{"id":432,"date":"2023-07-29T23:07:33","date_gmt":"2023-07-29T23:07:33","guid":{"rendered":"https:\/\/statorials.org\/my\/skewness-%e1%80%94%e1%80%be%e1%80%84%e1%80%b7%e1%80%ba-kurtosis-%e1%80%82%e1%80%8f%e1%80%94%e1%80%ba%e1%80%b8%e1%80%95%e1%80%b1%e1%80%ab%e1%80%84%e1%80%ba%e1%80%b8%e1%80%85%e1%80%80%e1%80%ba\/"},"modified":"2023-07-29T23:07:33","modified_gmt":"2023-07-29T23:07:33","slug":"skewness-%e1%80%94%e1%80%be%e1%80%84%e1%80%b7%e1%80%ba-kurtosis-%e1%80%82%e1%80%8f%e1%80%94%e1%80%ba%e1%80%b8%e1%80%95%e1%80%b1%e1%80%ab%e1%80%84%e1%80%ba%e1%80%b8%e1%80%85%e1%80%80%e1%80%ba","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/skewness-%e1%80%94%e1%80%be%e1%80%84%e1%80%b7%e1%80%ba-kurtosis-%e1%80%82%e1%80%8f%e1%80%94%e1%80%ba%e1%80%b8%e1%80%95%e1%80%b1%e1%80%ab%e1%80%84%e1%80%ba%e1%80%b8%e1%80%85%e1%80%80%e1%80%ba\/","title":{"rendered":"Skewness \u1014\u103e\u1004\u1037\u103a kurtosis \u1002\u100f\u1014\u103a\u1038\u1010\u103d\u1000\u103a\u1005\u1000\u103a"},"content":{"rendered":"<p><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>.axis--y .domain {\n  display: none;\n}<\/p>\n<p>h1 {\ncolor: black;\ntext-align: center;\nmargin-bottom: 0px;\nmargin-top: 15px;\nfont-family: 'Raleway', sans-serif;\n}<\/p>\n<p>p {\ncolor: black;\ntext-align: center;\nmargin-bottom: 15px;\nmargin-top: 15px;\nfont-family: 'Raleway', sans-serif;\n}<\/p>\n<p>#words {\ncolor: black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\npadding-left: 100px;\n}<\/p>\n<p>#words_text {\ncolor: black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\n}<\/p>\n<p>#words_text_area {\ndisplay:inline-block;\ncolor: 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;\n      padding: 10px 10px;\n      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.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.table_span_x, .table_span_y {\n    width: 100%;\n    display: block;\n}<\/p>\n<p>#words_table {\ncolor: black;\nfont-family: Raleway;\nmax-width: 350px;\nmargin: 25px auto;\nline-height: 1.75;\npadding-left: 20px;\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>    .label_radio {\n\ttext-align: center;\n}<\/p>\n<p>#text_area_input {\n\tpadding: 0 50px;\n}<\/p>\n<p>textarea, textarea:focus {\n\toutline: 1px solid #aeaeae;\n}\n<\/style>\n<div id=\"words_text\">\n<p style=\"text-align: left\"><b>Skewness<\/b> \u101e\u100a\u103a \u1012\u1031\u1010\u102c\u1021\u1005\u102f \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f\u104f \u1015\u1031\u102b\u1037\u1015\u102b\u1038\u1019\u103e\u102f\u104f \u1021\u1010\u102d\u102f\u1004\u103a\u1038\u1021\u1010\u102c\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1024\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u101e\u100a\u103a \u1021\u1015\u1031\u102b\u1004\u103a\u1038 \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1021\u1014\u102f\u1010\u103a\u101c\u1000\u1039\u1001\u100f\u102c \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b \u101a\u1031\u1018\u102f\u101a\u103b\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u1021\u1014\u102f\u1010\u103a\u101c\u1000\u1039\u1001\u100f\u102c \u101c\u103d\u1032\u1001\u103b\u1031\u102c\u103a\u1019\u103e\u102f\u101e\u100a\u103a \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u104f \u1018\u101a\u103a\u1018\u1000\u103a\u1001\u103c\u1019\u103a\u1038\u1010\u103d\u1004\u103a <i>\u1021\u1019\u103c\u102e\u1038<\/i> \u101b\u103e\u102d\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1016\u1031\u102c\u103a\u1015\u103c\u101e\u100a\u103a\u104b \u101a\u1031\u1018\u102f\u101a\u103b\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u1021\u1019\u103c\u102e\u1038\u101e\u100a\u103a \u100a\u102c\u1018\u1000\u103a\u1010\u103d\u1004\u103a \u101b\u103e\u102d\u1014\u1031\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1021\u1015\u103c\u102f\u101e\u1018\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000 \u100a\u103d\u103e\u1014\u103a\u1015\u103c\u101e\u100a\u103a\u104b<\/p>\n<p style=\"text-align: left\"> <b>Kurtosis<\/b> \u101e\u100a\u103a \u1012\u1031\u1010\u102c\u1021\u1005\u102f \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u104f \u201c\u1021\u1019\u103c\u102e\u1038\u201d \u104f \u1021\u1010\u102d\u102f\u1004\u103a\u1038\u1021\u1010\u102c\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1024\u1002\u100f\u1014\u103a\u1038\u1010\u103d\u1000\u103a\u1005\u1000\u103a\u1019\u103e\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u1031\u102c kurtosis \u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u101e\u100a\u103a Excel \u1010\u103d\u1004\u103a\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u1037\u103a\u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u1014\u103e\u1004\u1037\u103a \u1021\u1010\u1030\u1010\u1030\u1015\u1004\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104a <i>\u1021\u101c\u103d\u1014\u103a\u1021\u1000\u103b\u103d\u1036 kurtosis<\/i> \u101f\u102f\u1001\u1031\u102b\u103a\u101e\u100a\u103a\u1021\u101b\u102c\u1000\u102d\u102f\u101b\u103e\u102c\u1016\u103d\u1031\u1010\u103d\u1031\u1037\u101b\u103e\u102d\u101e\u100a\u103a\u104b<\/p>\n<p style=\"text-align: left\"> \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1010\u1005\u103a\u1001\u102f\u104f \u101c\u103d\u1032\u1019\u103e\u102c\u1038\u1019\u103e\u102f\u1014\u103e\u1004\u1037\u103a kurtosis \u1000\u102d\u102f\u101b\u103e\u102c\u1016\u103d\u1031\u101b\u1014\u103a\u104a \u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b\u1021\u1000\u103d\u1000\u103a\u1010\u103d\u1004\u103a \u1000\u1031\u102c\u103a\u1019\u102c\u1001\u103d\u1032\u1011\u102c\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u101b\u102d\u102f\u1038\u101b\u102d\u102f\u1038\u101b\u103e\u1004\u103a\u1038\u101b\u103e\u1004\u103a\u1038\u1011\u100a\u1037\u103a\u1015\u102b\u104a \u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a &#8220; \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a&#8221;  \u1001\u101c\u102f\u1010\u103a\u1000\u102d\u102f\u1014\u103e\u102d\u1015\u103a\u1015\u102b\u104b <\/p>\n<\/div>\n<div id=\"words_text\">\n<div id=\"text_area_input\"><textarea id=\"input_data\" name=\"input_data\" rows=\"5\" cols=\"40\"><\/textarea><\/div>\n<\/div>\n<div id=\"words\"><input type=\"button\" id=\"button\" onclick=\"calc()\" value=\"Calculate\"><\/div>\n<div>\n<p><span id=\"skewness\"><\/span><\/p>\n<\/div>\n<div>\n<p><span id=\"kurtosis\"><\/span><\/p>\n<\/div>\n<p><script><\/p>\n<p>\/\/define addition function\n\tfunction add(a, b) {\n\t    return a + b;\n\t}<\/p>\n<p>\/\/create function that performs t test calculations\nfunction calc() {<\/p>\n<p>\/\/get user input data\t\nvar input_data = document.getElementById('input_data').value.match(\/\\d+\/g).map(Number);<\/p>\n<p>\/\/find summary statistics\nvar n = input_data.length;\nvar total_mean = math.mean(input_data);\nvar total_var = math.var(input_data)\nvar total_sd = Math.sqrt(total_var);<\/p>\n<p>\/\/calculate skewness\nvar term1 = n \/ ( (n-1)*(n-2) );\nvar term2 = (input_data.map(function(x) { return Math.pow((x-total_mean) \/ total_sd, 3); })).reduce(add, 0)\nvar skewness = term1 * term2;<\/p>\n<p>\/\/calculate kurtosis\nvar term1 = ( n*(n+1) ) \/ ( (n-1)*(n-2)*(n-3) );\nvar term2 = ( (input_data.map(function(x) { return Math.pow(x-total_mean, 4); })).reduce(add, 0) ) \/ ( Math.pow(total_var, 2) );\nvar term3 = ( 3 * (Math.pow(n-1, 2)) ) \/ ( (n-2)*(n-3) );\nvar kurtosis = term1 * term2 - term3;<\/p>\n<p>\/\/output results \ndocument.getElementById('skewness').innerHTML = \"Skewness: \" + skewness.toFixed(5);\ndocument.getElementById('kurtosis').innerHTML = \"Kurtosis: \" + kurtosis.toFixed(5);<\/p>\n<p>}<\/p>\n<p><\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Skewness \u101e\u100a\u103a \u1012\u1031\u1010\u102c\u1021\u1005\u102f \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f\u104f \u1015\u1031\u102b\u1037\u1015\u102b\u1038\u1019\u103e\u102f\u104f \u1021\u1010\u102d\u102f\u1004\u103a\u1038\u1021\u1010\u102c\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1024\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u101e\u100a\u103a \u1021\u1015\u1031\u102b\u1004\u103a\u1038 \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1021\u1014\u102f\u1010\u103a\u101c\u1000\u1039\u1001\u100f\u102c \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b \u101a\u1031\u1018\u102f\u101a\u103b\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u1021\u1014\u102f\u1010\u103a\u101c\u1000\u1039\u1001\u100f\u102c \u101c\u103d\u1032\u1001\u103b\u1031\u102c\u103a\u1019\u103e\u102f\u101e\u100a\u103a \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u104f \u1018\u101a\u103a\u1018\u1000\u103a\u1001\u103c\u1019\u103a\u1038\u1010\u103d\u1004\u103a \u1021\u1019\u103c\u102e\u1038 \u101b\u103e\u102d\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1016\u1031\u102c\u103a\u1015\u103c\u101e\u100a\u103a\u104b \u101a\u1031\u1018\u102f\u101a\u103b\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u1021\u1019\u103c\u102e\u1038\u101e\u100a\u103a \u100a\u102c\u1018\u1000\u103a\u1010\u103d\u1004\u103a \u101b\u103e\u102d\u1014\u1031\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1021\u1015\u103c\u102f\u101e\u1018\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000 \u100a\u103d\u103e\u1014\u103a\u1015\u103c\u101e\u100a\u103a\u104b Kurtosis \u101e\u100a\u103a \u1012\u1031\u1010\u102c\u1021\u1005\u102f \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u104f \u201c\u1021\u1019\u103c\u102e\u1038\u201d \u104f \u1021\u1010\u102d\u102f\u1004\u103a\u1038\u1021\u1010\u102c\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1024\u1002\u100f\u1014\u103a\u1038\u1010\u103d\u1000\u103a\u1005\u1000\u103a\u1019\u103e\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u1031\u102c kurtosis \u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u101e\u100a\u103a Excel \u1010\u103d\u1004\u103a\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u1037\u103a\u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u1014\u103e\u1004\u1037\u103a \u1021\u1010\u1030\u1010\u1030\u1015\u1004\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104a \u1021\u101c\u103d\u1014\u103a\u1021\u1000\u103b\u103d\u1036 kurtosis \u101f\u102f\u1001\u1031\u102b\u103a\u101e\u100a\u103a\u1021\u101b\u102c\u1000\u102d\u102f\u101b\u103e\u102c\u1016\u103d\u1031\u1010\u103d\u1031\u1037\u101b\u103e\u102d\u101e\u100a\u103a\u104b \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1010\u1005\u103a\u1001\u102f\u104f \u101c\u103d\u1032\u1019\u103e\u102c\u1038\u1019\u103e\u102f\u1014\u103e\u1004\u1037\u103a kurtosis 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