{"id":863,"date":"2023-03-20T19:17:39","date_gmt":"2023-03-20T19:17:39","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/comparing-boxplot-data-and-displays-learn-it-1\/"},"modified":"2025-05-11T22:38:21","modified_gmt":"2025-05-11T22:38:21","slug":"comparing-boxplot-data-and-displays-learn-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/comparing-boxplot-data-and-displays-learn-it-1\/","title":{"raw":"Boxplot Data and Displays: Learn It 1","rendered":"Boxplot Data and Displays: Learn It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Read information from a boxplot and make conclusions&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;}\">Read information from a boxplot and make conclusions<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Read information from a boxplot and make conclusions&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;}\">Compare boxplots<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>When we describe the distribution of a quantitative variable, we describe the overall pattern (shape, center, and spread) in the data and deviations from the pattern (outliers). A graphical visualization of a data set is very useful in giving us a glimpse into the distribution of the data set. In this section, we are going to focus on boxplots, a graphical representation of a quantitative variable. Boxplots are helpful for visualizing the distribution of a quantitative variable.<\/p>\r\n<h2>Boxplots<\/h2>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>boxplot<\/h3>\r\n<p>A\u00a0<b>boxplot<\/b> is a graphical visualization of a quantitative variable that shows median, spread, skew, and outliers by illustrating a set of numbers (minimum, [latex]Q1[\/latex], median, [latex]Q3[\/latex], and maximum) called the <strong>five-number summary<\/strong>.<\/p>\r\n<p>A boxplot clearly shows the center of the data set and provides a summary at a glance of the bulk of the data and the presence of outliers.<\/p>\r\n\r\n[caption id=\"attachment_5531\" align=\"aligncenter\" width=\"575\"]<img class=\"wp-image-5531 size-full\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/10\/28231653\/Screen-Shot-2022-02-11-at-1.09.31-PM.png\" alt=\"Image describing the characteristics of a boxplot. From left to right, the image first shows two outliers outside of the boxplot, and then the line marking the minimum. Then it shows Q1, the median, and Q3 with a textbox explaining that the Interquartile Range, or the IQR, is Q3-Q1. Moving to the right there is a line indicating the maximum value, with two outliers outside of that.\" width=\"575\" height=\"319\" \/> Figure 1. A boxplot creates a visual summary of a data set using five important values: the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. It also shows the outliers in the data.[\/caption]\r\n<\/section>\r\n<h3>Shape and Center<\/h3>\r\n<p>Boxplots, like histograms and dotplots, can also tell us about the shape of a distribution.<\/p>\r\n<section class=\"textbox recall\">\r\n<ul>\r\n\t<li><strong>Left-skewed<\/strong>:\u00a0A cluster of data on the right with a tail of data tapering off to the left.<\/li>\r\n\t<li><strong>Symmetric<\/strong>: A cluster of data where the left and right sides of the distribution <em>closely<\/em>\u00a0<em>mirror<\/em>\u00a0each other.<\/li>\r\n\t<li><strong>Right-skewed<\/strong>: A cluster of data on the left with a tail of data tapering off to the right.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>We can describe the center of a boxplot's distribution with the mean and median. Recall the effect that skew has on the relationship between the mean and median in a data set. A right-skewed data set will pull the mean to the right of the median, while a left-skewed data set will pull the mean to the left. We can use visual clues to observe the skew in a boxplot in the same way that we can in a histogram or a dotplot.<\/p>\r\n<section class=\"textbox example\">The descriptive statistics and graphs below describe the 184 observations of the ages of the best actress\/actor winners from movies from the Oscars awards ceremonies.\r\n[caption id=\"attachment_1057\" align=\"aligncenter\" width=\"700\"]<img class=\"wp-image-1057 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5772\/2022\/02\/12234214\/Skew_OscarsAge_smaller.png\" alt=\"Descriptive statistics (mean 40, median 38), and a histogram with a tail to the right, and a boxplot with three outliers to the right.\" width=\"700\" height=\"551\" \/> Figure 2. A histogram and boxplot displaying the ages of 184 Oscar-winning actors and actresses.[\/caption]\r\n\r\n<ol>\r\n\t<li>Do you notice any skew in the histogram of this dataset?<\/li>\r\n\t<li>Can you point out the corresponding outliers in the boxplot of the data?<\/li>\r\n\t<li>What is the relationship between the mean and median of the data? Is the mean less than, greater than, or roughly similar to the median?<\/li>\r\n\t<li>What can you conclude about the shape of the data?<\/li>\r\n\t<li>What visual clue in the boxplot led to your conclusion?<\/li>\r\n<\/ol>\r\n<p>[reveal-answer q=\"321107\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"321107\"]<\/p>\r\n<ol>\r\n\t<li>The histogram appears to have a pronounced right tail, which would indicate a right skew.<\/li>\r\n\t<li>There are three distinct outliers to the right of the bulk of the data.<\/li>\r\n\t<li>The descriptive statistics give the median as 38 and the mean as 40. The mean is greater than the median.<\/li>\r\n\t<li>The data is right-skewed. The extreme values greater than the bulk of the data have pulled the mean to the right of the median.<\/li>\r\n\t<li>The skew can be seen in the boxplot by observing outliers only to the right of the bulk of the data, with no corresponding, symmetrical outliers to the left.<\/li>\r\n<\/ol>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2101[\/ohm2_question]<\/section>\r\n<section>Note that the boxplots we have seen presented so far are along a horizontal axis, from left to right. It is also common to see boxplots displayed along a vertical axis, from bottom to top, least to greatest.<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]4710[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Read information from a boxplot and make conclusions&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;}\">Read information from a boxplot and make conclusions<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Read information from a boxplot and make conclusions&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;}\">Compare boxplots<\/span><\/li>\n<\/ul>\n<\/section>\n<p>When we describe the distribution of a quantitative variable, we describe the overall pattern (shape, center, and spread) in the data and deviations from the pattern (outliers). A graphical visualization of a data set is very useful in giving us a glimpse into the distribution of the data set. In this section, we are going to focus on boxplots, a graphical representation of a quantitative variable. Boxplots are helpful for visualizing the distribution of a quantitative variable.<\/p>\n<h2>Boxplots<\/h2>\n<section class=\"textbox keyTakeaway\">\n<h3>boxplot<\/h3>\n<p>A\u00a0<b>boxplot<\/b> is a graphical visualization of a quantitative variable that shows median, spread, skew, and outliers by illustrating a set of numbers (minimum, [latex]Q1[\/latex], median, [latex]Q3[\/latex], and maximum) called the <strong>five-number summary<\/strong>.<\/p>\n<p>A boxplot clearly shows the center of the data set and provides a summary at a glance of the bulk of the data and the presence of outliers.<\/p>\n<figure id=\"attachment_5531\" aria-describedby=\"caption-attachment-5531\" style=\"width: 575px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-5531 size-full\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/10\/28231653\/Screen-Shot-2022-02-11-at-1.09.31-PM.png\" alt=\"Image describing the characteristics of a boxplot. From left to right, the image first shows two outliers outside of the boxplot, and then the line marking the minimum. Then it shows Q1, the median, and Q3 with a textbox explaining that the Interquartile Range, or the IQR, is Q3-Q1. Moving to the right there is a line indicating the maximum value, with two outliers outside of that.\" width=\"575\" height=\"319\" \/><figcaption id=\"caption-attachment-5531\" class=\"wp-caption-text\">Figure 1. A boxplot creates a visual summary of a data set using five important values: the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. It also shows the outliers in the data.<\/figcaption><\/figure>\n<\/section>\n<h3>Shape and Center<\/h3>\n<p>Boxplots, like histograms and dotplots, can also tell us about the shape of a distribution.<\/p>\n<section class=\"textbox recall\">\n<ul>\n<li><strong>Left-skewed<\/strong>:\u00a0A cluster of data on the right with a tail of data tapering off to the left.<\/li>\n<li><strong>Symmetric<\/strong>: A cluster of data where the left and right sides of the distribution <em>closely<\/em>\u00a0<em>mirror<\/em>\u00a0each other.<\/li>\n<li><strong>Right-skewed<\/strong>: A cluster of data on the left with a tail of data tapering off to the right.<\/li>\n<\/ul>\n<\/section>\n<p>We can describe the center of a boxplot&#8217;s distribution with the mean and median. Recall the effect that skew has on the relationship between the mean and median in a data set. A right-skewed data set will pull the mean to the right of the median, while a left-skewed data set will pull the mean to the left. We can use visual clues to observe the skew in a boxplot in the same way that we can in a histogram or a dotplot.<\/p>\n<section class=\"textbox example\">The descriptive statistics and graphs below describe the 184 observations of the ages of the best actress\/actor winners from movies from the Oscars awards ceremonies.<\/p>\n<figure id=\"attachment_1057\" aria-describedby=\"caption-attachment-1057\" style=\"width: 700px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1057 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5772\/2022\/02\/12234214\/Skew_OscarsAge_smaller.png\" alt=\"Descriptive statistics (mean 40, median 38), and a histogram with a tail to the right, and a boxplot with three outliers to the right.\" width=\"700\" height=\"551\" \/><figcaption id=\"caption-attachment-1057\" class=\"wp-caption-text\">Figure 2. A histogram and boxplot displaying the ages of 184 Oscar-winning actors and actresses.<\/figcaption><\/figure>\n<ol>\n<li>Do you notice any skew in the histogram of this dataset?<\/li>\n<li>Can you point out the corresponding outliers in the boxplot of the data?<\/li>\n<li>What is the relationship between the mean and median of the data? Is the mean less than, greater than, or roughly similar to the median?<\/li>\n<li>What can you conclude about the shape of the data?<\/li>\n<li>What visual clue in the boxplot led to your conclusion?<\/li>\n<\/ol>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q321107\">Show Solution<\/button><\/p>\n<div id=\"q321107\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>The histogram appears to have a pronounced right tail, which would indicate a right skew.<\/li>\n<li>There are three distinct outliers to the right of the bulk of the data.<\/li>\n<li>The descriptive statistics give the median as 38 and the mean as 40. The mean is greater than the median.<\/li>\n<li>The data is right-skewed. The extreme values greater than the bulk of the data have pulled the mean to the right of the median.<\/li>\n<li>The skew can be seen in the boxplot by observing outliers only to the right of the bulk of the data, with no corresponding, symmetrical outliers to the left.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2101\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2101&theme=lumen&iframe_resize_id=ohm2101&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section>Note that the boxplots we have seen presented so far are along a horizontal axis, from left to right. It is also common to see boxplots displayed along a vertical axis, from bottom to top, least to greatest.<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm4710\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=4710&theme=lumen&iframe_resize_id=ohm4710&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":13,"menu_order":20,"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\/863"}],"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":12,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/863\/revisions"}],"predecessor-version":[{"id":6629,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/863\/revisions\/6629"}],"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\/863\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=863"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=863"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=863"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=863"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}