{"id":507,"date":"2024-04-09T01:08:03","date_gmt":"2024-04-09T05:08:03","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/?post_type=chapter&#038;p=507"},"modified":"2024-06-11T15:56:33","modified_gmt":"2024-06-11T19:56:33","slug":"the-standard-deviation","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/chapter\/the-standard-deviation\/","title":{"raw":"The Coefficient of Variation","rendered":"The Coefficient of Variation"},"content":{"raw":"<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Learning Objectives<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nCalculate and understand the coefficient of variation.\r\n\r\n<\/div>\r\n<\/div>\r\nThe Coefficient of Variation (CV):\r\n<ul>\r\n \t<li>Is the best metric to compare two different data sets with fairly different means<\/li>\r\n \t<li>It measures the standard deviation, [latex]s [\/latex] or [latex]\\sigma [\/latex] as a percent of the mean<\/li>\r\n<\/ul>\r\nThe SAMPLE coefficient of variation is defined as:\r\n\r\n\\[ CV_{sample} = \\frac{s}{\\bar{x}} \\times 100 \\% \\]\r\n\r\nThe POPULATION coefficient of variation is defined as:\r\n\r\n\\[ CV_{population} = \\frac{\\sigma}{\\mu} \\times 100 \\% \\]\r\n<h1>Example 8.1 - Sunita and Sanjay's Coefficients of Variation<\/h1>\r\nLet us re-examine how Sunita and Sanjay's grades are distributed. We calculated the following metrics in previous sections for the distribution of their grades:\r\n<table class=\"grid aligncenter\" style=\"border-collapse: collapse;width: 68.4408%;height: 124px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 36px\">\r\n<th class=\"shaded\" style=\"width: 7.31908%;height: 36px;text-align: center;vertical-align: middle\">Name<\/th>\r\n<th class=\"shaded\" style=\"width: 7.81683%;height: 36px;text-align: center;vertical-align: middle\">Mean<\/th>\r\n<th class=\"shaded\" style=\"width: 12.6027%;height: 36px;text-align: center;vertical-align: middle\">Median<\/th>\r\n<th class=\"shaded\" style=\"width: 12.7488%;height: 36px;text-align: center;vertical-align: middle\">Range<\/th>\r\n<th class=\"shaded\" style=\"width: 12.8627%;height: 36px;text-align: center;vertical-align: middle\">St Dev<\/th>\r\n<th class=\"shaded\" style=\"width: 12.6032%;height: 36px;text-align: center;vertical-align: middle\">Variance<\/th>\r\n<\/tr>\r\n<tr style=\"height: 18px\">\r\n<td style=\"width: 7.31908%;height: 18px;text-align: center;vertical-align: middle\">Sunita<\/td>\r\n<td style=\"width: 7.81683%;height: 18px;text-align: center;vertical-align: middle\">81<\/td>\r\n<td style=\"width: 12.6027%;height: 18px;text-align: center;vertical-align: middle\">80<\/td>\r\n<td style=\"width: 12.7488%;height: 18px;text-align: center;vertical-align: middle\">3<\/td>\r\n<td style=\"width: 12.8627%;height: 18px;text-align: center;vertical-align: middle\">1.41421<\/td>\r\n<td style=\"width: 12.6032%;height: 18px;text-align: center;vertical-align: middle\">2<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px\">\r\n<td style=\"width: 7.31908%;height: 18px;text-align: center;vertical-align: middle\">Sanjay<\/td>\r\n<td style=\"width: 7.81683%;height: 18px;text-align: center;vertical-align: middle\">81<\/td>\r\n<td style=\"width: 12.6027%;height: 18px;text-align: center;vertical-align: middle\">80<\/td>\r\n<td style=\"width: 12.7488%;height: 18px;text-align: center;vertical-align: middle\">51<\/td>\r\n<td style=\"width: 12.8627%;height: 18px;text-align: center;vertical-align: middle\">20.6398<\/td>\r\n<td style=\"width: 12.6032%;height: 18px;text-align: center;vertical-align: middle\">426<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWe can then calculate the coefficient of variation for both Sunita and Sanjay from the above metrics:\r\n<ul>\r\n \t<li>Sunita's coefficient of variation is:<\/li>\r\n<\/ul>\r\n\\[ CV_{Sunita} = \\frac{1.41421}{81} \\times 100 \\% = 1.75\\% \\]\r\n<ul>\r\n \t<li>Sanjay's coefficient of variation is:<\/li>\r\n<\/ul>\r\n\\[ CV_{Sanjay} = \\frac{20.6398}{81} \\times 100 \\% = 25.48\\%\\]\r\n\r\n<a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/04\/8-1.xlsx\">Click here to download the Excel spreadsheet with the above calculations.<\/a>\r\n<h1>Key Takeaways<\/h1>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Key Takeaways: The Coefficient of Variation<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ul>\r\n \t<li>The coefficient of variation should be used when comparing populations with very different means.<\/li>\r\n \t<li>It measures the standard deviation as a percent of the mean.<\/li>\r\n \t<li>It is expressed as a percent (and not usually as a decimal).<\/li>\r\n \t<li>It is often used in business and finance (ex: when comparing investments).<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<h1>Your Own Notes<\/h1>\r\n<ul>\r\n \t<li>Are there any notes you want to take from this section? Is there anything you'd like to copy and paste below?<\/li>\r\n \t<li>These notes are for you only (they will not be stored anywhere)<\/li>\r\n \t<li>Make sure to download them at the end to use as a reference<\/li>\r\n<\/ul>\r\n[h5p id=\"16\"]","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Calculate and understand the coefficient of variation.<\/p>\n<\/div>\n<\/div>\n<p>The Coefficient of Variation (CV):<\/p>\n<ul>\n<li>Is the best metric to compare two different data sets with fairly different means<\/li>\n<li>It measures the standard deviation, [latex]s[\/latex] or [latex]\\sigma[\/latex] as a percent of the mean<\/li>\n<\/ul>\n<p>The SAMPLE coefficient of variation is defined as:<\/p>\n<p>\\[ CV_{sample} = \\frac{s}{\\bar{x}} \\times 100 \\% \\]<\/p>\n<p>The POPULATION coefficient of variation is defined as:<\/p>\n<p>\\[ CV_{population} = \\frac{\\sigma}{\\mu} \\times 100 \\% \\]<\/p>\n<h1>Example 8.1 &#8211; Sunita and Sanjay&#8217;s Coefficients of Variation<\/h1>\n<p>Let us re-examine how Sunita and Sanjay&#8217;s grades are distributed. We calculated the following metrics in previous sections for the distribution of their grades:<\/p>\n<table class=\"grid aligncenter\" style=\"border-collapse: collapse;width: 68.4408%;height: 124px\">\n<tbody>\n<tr style=\"height: 36px\">\n<th class=\"shaded\" style=\"width: 7.31908%;height: 36px;text-align: center;vertical-align: middle\">Name<\/th>\n<th class=\"shaded\" style=\"width: 7.81683%;height: 36px;text-align: center;vertical-align: middle\">Mean<\/th>\n<th class=\"shaded\" style=\"width: 12.6027%;height: 36px;text-align: center;vertical-align: middle\">Median<\/th>\n<th class=\"shaded\" style=\"width: 12.7488%;height: 36px;text-align: center;vertical-align: middle\">Range<\/th>\n<th class=\"shaded\" style=\"width: 12.8627%;height: 36px;text-align: center;vertical-align: middle\">St Dev<\/th>\n<th class=\"shaded\" style=\"width: 12.6032%;height: 36px;text-align: center;vertical-align: middle\">Variance<\/th>\n<\/tr>\n<tr style=\"height: 18px\">\n<td style=\"width: 7.31908%;height: 18px;text-align: center;vertical-align: middle\">Sunita<\/td>\n<td style=\"width: 7.81683%;height: 18px;text-align: center;vertical-align: middle\">81<\/td>\n<td style=\"width: 12.6027%;height: 18px;text-align: center;vertical-align: middle\">80<\/td>\n<td style=\"width: 12.7488%;height: 18px;text-align: center;vertical-align: middle\">3<\/td>\n<td style=\"width: 12.8627%;height: 18px;text-align: center;vertical-align: middle\">1.41421<\/td>\n<td style=\"width: 12.6032%;height: 18px;text-align: center;vertical-align: middle\">2<\/td>\n<\/tr>\n<tr style=\"height: 18px\">\n<td style=\"width: 7.31908%;height: 18px;text-align: center;vertical-align: middle\">Sanjay<\/td>\n<td style=\"width: 7.81683%;height: 18px;text-align: center;vertical-align: middle\">81<\/td>\n<td style=\"width: 12.6027%;height: 18px;text-align: center;vertical-align: middle\">80<\/td>\n<td style=\"width: 12.7488%;height: 18px;text-align: center;vertical-align: middle\">51<\/td>\n<td style=\"width: 12.8627%;height: 18px;text-align: center;vertical-align: middle\">20.6398<\/td>\n<td style=\"width: 12.6032%;height: 18px;text-align: center;vertical-align: middle\">426<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>We can then calculate the coefficient of variation for both Sunita and Sanjay from the above metrics:<\/p>\n<ul>\n<li>Sunita&#8217;s coefficient of variation is:<\/li>\n<\/ul>\n<p>\\[ CV_{Sunita} = \\frac{1.41421}{81} \\times 100 \\% = 1.75\\% \\]<\/p>\n<ul>\n<li>Sanjay&#8217;s coefficient of variation is:<\/li>\n<\/ul>\n<p>\\[ CV_{Sanjay} = \\frac{20.6398}{81} \\times 100 \\% = 25.48\\%\\]<\/p>\n<p><a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/04\/8-1.xlsx\">Click here to download the Excel spreadsheet with the above calculations.<\/a><\/p>\n<h1>Key Takeaways<\/h1>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Key Takeaways: The Coefficient of Variation<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ul>\n<li>The coefficient of variation should be used when comparing populations with very different means.<\/li>\n<li>It measures the standard deviation as a percent of the mean.<\/li>\n<li>It is expressed as a percent (and not usually as a decimal).<\/li>\n<li>It is often used in business and finance (ex: when comparing investments).<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Your Own Notes<\/h1>\n<ul>\n<li>Are there any notes you want to take from this section? Is there anything you&#8217;d like to copy and paste below?<\/li>\n<li>These notes are for you only (they will not be stored anywhere)<\/li>\n<li>Make sure to download them at the end to use as a reference<\/li>\n<\/ul>\n<div id=\"h5p-16\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-16\" class=\"h5p-iframe\" data-content-id=\"16\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Key takeaways, notes and comments from this section document tool.\"><\/iframe><\/div>\n<\/div>\n","protected":false},"author":865,"menu_order":4,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-507","chapter","type-chapter","status-publish","hentry"],"part":22,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/507","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/users\/865"}],"version-history":[{"count":25,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/507\/revisions"}],"predecessor-version":[{"id":1941,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/507\/revisions\/1941"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/parts\/22"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/507\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/media?parent=507"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapter-type?post=507"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/contributor?post=507"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/license?post=507"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}