{"id":892,"date":"2023-03-20T19:18:05","date_gmt":"2023-03-20T19:18:05","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/z-score-and-the-empirical-rule-learn-it-4\/"},"modified":"2025-05-11T22:48:33","modified_gmt":"2025-05-11T22:48:33","slug":"z-score-and-the-empirical-rule-learn-it-4","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/z-score-and-the-empirical-rule-learn-it-4\/","title":{"raw":"Z-Score and the Empirical Rule: Learn It 4","rendered":"Z-Score and the Empirical Rule: Learn It 4"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Calculate z-scores to explain the location of data points.<\/li>\r\n\t<li>Compare observations using z-scores and the Empirical Rule.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2 id=\"convert\">Standardizing a Score<\/h2>\r\n<p>[reveal-answer q=\"53723\"]Steps to open Movie Runtime (G Rated 1990-2016) data set[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"53723\"]<\/p>\r\n<p style=\"text-align: left; padding-left: 30px;\"><strong>Step 1:<\/strong> Select the <strong>Single Group <\/strong>tab.<\/p>\r\n<p style=\"text-align: left; padding-left: 30px;\"><strong>Step 2:<\/strong> Locate the drop-down under <strong>Enter Data<\/strong> and select <strong>From Textbook<\/strong>.<\/p>\r\n<p style=\"text-align: left; padding-left: 30px;\"><strong>Step 3:<\/strong> Locate the drop-down menu under <strong>Dataset<\/strong> and select <strong>Movie Runtime (G Rated 1990-2016)<\/strong>.<\/p>\r\n<p style=\"text-align: left; padding-left: 30px;\"><strong>Step 4:<\/strong> Under <strong>Choose Type of Plot<\/strong>, select the options to create a <strong>Histogram<\/strong> and a <strong>Dotplot<\/strong>\u00a0of runtime (in minutes).<\/p>\r\n<p>[\/hidden-answer]<\/p>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/eda_quantitative\/\" width=\"100%\" height=\"850\"><\/iframe><\/p>\r\n<p><br \/>\r\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/eda_quantitative\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\r\n<p>Now that you know the mean and standard deviation of the data set Movie Runtimes (G Rated 1990-2016) using the statistical tool above, you can calculate any observation's [latex]z[\/latex]-score to locate it in the data set relative to the mean.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2151[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2152[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2153[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2154[\/ohm2_question]<\/section>\r\n<p>It is important to note that the distance of a particular movie runtime from the mean is not measured in minutes; rather, it is measured in standard deviations.<\/p>\r\n<p>A [latex]z[\/latex]-score simply tells us how many standard deviations a given value is from the mean. Thus, a [latex]z[\/latex]-score of\u00a0[latex]-2.3[\/latex] is an observation that is\u00a0[latex]2.3[\/latex] standard deviations <em>below<\/em> the mean, and a [latex]z[\/latex]-score of [latex]2.3[\/latex] is an observation that is [latex]2.3[\/latex] standard deviations <em>above<\/em> the mean. It is important to note that [latex]z[\/latex]-scores do not have units associated with them.<\/p>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Calculate z-scores to explain the location of data points.<\/li>\n<li>Compare observations using z-scores and the Empirical Rule.<\/li>\n<\/ul>\n<\/section>\n<h2 id=\"convert\">Standardizing a Score<\/h2>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q53723\">Steps to open Movie Runtime (G Rated 1990-2016) data set<\/button><\/p>\n<div id=\"q53723\" class=\"hidden-answer\" style=\"display: none\">\n<p style=\"text-align: left; padding-left: 30px;\"><strong>Step 1:<\/strong> Select the <strong>Single Group <\/strong>tab.<\/p>\n<p style=\"text-align: left; padding-left: 30px;\"><strong>Step 2:<\/strong> Locate the drop-down under <strong>Enter Data<\/strong> and select <strong>From Textbook<\/strong>.<\/p>\n<p style=\"text-align: left; padding-left: 30px;\"><strong>Step 3:<\/strong> Locate the drop-down menu under <strong>Dataset<\/strong> and select <strong>Movie Runtime (G Rated 1990-2016)<\/strong>.<\/p>\n<p style=\"text-align: left; padding-left: 30px;\"><strong>Step 4:<\/strong> Under <strong>Choose Type of Plot<\/strong>, select the options to create a <strong>Histogram<\/strong> and a <strong>Dotplot<\/strong>\u00a0of runtime (in minutes).<\/p>\n<\/div>\n<\/div>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/eda_quantitative\/\" width=\"100%\" height=\"850\"><\/iframe><\/p>\n<p>\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/eda_quantitative\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<p>Now that you know the mean and standard deviation of the data set Movie Runtimes (G Rated 1990-2016) using the statistical tool above, you can calculate any observation&#8217;s [latex]z[\/latex]-score to locate it in the data set relative to the mean.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2151\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2151&theme=lumen&iframe_resize_id=ohm2151&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2152\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2152&theme=lumen&iframe_resize_id=ohm2152&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2153\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2153&theme=lumen&iframe_resize_id=ohm2153&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2154\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2154&theme=lumen&iframe_resize_id=ohm2154&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>It is important to note that the distance of a particular movie runtime from the mean is not measured in minutes; rather, it is measured in standard deviations.<\/p>\n<p>A [latex]z[\/latex]-score simply tells us how many standard deviations a given value is from the mean. Thus, a [latex]z[\/latex]-score of\u00a0[latex]-2.3[\/latex] is an observation that is\u00a0[latex]2.3[\/latex] standard deviations <em>below<\/em> the mean, and a [latex]z[\/latex]-score of [latex]2.3[\/latex] is an observation that is [latex]2.3[\/latex] standard deviations <em>above<\/em> the mean. It is important to note that [latex]z[\/latex]-scores do not have units associated with them.<\/p>\n","protected":false},"author":13,"menu_order":42,"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\/892"}],"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\/892\/revisions"}],"predecessor-version":[{"id":6638,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/892\/revisions\/6638"}],"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\/892\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=892"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=892"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=892"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=892"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}