{"id":859,"date":"2023-03-20T19:17:36","date_gmt":"2023-03-20T19:17:36","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/interpreting-the-mean-and-median-of-a-dataset-apply-it-3\/"},"modified":"2025-04-17T03:24:15","modified_gmt":"2025-04-17T03:24:15","slug":"interpreting-the-mean-and-median-of-a-dataset-apply-it-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/interpreting-the-mean-and-median-of-a-dataset-apply-it-3\/","title":{"raw":"Interpreting the Mean and Median: Apply It 3","rendered":"Interpreting the Mean and Median: Apply It 3"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Name the features of the distribution of a data set using statistical language<\/li>\r\n\t<li>Describe the connection between the distribution of a data set and its mean and median<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2 id=\"MeanOrMedian\">Appropriate Measures of Center<\/h2>\r\n<p>In the previous example, we saw how the mean was not an accurate representation of the typical salary for a Texas NBA player due to the existence of outliers. Now, let's take a look at other situations to determine whether it would be more appropriate to use the mean or median to describe a typical observation.<\/p>\r\n<p>Consider the distribution of three different sets of data:<\/p>\r\n<ol>\r\n\t<li>Income in New York City<\/li>\r\n\t<li>GPA at a local college<\/li>\r\n\t<li>Body temperature<\/li>\r\n<\/ol>\r\n<p><span style=\"font-size: 1rem; text-align: initial; background-color: initial;\"><strong>Situation 1: <\/strong>Data are collected on the income of residents in New York City.<\/span><\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2079[\/ohm2_question]<\/section>\r\n<p><span style=\"font-size: 1rem; text-align: initial; background-color: initial;\"><strong>Situation 2: <\/strong>Data are collected on the GPAs of students enrolled at a local college.<br \/>\r\n<\/span><\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2080[\/ohm2_question]<\/section>\r\n<p><span style=\"font-size: 1rem; text-align: initial; background-color: initial;\"><strong>Situation 3: <\/strong>Data are collected on people's body temperatures.<br \/>\r\n<\/span><\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2081[\/ohm2_question]<\/section>\r\n<p>These examples illustrate some general guidelines for choosing numerical summaries:<\/p>\r\n<ul>\r\n\t<li>Use the <strong>mean<\/strong> as a measure of center <em>only <\/em>for distributions that are reasonably symmetric with a central peak. When outliers or skew are present, the mean is not a good choice.<\/li>\r\n\t<li>Use the <strong>median<\/strong> as a measure of center for all other cases.<\/li>\r\n<\/ul>\r\n<p>Both of these examples also highlight another important principle: Always plot the data.<\/p>\r\n<p>We need to see the distribution to help us determine the shape of the distribution. By looking at the shape, we can determine which measures of center best describe the data.<\/p>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Name the features of the distribution of a data set using statistical language<\/li>\n<li>Describe the connection between the distribution of a data set and its mean and median<\/li>\n<\/ul>\n<\/section>\n<h2 id=\"MeanOrMedian\">Appropriate Measures of Center<\/h2>\n<p>In the previous example, we saw how the mean was not an accurate representation of the typical salary for a Texas NBA player due to the existence of outliers. Now, let&#8217;s take a look at other situations to determine whether it would be more appropriate to use the mean or median to describe a typical observation.<\/p>\n<p>Consider the distribution of three different sets of data:<\/p>\n<ol>\n<li>Income in New York City<\/li>\n<li>GPA at a local college<\/li>\n<li>Body temperature<\/li>\n<\/ol>\n<p><span style=\"font-size: 1rem; text-align: initial; background-color: initial;\"><strong>Situation 1: <\/strong>Data are collected on the income of residents in New York City.<\/span><\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2079\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2079&theme=lumen&iframe_resize_id=ohm2079&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p><span style=\"font-size: 1rem; text-align: initial; background-color: initial;\"><strong>Situation 2: <\/strong>Data are collected on the GPAs of students enrolled at a local college.<br \/>\n<\/span><\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2080\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2080&theme=lumen&iframe_resize_id=ohm2080&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p><span style=\"font-size: 1rem; text-align: initial; background-color: initial;\"><strong>Situation 3: <\/strong>Data are collected on people&#8217;s body temperatures.<br \/>\n<\/span><\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2081\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2081&theme=lumen&iframe_resize_id=ohm2081&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>These examples illustrate some general guidelines for choosing numerical summaries:<\/p>\n<ul>\n<li>Use the <strong>mean<\/strong> as a measure of center <em>only <\/em>for distributions that are reasonably symmetric with a central peak. When outliers or skew are present, the mean is not a good choice.<\/li>\n<li>Use the <strong>median<\/strong> as a measure of center for all other cases.<\/li>\n<\/ul>\n<p>Both of these examples also highlight another important principle: Always plot the data.<\/p>\n<p>We need to see the distribution to help us determine the shape of the distribution. By looking at the shape, we can determine which measures of center best describe the data.<\/p>\n","protected":false},"author":13,"menu_order":18,"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":"apply_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\/859"}],"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":6,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/859\/revisions"}],"predecessor-version":[{"id":6447,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/859\/revisions\/6447"}],"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\/859\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=859"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=859"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=859"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=859"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}