{"id":842,"date":"2023-03-20T19:17:21","date_gmt":"2023-03-20T19:17:21","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/understand-means-and-medians-as-measures-of-centers-learn-it-3\/"},"modified":"2025-05-08T02:48:45","modified_gmt":"2025-05-08T02:48:45","slug":"understand-means-and-medians-as-measures-of-centers-learn-it-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/understand-means-and-medians-as-measures-of-centers-learn-it-3\/","title":{"raw":"Measures of Center: Learn It 3","rendered":"Measures of Center: Learn It 3"},"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;Name and compare the measures of center shown in a graph&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;}\">Name and compare the measures of center shown in a graph<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2 id=\"MeanMedianHist\">Mean and Median as Measures of Center<\/h2>\r\n<p>There are other ways that we can think about the mean and median as measures of the center of numerical data when we are examining a graphical representation of the data set.<\/p>\r\n<ul>\r\n\t<li>The mean represents the balance point of the data (think about where you will need to place your finger if you are balancing the graph on top of it).<\/li>\r\n\t<li>The median represents the [latex]50[\/latex]<sup>th<\/sup><span style=\"font-size: 1em; text-align: initial;\"> percentile, or the value that splits the data in half (i.e., half of the data are below the median and the other half of the data are above the median).<\/span><\/li>\r\n<\/ul>\r\n<section class=\"textbox tryIt\">Consider the following histogram and determine its mean and median.<br \/>\r\nHistogram A:\r\n[caption id=\"\" align=\"alignnone\" width=\"229\"]<img src=\"https:\/\/assets.coursehero.com\/study-guides\/lumen\/images\/introstats1\/skewness-and-the-mean-median-and-mode\/fig-ch02_08_011.jpg\" alt=\"This histogram matches the supplied data. It consists of 7 adjacent bars with the x-axis split into intervals of 1 from 4 to 10. The heighs of the bars peak in the middle and taper symmetrically to the right and left.\" width=\"229\" height=\"124\" \/> <strong>Histogram A: Both the mean and median are 7.<\/strong>[\/caption]\r\n\r\n<p>[reveal-answer q=\"3\"]Show detailed solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"3\"]7 is the center of the histogram, both as the balance point of the data and the bar that splits the data in half.[\/hidden-answer]<\/p>\r\n<p>Histogram B:<\/p>\r\n\r\n[caption id=\"\" align=\"alignnone\" width=\"221\"]<img src=\"https:\/\/assets.coursehero.com\/study-guides\/lumen\/images\/introstats1\/skewness-and-the-mean-median-and-mode\/fig-ch02_08_022.jpg\" alt=\"This histogram matches the supplied data. It consists of 5 adjacent bars with the x-axis split into intervals of 1 from 4 to 8. The peak is to the right, and the heights of the bars taper down to the left.\" width=\"221\" height=\"160\" \/> <strong>Histogram B: The mean is approximately 6.3, and the median is approximately 6.5.<\/strong>[\/caption]\r\n\r\n<p>[reveal-answer q=\"4\"]Show detailed solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"4\"]Notice that the mean is less than the median. The mean and median is smaller because of the skewness of the data. For the mean, in order to balance the histogram on top of your finger, you'd have to place it a little bit to the left of the peak of the histogram.[\/hidden-answer]<\/p>\r\n<p>Histogram C:<\/p>\r\n\r\n[caption id=\"\" align=\"alignnone\" width=\"225\"]<img src=\"https:\/\/assets.coursehero.com\/study-guides\/lumen\/images\/introstats1\/skewness-and-the-mean-median-and-mode\/fig-ch02_08_033.jpg\" alt=\"This histogram matches the supplied data. It consists of 5 adjacent bars with the x-axis split into intervals of 1 from 6 to 10. The peak is to the left, and the heights of the bars taper down to the right.\" width=\"225\" height=\"162\" \/> <strong>Histogram C: The mean is approximately 7.7, and the median is approximately 7.5.<\/strong>[\/caption]\r\n\r\n<p>[reveal-answer q=\"5\"]Show detailed solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"5\"]<\/p>\r\n<p>Notice that the mean is more than the median. The mean and median are larger because of the skewness of the data. For the mean, in order to balance the histogram on top of your finger, you'd have to place it a little bit to the right of the peak of the histogram.<\/p>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2033[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2034[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Name and compare the measures of center shown in a graph&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;}\">Name and compare the measures of center shown in a graph<\/span><\/li>\n<\/ul>\n<\/section>\n<h2 id=\"MeanMedianHist\">Mean and Median as Measures of Center<\/h2>\n<p>There are other ways that we can think about the mean and median as measures of the center of numerical data when we are examining a graphical representation of the data set.<\/p>\n<ul>\n<li>The mean represents the balance point of the data (think about where you will need to place your finger if you are balancing the graph on top of it).<\/li>\n<li>The median represents the [latex]50[\/latex]<sup>th<\/sup><span style=\"font-size: 1em; text-align: initial;\"> percentile, or the value that splits the data in half (i.e., half of the data are below the median and the other half of the data are above the median).<\/span><\/li>\n<\/ul>\n<section class=\"textbox tryIt\">Consider the following histogram and determine its mean and median.<br \/>\nHistogram A:<\/p>\n<figure style=\"width: 229px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/assets.coursehero.com\/study-guides\/lumen\/images\/introstats1\/skewness-and-the-mean-median-and-mode\/fig-ch02_08_011.jpg\" alt=\"This histogram matches the supplied data. It consists of 7 adjacent bars with the x-axis split into intervals of 1 from 4 to 10. The heighs of the bars peak in the middle and taper symmetrically to the right and left.\" width=\"229\" height=\"124\" \/><figcaption class=\"wp-caption-text\"><strong>Histogram A: Both the mean and median are 7.<\/strong><\/figcaption><\/figure>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q3\">Show detailed solution<\/button><\/p>\n<div id=\"q3\" class=\"hidden-answer\" style=\"display: none\">7 is the center of the histogram, both as the balance point of the data and the bar that splits the data in half.<\/div>\n<\/div>\n<p>Histogram B:<\/p>\n<figure style=\"width: 221px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/assets.coursehero.com\/study-guides\/lumen\/images\/introstats1\/skewness-and-the-mean-median-and-mode\/fig-ch02_08_022.jpg\" alt=\"This histogram matches the supplied data. It consists of 5 adjacent bars with the x-axis split into intervals of 1 from 4 to 8. The peak is to the right, and the heights of the bars taper down to the left.\" width=\"221\" height=\"160\" \/><figcaption class=\"wp-caption-text\"><strong>Histogram B: The mean is approximately 6.3, and the median is approximately 6.5.<\/strong><\/figcaption><\/figure>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q4\">Show detailed solution<\/button><\/p>\n<div id=\"q4\" class=\"hidden-answer\" style=\"display: none\">Notice that the mean is less than the median. The mean and median is smaller because of the skewness of the data. For the mean, in order to balance the histogram on top of your finger, you&#8217;d have to place it a little bit to the left of the peak of the histogram.<\/div>\n<\/div>\n<p>Histogram C:<\/p>\n<figure style=\"width: 225px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/assets.coursehero.com\/study-guides\/lumen\/images\/introstats1\/skewness-and-the-mean-median-and-mode\/fig-ch02_08_033.jpg\" alt=\"This histogram matches the supplied data. It consists of 5 adjacent bars with the x-axis split into intervals of 1 from 6 to 10. The peak is to the left, and the heights of the bars taper down to the right.\" width=\"225\" height=\"162\" \/><figcaption class=\"wp-caption-text\"><strong>Histogram C: The mean is approximately 7.7, and the median is approximately 7.5.<\/strong><\/figcaption><\/figure>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q5\">Show detailed solution<\/button><\/p>\n<div id=\"q5\" class=\"hidden-answer\" style=\"display: none\">\n<p>Notice that the mean is more than the median. The mean and median are larger because of the skewness of the data. For the mean, in order to balance the histogram on top of your finger, you&#8217;d have to place it a little bit to the right of the peak of the histogram.<\/p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2033\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2033&theme=lumen&iframe_resize_id=ohm2033&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2034\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2034&theme=lumen&iframe_resize_id=ohm2034&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":13,"menu_order":8,"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\/842"}],"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":5,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/842\/revisions"}],"predecessor-version":[{"id":6464,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/842\/revisions\/6464"}],"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\/842\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=842"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=842"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=842"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=842"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}