{"id":156248,"date":"2022-03-26T01:32:45","date_gmt":"2022-03-25T20:02:45","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/standard-deviation\/"},"modified":"2022-12-22T21:37:50","modified_gmt":"2022-12-22T16:07:50","slug":"standard-deviation","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/standard-deviation\/","title":{"rendered":"Standard Deviation- Introduction"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/standard-deviation\/#Formula_and_Calculation_of_Standard_Deviation\" title=\"Formula and Calculation of Standard Deviation\">Formula and Calculation of Standard Deviation<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/standard-deviation\/#What_are_the_Variance_and_Standard_Deviation\" title=\"What are the Variance and Standard Deviation?\">What are the Variance and Standard Deviation?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/standard-deviation\/#Standard_Deviation_vs_Variance\" title=\"Standard Deviation v\/s Variance\">Standard Deviation v\/s Variance<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/standard-deviation\/#Variance_and_Standard_Deviation_Formula\" title=\"Variance and Standard Deviation Formula\">Variance and Standard Deviation Formula<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/standard-deviation\/#How_to_Calculate_the_Standard_Deviation\" title=\"How to Calculate the Standard Deviation?\">How to Calculate the Standard Deviation?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/standard-deviation\/#Steps_to_Calculate_the_Standard_Deviation\" title=\"Steps to Calculate the Standard Deviation\">Steps to Calculate the Standard Deviation<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Formula_and_Calculation_of_Standard_Deviation\"><\/span>Formula and Calculation of Standard Deviation<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Standard deviation- Introduction: S<a href=\"https:\/\/en.wikipedia.org\/wiki\/Standard_deviation\">tandard deviation<\/a> of a set of data is a measure of how spread out the data is. It is calculated by taking the square root of the average of the squared differences between each data point and the mean of the data.<\/p>\n<p>For example, if you have the following data set:<\/p>\n<p>1, 2, 3, 4, 5<\/p>\n<p>The mean is 3 and the squared differences are:<\/p>\n<p>1-3 = -2<\/p>\n<p>2-3 = -1<\/p>\n<p>3-3 = 0<\/p>\n<p>4-3 = 1<\/p>\n<p>5-3 = 2<\/p>\n<p>The standard deviation is the square root of the average of the squared differences, or 1.4.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-156247 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/standard-deviation.jpg\" alt=\"Standard Deviation- Introduction\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/standard-deviation.jpg?v=1648238563 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/standard-deviation-300x212.jpg?v=1648238563 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"What_are_the_Variance_and_Standard_Deviation\"><\/span>What are the Variance and Standard Deviation?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The variance is a measure of how spread out a set of data is. It is calculated by taking the sum of the squared differences between each data point and the mean, divided by the number of data points. The standard deviation is the square root of the variance. It is a measure of how spread out the data is around the mean.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Standard_Deviation_vs_Variance\"><\/span>Standard Deviation v\/s Variance<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li><a href=\"https:\/\/infinitylearn.com\/surge\/maths\/standard-deviation\/\">Standard deviation<\/a> is a measure of how dispersed the values in a set of data are from the mean. It is calculated by taking the square root of the variance.<\/li>\n<li>Variance is a measure of how spread out the values in a set of data are. It is calculated by taking the sum of the squared differences between each value and the mean, divided by the number of data points.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Variance_and_Standard_Deviation_Formula\"><\/span>Variance and Standard Deviation Formula<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>As discussed, the variance of the data set is the average square distance between the mean value and each data value. And standard deviation defines the spread of data values around the mean.<\/p>\n<p><img src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2021\/03\/variance-and-sd-formula.png\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_to_Calculate_the_Standard_Deviation\"><\/span>How to Calculate the Standard Deviation?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The standard deviation is calculated by taking the average of the squared differences of each number from the mean, then dividing by the number of data points.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Steps_to_Calculate_the_Standard_Deviation\"><\/span>Steps to Calculate the Standard Deviation<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>1. Add up the numbers in the data set.<\/p>\n<p>2. Square each number in the data set.<\/p>\n<p>3. Add up the squares of the numbers in the data set.<\/p>\n<p>4. Divide the sum of the squares by the number of data points in the set.<\/p>\n<p>5. Take the square root of the number you obtained in step four.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Formula and Calculation of Standard Deviation Standard deviation- Introduction: Standard deviation of a set of data is a measure of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Standard Deviation- Introduction","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Standard deviation of a set of data is a measure of how spread out the data is. 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