{"id":890,"date":"2023-03-20T19:18:03","date_gmt":"2023-03-20T19:18:03","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/z-score-and-the-empirical-rule-learn-it-2\/"},"modified":"2024-03-26T18:05:14","modified_gmt":"2024-03-26T18:05:14","slug":"z-score-and-the-empirical-rule-learn-it-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/z-score-and-the-empirical-rule-learn-it-2\/","title":{"raw":"Z-Score and the Empirical Rule: Learn It 2","rendered":"Z-Score and the Empirical Rule: Learn It 2"},"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>Standardize Value ([latex]z[\/latex]-score)<\/h2>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2136[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2137[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2138[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2139[\/ohm2_question]<\/section>\r\n<p>So far, you have calculated values that were a given number of standard deviations above and below the mean. You discovered when you divided the difference between the value and the mean by the standard deviation, that the result was a positive number of standard deviations (for values above the mean) or a negative number of standard deviations (for values below the mean). That is, a resulting negative can be thought of as indicating a value that lies <em>to the left<\/em> of the mean, and the positive indicates a value that lies\u00a0<em>to the right<\/em> of the mean.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2140[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2141[\/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<h2>Standardize Value ([latex]z[\/latex]-score)<\/h2>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2136\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2136&theme=lumen&iframe_resize_id=ohm2136&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2137\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2137&theme=lumen&iframe_resize_id=ohm2137&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2138\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2138&theme=lumen&iframe_resize_id=ohm2138&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2139\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2139&theme=lumen&iframe_resize_id=ohm2139&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>So far, you have calculated values that were a given number of standard deviations above and below the mean. You discovered when you divided the difference between the value and the mean by the standard deviation, that the result was a positive number of standard deviations (for values above the mean) or a negative number of standard deviations (for values below the mean). That is, a resulting negative can be thought of as indicating a value that lies <em>to the left<\/em> of the mean, and the positive indicates a value that lies\u00a0<em>to the right<\/em> of the mean.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2140\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2140&theme=lumen&iframe_resize_id=ohm2140&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2141\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2141&theme=lumen&iframe_resize_id=ohm2141&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":13,"menu_order":40,"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\/890"}],"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\/890\/revisions"}],"predecessor-version":[{"id":5965,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/890\/revisions\/5965"}],"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\/890\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=890"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=890"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=890"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=890"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}