{"id":855,"date":"2023-03-20T19:17:33","date_gmt":"2023-03-20T19:17:33","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/interpreting-the-mean-and-median-of-a-data-set-learn-it-3\/"},"modified":"2025-05-11T22:35:29","modified_gmt":"2025-05-11T22:35:29","slug":"interpreting-the-mean-and-median-of-a-data-set-learn-it-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/interpreting-the-mean-and-median-of-a-data-set-learn-it-3\/","title":{"raw":"Interpreting the Mean and Median: Learn It 3","rendered":"Interpreting the Mean and Median: Learn 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>Mean and Median Under Skew<\/h2>\r\n<p>Let's see if we can choose the description that matches the shape of the data\u2019s distribution, and then select the choice that gives the relationship between the mean and median for the data. Is the mean value impacted by the data's distribution? Is the median value impacted by the data's distribution?<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2069[\/ohm2_question]<\/section>\r\n<section>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>Mean and Median for Skewed Distributions<\/h3>\r\n<ul>\r\n\t<li>When the graph is skewed to the right, the mean will be greater than the median.<\/li>\r\n\t<li>When the graph is skewed to the left, the mean will be less than the median.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/section>\r\n<\/section>\r\n<h3>Resistance<\/h3>\r\n<p>Based on your answers to the question above, you might have noticed the direction the mean was pulled in under the skewness in the data set.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2070[\/ohm2_question]<\/section>\r\n<p>When a distribution is symmetric, the mean and median occupy the same value. But under a skew, the mean is \"pulled\" in the direction of the outliers: greater than the median in the case of positive (right) skew, and less than the median in the case of negative (left) skew. The value of the mean is affected by the presence of outliers and skew, while the median is not.<\/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>Mean and Median Under Skew<\/h2>\n<p>Let&#8217;s see if we can choose the description that matches the shape of the data\u2019s distribution, and then select the choice that gives the relationship between the mean and median for the data. Is the mean value impacted by the data&#8217;s distribution? Is the median value impacted by the data&#8217;s distribution?<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2069\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2069&theme=lumen&iframe_resize_id=ohm2069&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>Mean and Median for Skewed Distributions<\/h3>\n<ul>\n<li>When the graph is skewed to the right, the mean will be greater than the median.<\/li>\n<li>When the graph is skewed to the left, the mean will be less than the median.<\/li>\n<\/ul>\n<\/div>\n<\/section>\n<\/section>\n<h3>Resistance<\/h3>\n<p>Based on your answers to the question above, you might have noticed the direction the mean was pulled in under the skewness in the data set.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2070\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2070&theme=lumen&iframe_resize_id=ohm2070&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>When a distribution is symmetric, the mean and median occupy the same value. But under a skew, the mean is &#8220;pulled&#8221; in the direction of the outliers: greater than the median in the case of positive (right) skew, and less than the median in the case of negative (left) skew. The value of the mean is affected by the presence of outliers and skew, while the median is not.<\/p>\n","protected":false},"author":13,"menu_order":15,"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\/855"}],"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":9,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/855\/revisions"}],"predecessor-version":[{"id":6628,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/855\/revisions\/6628"}],"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\/855\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=855"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=855"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=855"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=855"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}