{"id":307,"date":"2022-02-19T00:04:44","date_gmt":"2022-02-19T00:04:44","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/?post_type=chapter&#038;p=307"},"modified":"2022-05-20T16:44:33","modified_gmt":"2022-05-20T16:44:33","slug":"comparing-variability-of-datasets-what-to-know","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/chapter\/comparing-variability-of-datasets-what-to-know\/","title":{"raw":"Comparing Variability of Data Sets: What to Know","rendered":"Comparing Variability of Data Sets: What to Know"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Goals<\/h3>\r\nAfter completing this section, you should feel comfortable performing these skills.\r\n<ul>\r\n \t<li><a href=\"#VarHist\">Compare the variability of multiple data sets visually using histograms.<\/a><\/li>\r\n \t<li><a href=\"#VarDot\">Compare the variability of multiple data sets visually using dotplots.<\/a><\/li>\r\n<\/ul>\r\n<ul>\r\n \t<li><a href=\"#StdDev\">Use a data analysis tool to identify the standard deviation of a data set.<\/a><\/li>\r\n \t<li><a href=\"#Variance\">Calculate the variance of a data set given standard deviation<\/a><\/li>\r\n \t<li><a href=\"#Range\">Use a data analysis tool to calculate variability by identifying the range of a data set.<\/a><\/li>\r\n<\/ul>\r\nClick on a skill above to jump to its location in this section.\r\n\r\n<\/div>\r\nIn the next activity, you will be exploring data and using the measures of center and measures of spread to describe the data. This section will introduce you to <strong>variability<\/strong>, which is a\u00a0measure of how dispersed (spread out) the data are.\u00a0You'll learn to recognize variability in histograms and dotplots by using visual clues. You'll also learn how to calculate measures of variability including standard deviation, variance, and range.\r\n<h2>Comparing Variability<\/h2>\r\nThe <strong>variability<\/strong> of a data set is often referred to as the spread of a data set. We can visually assess variability using graphical displays such as histograms and dotplots.\u00a0 When answering Questions 1 - 3 below to estimate variability of data visually using histograms and dotplots , consider whether the data <em>appears<\/em> to be more spread out from the center (greater variability) or more clustered toward the center (less variability). See the interactive video below for a demonstration of clues to look for in the graphical display.\r\n<div class=\"textbox exercises\">\r\n<h3>interactive example<\/h3>\r\nWhether presented with distributions of quantitative variables in histograms or in dotplots, similar visual clues can help you to recognize distributions that have more or less variability than others.\r\n\r\nHistograms displaying the distribution of two quantitative variables with different amounts of variability are shown below. Which do you think has less variability than the other? Explain your reasoning. For example, what visual clue could help you decide if your answer were correct?\r\n\r\n<img class=\"aligncenter size-full wp-image-1039\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5772\/2022\/02\/12025120\/LessMore_Question.jpg\" alt=\"Two histograms are shown. The one on the left appears tightly clustered. The one on the right appears more widely dispersed.\" width=\"1196\" height=\"250\" \/>\r\n\r\n[reveal-answer q=\"510090\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"510090\"]\u00a0 The data in the distribution on the left varies less than that of the one on the right. Note how the data in the first histogram is tightly clustered around the center, and tails off quickly to either side. The data in the second histogram is widely dispersed across the graph.\r\n\r\n&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-1037\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5772\/2022\/02\/12024114\/LessMoreVariabiliy.jpg\" alt=\"Two histograms side by side. The one on the left has data tightly clustered toward the center while the one on the right shows data spread out widely and evenly across the graph.\" width=\"1156\" height=\"290\" \/>\r\n\r\nThe visual indication of variability is how tightly clustered or widely dispersed the data appears in the display. [\/hidden-answer]\r\n\r\n<\/div>\r\nOn the next page, you will see more about histograms and dotplots.","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Goals<\/h3>\n<p>After completing this section, you should feel comfortable performing these skills.<\/p>\n<ul>\n<li><a href=\"#VarHist\">Compare the variability of multiple data sets visually using histograms.<\/a><\/li>\n<li><a href=\"#VarDot\">Compare the variability of multiple data sets visually using dotplots.<\/a><\/li>\n<\/ul>\n<ul>\n<li><a href=\"#StdDev\">Use a data analysis tool to identify the standard deviation of a data set.<\/a><\/li>\n<li><a href=\"#Variance\">Calculate the variance of a data set given standard deviation<\/a><\/li>\n<li><a href=\"#Range\">Use a data analysis tool to calculate variability by identifying the range of a data set.<\/a><\/li>\n<\/ul>\n<p>Click on a skill above to jump to its location in this section.<\/p>\n<\/div>\n<p>In the next activity, you will be exploring data and using the measures of center and measures of spread to describe the data. This section will introduce you to <strong>variability<\/strong>, which is a\u00a0measure of how dispersed (spread out) the data are.\u00a0You&#8217;ll learn to recognize variability in histograms and dotplots by using visual clues. You&#8217;ll also learn how to calculate measures of variability including standard deviation, variance, and range.<\/p>\n<h2>Comparing Variability<\/h2>\n<p>The <strong>variability<\/strong> of a data set is often referred to as the spread of a data set. We can visually assess variability using graphical displays such as histograms and dotplots.\u00a0 When answering Questions 1 &#8211; 3 below to estimate variability of data visually using histograms and dotplots , consider whether the data <em>appears<\/em> to be more spread out from the center (greater variability) or more clustered toward the center (less variability). See the interactive video below for a demonstration of clues to look for in the graphical display.<\/p>\n<div class=\"textbox exercises\">\n<h3>interactive example<\/h3>\n<p>Whether presented with distributions of quantitative variables in histograms or in dotplots, similar visual clues can help you to recognize distributions that have more or less variability than others.<\/p>\n<p>Histograms displaying the distribution of two quantitative variables with different amounts of variability are shown below. Which do you think has less variability than the other? Explain your reasoning. For example, what visual clue could help you decide if your answer were correct?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1039\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5772\/2022\/02\/12025120\/LessMore_Question.jpg\" alt=\"Two histograms are shown. The one on the left appears tightly clustered. The one on the right appears more widely dispersed.\" width=\"1196\" height=\"250\" \/><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q510090\">Show Answer<\/span><\/p>\n<div id=\"q510090\" class=\"hidden-answer\" style=\"display: none\">\u00a0 The data in the distribution on the left varies less than that of the one on the right. Note how the data in the first histogram is tightly clustered around the center, and tails off quickly to either side. The data in the second histogram is widely dispersed across the graph.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1037\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5772\/2022\/02\/12024114\/LessMoreVariabiliy.jpg\" alt=\"Two histograms side by side. The one on the left has data tightly clustered toward the center while the one on the right shows data spread out widely and evenly across the graph.\" width=\"1156\" height=\"290\" \/><\/p>\n<p>The visual indication of variability is how tightly clustered or widely dispersed the data appears in the display. <\/p><\/div>\n<\/div>\n<\/div>\n<p>On the next page, you will see more about histograms and dotplots.<\/p>\n","protected":false},"author":175116,"menu_order":36,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-307","chapter","type-chapter","status-publish","hentry"],"part":1252,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/307","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/users\/175116"}],"version-history":[{"count":19,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/307\/revisions"}],"predecessor-version":[{"id":1242,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/307\/revisions\/1242"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/parts\/1252"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapters\/307\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/media?parent=307"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/pressbooks\/v2\/chapter-type?post=307"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/contributor?post=307"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/exemplarstatistics\/wp-json\/wp\/v2\/license?post=307"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}