{"id":898,"date":"2023-03-20T19:18:11","date_gmt":"2023-03-20T19:18:11","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/z-score-and-the-empirical-rule-apply-it-3\/"},"modified":"2025-05-11T22:50:38","modified_gmt":"2025-05-11T22:50:38","slug":"z-score-and-the-empirical-rule-apply-it-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/z-score-and-the-empirical-rule-apply-it-3\/","title":{"raw":"Z-Score and the Empirical Rule: Apply It 3","rendered":"Z-Score and the Empirical Rule: Apply It 3"},"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;Calculate z-scores to explain the location of data points&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Calculate [latex]z[\/latex]-scores to explain the location of data points.<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Compare observations using z-scores and the Empirical Rule&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Compare observations using [latex]z[\/latex]-scores and the Empirical Rule.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2 id=\"CompUseZ\">[latex]z[\/latex]-Scores<\/h2>\r\n<p>A higher organ weight is an indicator of higher toxicity. Suppose researchers want to compare the toxicity of a randomly selected liver with that of a randomly selected spleen. How will they know if the weight is extreme? We can use the [latex]z[\/latex]-score for each of these values to help us answer these questions.<\/p>\r\n<section class=\"textbox recall\">\r\n<ul>\r\n\t<li>The [latex]z[\/latex]-score is the number of standard deviations an observation is away from the mean.<\/li>\r\n\t<li>The [latex]z[\/latex]-score has no units associated with it. It only gives relative proximity (distance and direction) from the mean of a quantitative variable. The formula for this is: [latex]z=\\dfrac{x-\\mu}{\\sigma}[\/latex], where [latex]x[\/latex] is an observation value, [latex]\\mu[\/latex] is the population mean, and [latex]\\sigma[\/latex] is the population standard deviation.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2161[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2162[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2163[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Calculate z-scores to explain the location of data points&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Calculate [latex]z[\/latex]-scores to explain the location of data points.<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Compare observations using z-scores and the Empirical Rule&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Compare observations using [latex]z[\/latex]-scores and the Empirical Rule.<\/span><\/li>\n<\/ul>\n<\/section>\n<h2 id=\"CompUseZ\">[latex]z[\/latex]-Scores<\/h2>\n<p>A higher organ weight is an indicator of higher toxicity. Suppose researchers want to compare the toxicity of a randomly selected liver with that of a randomly selected spleen. How will they know if the weight is extreme? We can use the [latex]z[\/latex]-score for each of these values to help us answer these questions.<\/p>\n<section class=\"textbox recall\">\n<ul>\n<li>The [latex]z[\/latex]-score is the number of standard deviations an observation is away from the mean.<\/li>\n<li>The [latex]z[\/latex]-score has no units associated with it. It only gives relative proximity (distance and direction) from the mean of a quantitative variable. The formula for this is: [latex]z=\\dfrac{x-\\mu}{\\sigma}[\/latex], where [latex]x[\/latex] is an observation value, [latex]\\mu[\/latex] is the population mean, and [latex]\\sigma[\/latex] is the population standard deviation.<\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2161\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2161&theme=lumen&iframe_resize_id=ohm2161&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2162\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2162&theme=lumen&iframe_resize_id=ohm2162&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2163\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2163&theme=lumen&iframe_resize_id=ohm2163&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":13,"menu_order":46,"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":"apply_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\/898"}],"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\/898\/revisions"}],"predecessor-version":[{"id":6641,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/898\/revisions\/6641"}],"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\/898\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=898"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=898"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=898"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=898"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}