{"id":845,"date":"2023-03-20T19:17:24","date_gmt":"2023-03-20T19:17:24","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/understand-means-and-medians-as-measures-of-centers-apply-it-1\/"},"modified":"2025-05-11T22:32:18","modified_gmt":"2025-05-11T22:32:18","slug":"understand-means-and-medians-as-measures-of-centers-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/understand-means-and-medians-as-measures-of-centers-apply-it-1\/","title":{"raw":"Measures of Center: Apply It 1","rendered":"Measures of Center: Apply 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;Find and use the measures of center to explain the behavior of a data set&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;}\">Find and use the measures of center to explain the behavior of a data set<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Feeling Sleepy!<\/h2>\r\n<p>Previously, we explored data from a study that asked college students whether they identified as owls, larks, or neither and collected other pieces of data related to academics, lifestyle, stress, and sleep.<\/p>\r\n<p>Recall that <span style=\"text-decoration: italic;\">owls were defined as night people<\/span> while <span style=\"text-decoration: italic;\">larks represented morning people<\/span>. Using the data set from the study, we visualized categorical data via pie charts and bar graphs. Now, let's use the same data set to explore distributions of quantitative variables. Let's see how the mean and median can be used as numerical measures of the center of quantitative data!<\/p>\r\n\r\n[caption id=\"attachment_1107\" align=\"aligncenter\" width=\"651\"]<img class=\"wp-image-1107\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/03\/20191723\/pexels-rodnae-productions-7683819-2.jpg\" alt=\"Student falling asleep with laptop, open book, and notepad in front of them.\" width=\"651\" height=\"434\" \/> Figure 1. Sleep habits\u2014like being a night owl or early bird\u2014can affect how students feel and perform during the day.[\/caption]\r\n\r\n<p>Before we begin, consider the following research question, which asks about differences between larks and owls with respect to factors contributing to the quality of sleep.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]11133[\/ohm2_question]<\/section>\r\n<p>Before we compare each of the groups (owl, lark, neither), let\u2019s consider two variables of interest for <em>all<\/em> college students in this study:<\/p>\r\n<ul>\r\n\t<li style=\"font-weight: 400;\"><strong><em>Poor Sleep Quality Score:<\/em><\/strong> A score indicating the average quality of sleep for the participants. The greater the score, the worse the quality of sleep.<\/li>\r\n\t<li style=\"font-weight: 400;\"><b><i>Number of Missed Classes:<\/i><\/b><span style=\"font-weight: 400;\"> The average number of classes missed by the participants.<\/span><\/li>\r\n<\/ul>\r\n<h3 id=\"compareHist\">Making Comparisons Using Histograms<\/h3>\r\n<p>Histograms provide a good way of examining the distribution of values in one sample. Superimposing one histogram on another with the same range of values can help us compare the distribution of two or more samples.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2662[\/ohm2_question]<\/section>\r\n<p>Let's look at another comparison using histograms. The following histograms illustrate the distributions of the Alcoholic Drinks per Week variable based on whether the participants identified as owls, larks, or neither.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]11134[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Find and use the measures of center to explain the behavior of a data set&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;}\">Find and use the measures of center to explain the behavior of a data set<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>Feeling Sleepy!<\/h2>\n<p>Previously, we explored data from a study that asked college students whether they identified as owls, larks, or neither and collected other pieces of data related to academics, lifestyle, stress, and sleep.<\/p>\n<p>Recall that <span style=\"text-decoration: italic;\">owls were defined as night people<\/span> while <span style=\"text-decoration: italic;\">larks represented morning people<\/span>. Using the data set from the study, we visualized categorical data via pie charts and bar graphs. Now, let&#8217;s use the same data set to explore distributions of quantitative variables. Let&#8217;s see how the mean and median can be used as numerical measures of the center of quantitative data!<\/p>\n<figure id=\"attachment_1107\" aria-describedby=\"caption-attachment-1107\" style=\"width: 651px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1107\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/03\/20191723\/pexels-rodnae-productions-7683819-2.jpg\" alt=\"Student falling asleep with laptop, open book, and notepad in front of them.\" width=\"651\" height=\"434\" \/><figcaption id=\"caption-attachment-1107\" class=\"wp-caption-text\">Figure 1. Sleep habits\u2014like being a night owl or early bird\u2014can affect how students feel and perform during the day.<\/figcaption><\/figure>\n<p>Before we begin, consider the following research question, which asks about differences between larks and owls with respect to factors contributing to the quality of sleep.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm11133\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=11133&theme=lumen&iframe_resize_id=ohm11133&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>Before we compare each of the groups (owl, lark, neither), let\u2019s consider two variables of interest for <em>all<\/em> college students in this study:<\/p>\n<ul>\n<li style=\"font-weight: 400;\"><strong><em>Poor Sleep Quality Score:<\/em><\/strong> A score indicating the average quality of sleep for the participants. The greater the score, the worse the quality of sleep.<\/li>\n<li style=\"font-weight: 400;\"><b><i>Number of Missed Classes:<\/i><\/b><span style=\"font-weight: 400;\"> The average number of classes missed by the participants.<\/span><\/li>\n<\/ul>\n<h3 id=\"compareHist\">Making Comparisons Using Histograms<\/h3>\n<p>Histograms provide a good way of examining the distribution of values in one sample. Superimposing one histogram on another with the same range of values can help us compare the distribution of two or more samples.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2662\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2662&theme=lumen&iframe_resize_id=ohm2662&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>Let&#8217;s look at another comparison using histograms. The following histograms illustrate the distributions of the Alcoholic Drinks per Week variable based on whether the participants identified as owls, larks, or neither.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm11134\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=11134&theme=lumen&iframe_resize_id=ohm11134&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":13,"menu_order":10,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Sleeping student image\",\"author\":\"ODNAE Productions\",\"organization\":\"Pexels\",\"url\":\"https:\/\/www.pexels.com\/photo\/a-young-college-student-that-has-fallen-asleep-while-studying-7683819\/\",\"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":"Sleeping student image","author":"ODNAE Productions","organization":"Pexels","url":"https:\/\/www.pexels.com\/photo\/a-young-college-student-that-has-fallen-asleep-while-studying-7683819\/","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\/845"}],"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":8,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/845\/revisions"}],"predecessor-version":[{"id":6624,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/845\/revisions\/6624"}],"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\/845\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=845"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=845"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=845"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=845"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}