{"id":30,"date":"2022-05-20T16:59:03","date_gmt":"2022-05-20T16:59:03","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/alphamodule\/chapter\/comparing-variability-of-datasets-what-to-know\/"},"modified":"2022-06-16T15:21:05","modified_gmt":"2022-06-16T15:21:05","slug":"comparing-variability-of-datasets-what-to-know","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/alphamodule\/chapter\/comparing-variability-of-datasets-what-to-know\/","title":{"raw":"Comparing Variability of Data Sets: Learn It 1","rendered":"Comparing Variability of Data Sets: Learn It 1"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Goals<\/h3>\r\n<ul>\r\n \t<li>Look at a histogram and summarize the important measures of center<\/li>\r\n \t<li>Take the measures of center to explain the behavior of the variables in a data set<\/li>\r\n<\/ul>\r\n<\/div>\r\nAnother way to describe data numerically is to find and use the measures of center and measures of spread.\r\n<div class=\"textbox shaded\">\r\n<h3 style=\"text-align: center;\">Variability<\/h3>\r\n\r\n<hr \/>\r\n<p style=\"text-align: center;\">Measure of how spread out, or dispersed, the data set is.<\/p>\r\n<p style=\"text-align: center;\">Standard deviation, variance, and range are all calculated measures of variability.<\/p>\r\n\r\n<\/div>\r\n<h2>Comparing Variability<\/h2>\r\nWe can visually assess variability using graphical displays such as histograms and dot plots.\u00a0 When looking at a histogram or dot plot, 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). These visual clues help us\u00a0recognize distributions that have more or less variability than others.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\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\nIt can often be easier to visualize variability using a dot plot than using a histogram, because the individual data points (or observations) are visible in the dot plot.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It 1<\/h3>\r\nTen customers rated four different smartphone apps. The customer\u00a0ratings for the four different apps are shown in the following dot plots.\u00a0The average rating for each app is equal to 3. Even though the mean, [latex]\\bar{x}[\/latex], is the same for each app, the dot plots for each app look very different.\r\n\r\n<strong><img class=\"alignnone wp-image-1004\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11193655\/Picture37-300x279.png\" alt=\"Four side by side dot plots with the horizontal axis labeled &quot;Rating,&quot; numbered in increments of 1 from 1 to 5. The first plot is labeled App 1. For rating 1, there is 1 dot. For rating 2, there are 2 dots. For rating 3, there are 3 dots. For rating 4, there are 2 dots. For rating 5, there is 1 dot. The next plot is titled App 2. For rating 3, there are 10 dots. The next graph is titled App 3. For rating 1, there are 5 dots. For rating 5, there are 5 dots. The next plot is titled App 4. For every rating, there are two dots.\" width=\"648\" height=\"603\" \/><\/strong>\r\n\r\n[ohm_question hide_question_numbers=1]241055[\/ohm_question]\r\n\r\n[reveal-answer q=\"506703\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"506703\"]Which app has the most similar rating responses?[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It 2<\/h3>\r\n[ohm_question hide_question_numbers=1]241057[\/ohm_question]\r\n\r\n[reveal-answer q=\"950930\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"950930\"]Which app has the most differing rating responses?[\/hidden-answer]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Goals<\/h3>\n<ul>\n<li>Look at a histogram and summarize the important measures of center<\/li>\n<li>Take the measures of center to explain the behavior of the variables in a data set<\/li>\n<\/ul>\n<\/div>\n<p>Another way to describe data numerically is to find and use the measures of center and measures of spread.<\/p>\n<div class=\"textbox shaded\">\n<h3 style=\"text-align: center;\">Variability<\/h3>\n<hr \/>\n<p style=\"text-align: center;\">Measure of how spread out, or dispersed, the data set is.<\/p>\n<p style=\"text-align: center;\">Standard deviation, variance, and range are all calculated measures of variability.<\/p>\n<\/div>\n<h2>Comparing Variability<\/h2>\n<p>We can visually assess variability using graphical displays such as histograms and dot plots.\u00a0 When looking at a histogram or dot plot, 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). These visual clues help us\u00a0recognize distributions that have more or less variability than others.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\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>It can often be easier to visualize variability using a dot plot than using a histogram, because the individual data points (or observations) are visible in the dot plot.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try It 1<\/h3>\n<p>Ten customers rated four different smartphone apps. The customer\u00a0ratings for the four different apps are shown in the following dot plots.\u00a0The average rating for each app is equal to 3. Even though the mean, [latex]\\bar{x}[\/latex], is the same for each app, the dot plots for each app look very different.<\/p>\n<p><strong><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1004\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11193655\/Picture37-300x279.png\" alt=\"Four side by side dot plots with the horizontal axis labeled &quot;Rating,&quot; numbered in increments of 1 from 1 to 5. The first plot is labeled App 1. For rating 1, there is 1 dot. For rating 2, there are 2 dots. For rating 3, there are 3 dots. For rating 4, there are 2 dots. For rating 5, there is 1 dot. The next plot is titled App 2. For rating 3, there are 10 dots. The next graph is titled App 3. For rating 1, there are 5 dots. For rating 5, there are 5 dots. The next plot is titled App 4. For every rating, there are two dots.\" width=\"648\" height=\"603\" \/><\/strong><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm241055\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=241055&theme=oea&iframe_resize_id=ohm241055\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q506703\">Hint<\/span><\/p>\n<div id=\"q506703\" class=\"hidden-answer\" style=\"display: none\">Which app has the most similar rating responses?<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It 2<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm241057\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=241057&theme=oea&iframe_resize_id=ohm241057\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q950930\">Hint<\/span><\/p>\n<div id=\"q950930\" class=\"hidden-answer\" style=\"display: none\">Which app has the most differing rating responses?<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":17533,"menu_order":20,"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-30","chapter","type-chapter","status-publish","hentry"],"part":20,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/30","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":5,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/30\/revisions"}],"predecessor-version":[{"id":169,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/30\/revisions\/169"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/parts\/20"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/30\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/media?parent=30"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapter-type?post=30"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/contributor?post=30"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/license?post=30"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}