{"id":891,"date":"2023-03-20T19:18:04","date_gmt":"2023-03-20T19:18:04","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/z-score-and-the-empirical-rule-learn-it-3\/"},"modified":"2024-09-23T17:44:06","modified_gmt":"2024-09-23T17:44:06","slug":"z-score-and-the-empirical-rule-learn-it-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/z-score-and-the-empirical-rule-learn-it-3\/","title":{"raw":"Z-Score and the Empirical Rule: Learn It 3","rendered":"Z-Score and the Empirical Rule: Learn It 3"},"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<section class=\"textbox recall\" aria-label=\"Recall\">\r\n<p>A <strong>standardized value<\/strong>, or <strong>[latex]z[\/latex]-score<\/strong>, is a statistical measure that describes how many standard deviations a data point is from the mean of the data set. It is used to standardize scores on different scales to a common scale with a mean of 0 and a standard deviation of 1.<\/p>\r\n<p style=\"text-align: center;\">[latex]z=\\dfrac{\\text{Observed Value}-\\text{mean}}{\\text{standard deviation}} = \\dfrac{x-\\mu}{\\sigma}[\/latex]<\/p>\r\n<p>where [latex]x=[\/latex] the value of the observation, [latex]\\mu=[\/latex] the population mean, [latex]\\sigma=[\/latex] the standard deviation, and [latex]z=[\/latex] the standardized value (or [latex]z[\/latex]-score).<\/p>\r\n<\/section>\r\n<p>Recall the data set about the movie runtimes for rated G (General Audiences, All Ages Admitted) and rated R (Restricted, Children Under 17 Require Accompanying Parent or Adult Guardian) movies.[footnote] <em>What do movie ratings mean?<\/em> (n.d.). Showbiz.Junkies. Retrieved from https:\/\/www.showbizjunkies.com\/mpaa-ratings\/ [\/footnote]<\/p>\r\n<section class=\"textbox interact\">\r\n<p style=\"text-align: left; padding-left: 30px;\"><strong>Step 1:<\/strong> Select the <strong>Single Group<\/strong>\u00a0tab.<\/p>\r\n<p style=\"text-align: left; padding-left: 30px;\"><strong>Step 2:<\/strong> Locate the dropdown 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>\u00a0and a <strong>Dotplot<\/strong>\u00a0of runtime (in minutes).<\/p>\r\n<\/section>\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<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2149[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2150[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2148[\/ohm2_question]<\/section>","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<section class=\"textbox recall\" aria-label=\"Recall\">\n<p>A <strong>standardized value<\/strong>, or <strong>[latex]z[\/latex]-score<\/strong>, is a statistical measure that describes how many standard deviations a data point is from the mean of the data set. It is used to standardize scores on different scales to a common scale with a mean of 0 and a standard deviation of 1.<\/p>\n<p style=\"text-align: center;\">[latex]z=\\dfrac{\\text{Observed Value}-\\text{mean}}{\\text{standard deviation}} = \\dfrac{x-\\mu}{\\sigma}[\/latex]<\/p>\n<p>where [latex]x=[\/latex] the value of the observation, [latex]\\mu=[\/latex] the population mean, [latex]\\sigma=[\/latex] the standard deviation, and [latex]z=[\/latex] the standardized value (or [latex]z[\/latex]-score).<\/p>\n<\/section>\n<p>Recall the data set about the movie runtimes for rated G (General Audiences, All Ages Admitted) and rated R (Restricted, Children Under 17 Require Accompanying Parent or Adult Guardian) movies.<a class=\"footnote\" title=\"What do movie ratings mean? (n.d.). Showbiz.Junkies. Retrieved from https:\/\/www.showbizjunkies.com\/mpaa-ratings\/\" id=\"return-footnote-891-1\" href=\"#footnote-891-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a><\/p>\n<section class=\"textbox interact\">\n<p style=\"text-align: left; padding-left: 30px;\"><strong>Step 1:<\/strong> Select the <strong>Single Group<\/strong>\u00a0tab.<\/p>\n<p style=\"text-align: left; padding-left: 30px;\"><strong>Step 2:<\/strong> Locate the dropdown 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>\u00a0and a <strong>Dotplot<\/strong>\u00a0of runtime (in minutes).<\/p>\n<\/section>\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<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2149\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2149&theme=lumen&iframe_resize_id=ohm2149&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2150\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2150&theme=lumen&iframe_resize_id=ohm2150&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2148\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2148&theme=lumen&iframe_resize_id=ohm2148&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-891-1\"> <em>What do movie ratings mean?<\/em> (n.d.). Showbiz.Junkies. Retrieved from https:\/\/www.showbizjunkies.com\/mpaa-ratings\/  <a href=\"#return-footnote-891-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":13,"menu_order":41,"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\/891"}],"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":11,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/891\/revisions"}],"predecessor-version":[{"id":6132,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/891\/revisions\/6132"}],"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\/891\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=891"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=891"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=891"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=891"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}