\/p>\n<p>\t#words_table {\ncolor: black;\nfont-family: Raleway;\nmax-width: 350px;\nmargin: 25px auto;\nline-height: 1.75;\n}<\/p>\n<p>#summary_table {\ncolor: black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\npadding-left: 20px;\n}<\/p>\n<p>\t.label_radio {\n\ttext-align: center;\n    }<\/p>\n<p>td, tr, th {\n    border: 1px solid black;\n}\ntable {\n    border-collapse: collapse;\n}\ntd, th {\n    min-width: 50px;\n    height: 21px;\n}\n    .label_radio {\n\ttext-align: center;\n}<\/p>\n<p>#text_area_input {\n\tpadding-left: 35%;\n\tfloat: left;\n}<\/p>\n<p>svg:not(:root) {\n  overflow: visible;\n}<\/p>\n<\/style>\n<div id=\"words\">\n<p style=\"text-align: left\">Ein <b>Ausrei\u00dfer<\/b> ist definiert als jede Beobachtung in einem Datensatz, die 1,5 IQR h\u00f6her als das dritte Quartil oder 1,5 IQR niedriger als das erste Quartil ist, wobei IQR f\u00fcr \u201eInterquartilbereich\u201c steht und die Differenz zwischen dem ersten und dritten Quartil darstellt.<\/p>\n<p style=\"text-align: left\"> Um Ausrei\u00dfer f\u00fcr einen bestimmten Datensatz zu identifizieren, geben Sie Ihre durch Kommas getrennten Daten in das Feld unten ein und klicken Sie dann auf die Schaltfl\u00e4che \u201eAusrei\u00dfer identifizieren\u201c: <\/p>\n<\/div>\n<div id=\"words_table\"><textarea id=\"input_data\" name=\"x\" rows=\"5\" cols=\"40\"><\/textarea><\/div>\n<div id=\"words_table\"><input type=\"button\" id=\"button\" onclick=\"calc()\" value=\"Identify Outliers\"><\/div>\n<div id=\"words_table\">\n<p style=\"text-align: left\"> <b>Ausrei\u00dfer:<\/b><span id=\"outliers\"><\/span><\/p>\n<p style=\"text-align: left\"> Minimum:<span id=\"min\"><\/span><\/p>\n<p style=\"text-align: left\"> Erstes Quartil:<span id=\"quartile1\"><\/span><\/p>\n<p style=\"text-align: left\"> Median:<span id=\"mid\"><\/span><\/p>\n<p style=\"text-align: left\"> Drittes Quartil:<span id=\"quartile3\"><\/span><\/p>\n<p style=\"text-align: left\"> Maximal:<span id=\"max\"><\/span><\/p>\n<\/div>\n<p><script><\/p>\n<p>\/\/function to get weird object keys from object that holds boxplot\nfunction resolve(path, obj=self, separator='.') {\n    var properties = Array.isArray(path) ? path : path.split(separator)\n    return properties.reduce((prev, curr) => prev && prev[curr], obj)\n}<\/p>\n<p>function calc() {<\/p>\n<p>var input_data = document.getElementById('input_data').value.match(\/\\d+\/g).map(Number);<\/p>\n<p>var data = [];\nfor (var i=0; i < input_data.length; i++) {\n    data.push({\n        Q1: input_data[i]\n    });\n}\n\nvar box = (values) => {\n  var sorted = values.slice();\n  sorted.sort((a, b) => a - b);<\/p>\n<p>  var max = sorted[sorted.length - 1];\n  var min = sorted[0];<\/p>\n<p>  \/\/var upper = d3.quantile(sorted, 0.75);\n  \/\/var mid = d3.quantile(sorted, 0.5);\n  \/\/var lower = d3.quantile(sorted, 0.25);<\/p>\n<p>\/\/ find the median of the sample\n    var mid = math.median(sorted);<\/p>\n<p>    \/\/ split the data by the median\n    var _firstHalf = sorted.filter(function(f){ return f < mid})\n    var _secondHalf = sorted.filter(function(f){ return f > mid})<\/p>\n<p>    \/\/ find the medians for each split, calculate IQR\n    var lower = math.median(_firstHalf);\n    var upper = math.median(_secondHalf);<\/p>\n<p>  var lowerLimit = lower - ((upper - lower) * 1.5);\n  var lowerWhisker = sorted.find(function(d) { return d > lowerLimit; });<\/p>\n<p>  var upperLimit = upper - (-1 * ((upper - lower) * 1.5));\n  var upperWhisker = sorted.reverse().find(function(d) { return d < upperLimit; });\n\n  return {\n    upper: upper, mid: mid, lower: lower, lowerWhisker: lowerWhisker,\n    upperWhisker: upperWhisker, max: max, min:min,\n    outliers: values.filter(function(d) { return d > upperWhisker || d < lowerWhisker; })\n  }\n}\n\nvar flatten = function(arrays) {\n  return arrays.reduce(function(a, b) {\n    return a.concat(b);\n  }, [])\n}\n  var quarters = Object.keys(data[0]);\n  var series = quarters.map(function(q) {\n    return {\n      quarter: q,\n      data: box(data.map(function(d) { return Number(d[q]); }))\n    };\n  })\n\n  var yFormat = d3.format(',.0f');\n\n  var yExtent = fc.extentLinear()\n    .accessors([function(d) { return d.max; }, function(d) { return d.min; }])\n    .pad([0, 0.1])\n    .include([0])\n\n  var boxplot = fc.seriesSvgBoxPlot()\n      .crossValue(function(d) { return d.quarter; })\n      .medianValue(function(d) { return d.data.mid; })\n      .barWidth(50)\n      .upperQuartileValue(function(d) { return d.data.upper; })\n      .lowerQuartileValue(function(d) { return d.data.lower; })\n      .highValue(function(d) { return d.data.upperWhisker; })\n      .lowValue(function(d) { return d.data.lowerWhisker; });\n\n  var point = fc.seriesSvgPoint()\n      .crossValue(function(d) { return d[0]; })\n      .mainValue(function(d) { return d[1]; });\n\n  var label = fc.seriesSvgPoint()\n      .crossValue(function(d) { return d[0]; })\n      .mainValue(function(d) { return d[1]; })\n      .decorate(function(selection) {\n        selection.enter()\n            .select('path')\n            .attr('display', 'none')\n        selection.enter()\n            .append('text')\n            .style('text-anchor', 'middle')\n            .attr('transform', function(d, i) { return  'translate(' + (i % 2 === 0 ? -50 : 50) + ', 5)'; })\n            .text(function(d) { return yFormat(d[1]); })\n            .attr('stroke', 'transparent')\n            .attr('fill', 'black');\n      });\n\n  var multi = fc.seriesSvgMulti()\n      .series([boxplot, point, label])\n      .mapping((data, index, series) => {\n        switch(series[index]) {\n          case point:\n            return flatten(data.map(function(s) {\n              return s.data.outliers.map(function(o) { return [s.quarter, o]; })\n            }))\n          case boxplot:\n            return data;\n        }\n      });<\/p>\n<p>  var chart = fc.chartSvgCartesian(\n        d3.scalePoint(),\n        d3.scaleLinear()\n      )\n      .xDomain(quarters)\n      .xPadding(0.1)\n      .yDomain(yExtent(series.map(function(d) { return d.data; })))\n      .yTickFormat(yFormat)\n      .plotArea(multi);<\/p>\n<p>      \/\/output results\n      var min = resolve('0->data->min', series, '->');\n      var quartile1 = resolve('0->data->lower', series, '->');\n      var mid = resolve('0->data->mid', series, '->');\n      var quartile3 = resolve('0->data->upper', series, '->');\n      var max = resolve('0->data->max', series, '->');\n      var outliers = resolve('0->data->outliers', series, '->');console.log(outliers);<\/p>\n<p>      if (outliers.length == 0) {\n      \tdocument.getElementById('outliers').innerHTML = \"<b>none<\/b>\";\n      } else {\n      \tdocument.getElementById('outliers').innerHTML = \"<b>\" + outliers + \"<\/b>\";\n      }\n      document.getElementById('min').innerHTML = min;\n      document.getElementById('quartile1').innerHTML = quartile1;\n      document.getElementById('mid').innerHTML = mid;\n      document.getElementById('quartile3').innerHTML = quartile3;\n      document.getElementById('max').innerHTML = max;<\/p>\n<p>} \/\/end calc function\n<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ein Ausrei\u00dfer ist definiert als jede Beobachtung in einem Datensatz, die 1,5 IQR h\u00f6her als das dritte Quartil oder 1,5 IQR niedriger als das erste Quartil ist, wobei IQR f\u00fcr \u201eInterquartilbereich\u201c steht und die Differenz zwischen dem ersten und dritten Quartil darstellt. Um Ausrei\u00dfer f\u00fcr einen bestimmten Datensatz zu identifizieren, geben Sie Ihre durch Kommas [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Ausrei\u00dferrechner \u2013 Statistik<\/title>\n<meta name=\"description\" content=\"Dieser Rechner identifiziert Ausrei\u00dfer f\u00fcr jeden Datensatz. 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