{"id":882,"date":"2023-03-20T19:17:56","date_gmt":"2023-03-20T19:17:56","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/comparing-variability-of-data-sets-learn-it-4\/"},"modified":"2025-05-11T22:45:29","modified_gmt":"2025-05-11T22:45:29","slug":"comparing-variability-of-data-sets-learn-it-4","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/comparing-variability-of-data-sets-learn-it-4\/","title":{"raw":"Measures of Variability: Learn It 5","rendered":"Measures of Variability: Learn It 5"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Describe the differences in variability in histograms and dotplots.\u00a0<\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Calculate the standard deviation and then describe what that value means&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4865,&quot;3&quot;:{&quot;1&quot;:0},&quot;11&quot;:0,&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Calculate and describe standard deviation.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Variance<\/h2>\r\n<p>Another measure of spread is called <strong>variance<\/strong>. Variance is the squared value of the standard deviation. Similar to standard deviation, the larger the value of the variance, the larger the variability of the data set. The smaller the value of the variance, the smaller variability exists within the data set.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>variance<\/h3>\r\n<p style=\"text-align: left;\"><strong>Variance<\/strong> is the standard deviation squared, [latex]\\sigma^{2}[\/latex] or [latex]s^{2}[\/latex].<\/p>\r\n<p style=\"text-align: left;\"><strong>Variance of a population<\/strong>:\u00a0 [latex]\\sigma^{2}=\\dfrac{\\sum\\left(x-\\mu\\right)^{2}}{n}[\/latex]<\/p>\r\n<p style=\"text-align: left;\"><strong>Variance of a sample<\/strong>:\u00a0 [latex]s^{2}=\\dfrac{\\sum\\left(x-\\bar{x}\\right)^{2}}{n-1}[\/latex]<\/p>\r\n<\/section>\r\n<p>The statistical tool does not calculate variance, so you will need to use the tool to calculate the standard deviation and then square it by hand or calculator in order to get the variance.<\/p>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/eda_quantitative\/\" width=\"100%\" height=\"850\"><\/iframe><\/p>\r\n<p><br \/>\r\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/eda_quantitative\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2125[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2126[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Describe the differences in variability in histograms and dotplots.\u00a0<\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Calculate the standard deviation and then describe what that value means&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4865,&quot;3&quot;:{&quot;1&quot;:0},&quot;11&quot;:0,&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Calculate and describe standard deviation.<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>Variance<\/h2>\n<p>Another measure of spread is called <strong>variance<\/strong>. Variance is the squared value of the standard deviation. Similar to standard deviation, the larger the value of the variance, the larger the variability of the data set. The smaller the value of the variance, the smaller variability exists within the data set.<\/p>\n<section class=\"textbox keyTakeaway\">\n<h3>variance<\/h3>\n<p style=\"text-align: left;\"><strong>Variance<\/strong> is the standard deviation squared, [latex]\\sigma^{2}[\/latex] or [latex]s^{2}[\/latex].<\/p>\n<p style=\"text-align: left;\"><strong>Variance of a population<\/strong>:\u00a0 [latex]\\sigma^{2}=\\dfrac{\\sum\\left(x-\\mu\\right)^{2}}{n}[\/latex]<\/p>\n<p style=\"text-align: left;\"><strong>Variance of a sample<\/strong>:\u00a0 [latex]s^{2}=\\dfrac{\\sum\\left(x-\\bar{x}\\right)^{2}}{n-1}[\/latex]<\/p>\n<\/section>\n<p>The statistical tool does not calculate variance, so you will need to use the tool to calculate the standard deviation and then square it by hand or calculator in order to get the variance.<\/p>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/eda_quantitative\/\" width=\"100%\" height=\"850\"><\/iframe><\/p>\n<p>\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/eda_quantitative\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2125\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2125&theme=lumen&iframe_resize_id=ohm2125&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2126\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2126&theme=lumen&iframe_resize_id=ohm2126&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":13,"menu_order":33,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":834,"module-header":"learn_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/882"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/users\/13"}],"version-history":[{"count":8,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/882\/revisions"}],"predecessor-version":[{"id":6635,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/882\/revisions\/6635"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/834"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/882\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=882"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=882"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=882"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=882"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}