{"id":857,"date":"2023-03-20T19:17:35","date_gmt":"2023-03-20T19:17:35","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/interpreting-the-mean-and-median-of-a-dataset-apply-it-1\/"},"modified":"2025-04-17T03:23:41","modified_gmt":"2025-04-17T03:23:41","slug":"interpreting-the-mean-and-median-of-a-dataset-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/interpreting-the-mean-and-median-of-a-dataset-apply-it-1\/","title":{"raw":"Interpreting the Mean and Median: Apply It 1","rendered":"Interpreting the Mean and Median: Apply It 1"},"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>Is It Worth It?<\/h2>\r\n<p>Consider this scenario: A college basketball player is skilled enough to make an NBA roster and is thinking about dropping out of college this year.<\/p>\r\n\r\n[caption id=\"attachment_1111\" align=\"aligncenter\" width=\"661\"]<img class=\"wp-image-1111\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/10\/31180256\/pexels-anna-nekrashevich-6801640-scaled-e1667239507595.jpg\" alt=\"Image of a stack of bills, money.\" width=\"661\" height=\"440\" \/> Figure 1. Big financial opportunities can be appealing\u2014but is it worth giving up a college education?[\/caption]\r\n\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2071[\/ohm2_question]<\/section>\r\n<p>To better understand the scenario and to be able to have a convincing argument, let's explore the distribution of professional basketball salaries. Let's use a data set to see how outliers influence different measures of center and how averages can be misleading.<\/p>\r\n<section class=\"textbox recall\">Take a moment to recall the meanings of the terms <strong>left-skewed<\/strong>,<strong> right-skewed<\/strong>,<strong> symmetric<\/strong>, and <strong>outlier<\/strong>. You'll need to be able to use those terms to describe features of a data set.[reveal-answer q=\"504559\"]Define <em>skew<\/em> and\u00a0<em>outlier.<\/em>[\/reveal-answer][hidden-answer a=\"504559\"]We say the quantitative variable is left-skewed, right-skewed, or symmetric if:\r\n\r\n<ul>\r\n\t<li><strong>left-skewed<\/strong> (negative skew): most of the data is bunched up to the right of the graph, with a tail of infrequent values to the left.<\/li>\r\n\t<li><strong>right-skewed<\/strong>\u00a0(positive skew): most of the data is bunched up to the left of the graph with a tail of infrequent values to the right.<\/li>\r\n\t<li><strong>symmetric:<\/strong>\u00a0values are similarly distributed\u00a0on either side of the mean\/median.<\/li>\r\n<\/ul>\r\n<p>We consider an\u00a0<strong>outlier<\/strong> to be an unusual or extreme value, given the other values in the data set.[\/hidden-answer]<\/p>\r\n<\/section>\r\n<p>Let's explore the data set and boxplot of NBA salaries[footnote]\u00a0<em>NBA player salary data set (2017-2018).<\/em> (2018) Kaggle. Retrieved from https:\/\/www.kaggle.com\/koki25ando\/salary [\/footnote] for Texas players in the 2017 \u2013 2018 season.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2072[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2074[\/ohm2_question]<\/section>","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>Is It Worth It?<\/h2>\n<p>Consider this scenario: A college basketball player is skilled enough to make an NBA roster and is thinking about dropping out of college this year.<\/p>\n<figure id=\"attachment_1111\" aria-describedby=\"caption-attachment-1111\" style=\"width: 661px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1111\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/10\/31180256\/pexels-anna-nekrashevich-6801640-scaled-e1667239507595.jpg\" alt=\"Image of a stack of bills, money.\" width=\"661\" height=\"440\" \/><figcaption id=\"caption-attachment-1111\" class=\"wp-caption-text\">Figure 1. Big financial opportunities can be appealing\u2014but is it worth giving up a college education?<\/figcaption><\/figure>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2071\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2071&theme=lumen&iframe_resize_id=ohm2071&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>To better understand the scenario and to be able to have a convincing argument, let&#8217;s explore the distribution of professional basketball salaries. Let&#8217;s use a data set to see how outliers influence different measures of center and how averages can be misleading.<\/p>\n<section class=\"textbox recall\">Take a moment to recall the meanings of the terms <strong>left-skewed<\/strong>,<strong> right-skewed<\/strong>,<strong> symmetric<\/strong>, and <strong>outlier<\/strong>. You&#8217;ll need to be able to use those terms to describe features of a data set.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q504559\">Define <em>skew<\/em> and\u00a0<em>outlier.<\/em><\/button><\/p>\n<div id=\"q504559\" class=\"hidden-answer\" style=\"display: none\">We say the quantitative variable is left-skewed, right-skewed, or symmetric if:<\/p>\n<ul>\n<li><strong>left-skewed<\/strong> (negative skew): most of the data is bunched up to the right of the graph, with a tail of infrequent values to the left.<\/li>\n<li><strong>right-skewed<\/strong>\u00a0(positive skew): most of the data is bunched up to the left of the graph with a tail of infrequent values to the right.<\/li>\n<li><strong>symmetric:<\/strong>\u00a0values are similarly distributed\u00a0on either side of the mean\/median.<\/li>\n<\/ul>\n<p>We consider an\u00a0<strong>outlier<\/strong> to be an unusual or extreme value, given the other values in the data set.<\/div>\n<\/div>\n<\/section>\n<p>Let&#8217;s explore the data set and boxplot of NBA salaries<a class=\"footnote\" title=\"\u00a0NBA player salary data set (2017-2018). (2018) Kaggle. Retrieved from https:\/\/www.kaggle.com\/koki25ando\/salary\" id=\"return-footnote-857-1\" href=\"#footnote-857-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a> for Texas players in the 2017 \u2013 2018 season.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2072\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2072&theme=lumen&iframe_resize_id=ohm2072&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2074\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2074&theme=lumen&iframe_resize_id=ohm2074&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-857-1\">\u00a0<em>NBA player salary data set (2017-2018).<\/em> (2018) Kaggle. Retrieved from https:\/\/www.kaggle.com\/koki25ando\/salary  <a href=\"#return-footnote-857-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":13,"menu_order":16,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Stack of hundred dollar bills image\",\"author\":\"Anna Nekrashevich\",\"organization\":\"Pexels\",\"url\":\"https:\/\/www.pexels.com\/photo\/person-hands-faceless-money-6801640\/\",\"project\":\"\",\"license\":\"cc0\",\"license_terms\":\"\"}]","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":[{"type":"cc","description":"Stack of hundred dollar bills image","author":"Anna Nekrashevich","organization":"Pexels","url":"https:\/\/www.pexels.com\/photo\/person-hands-faceless-money-6801640\/","project":"","license":"cc0","license_terms":""}],"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\/857"}],"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\/857\/revisions"}],"predecessor-version":[{"id":6446,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/857\/revisions\/6446"}],"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\/857\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=857"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=857"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=857"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=857"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}