{"id":75,"date":"2023-01-31T00:46:25","date_gmt":"2023-01-31T00:46:25","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/comparing-quantitative-distributions-apply-it-2\/"},"modified":"2024-01-31T02:08:06","modified_gmt":"2024-01-31T02:08:06","slug":"comparing-quantitative-distributions-apply-it-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/comparing-quantitative-distributions-apply-it-2\/","title":{"raw":"Comparing Quantitative Distributions: Apply It 2","rendered":"Comparing Quantitative Distributions: Apply It 2"},"content":{"raw":"<section class=\"textbox learningGoals focusable\" tabindex=\"-1\">\r\n<ul>\r\n\t<li>Compare data sets by describing their shapes, centers, spreads, and outliers<\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>Let's analyze the salary data set in the statistical tool and create side-by-side dotplots or histograms.<\/p>\r\n<p>By displaying the data set in side-by-side dotplots or histograms, we can describe and compare features of the distribution of the quantitative variable. The features used to describe the distribution of a quantitative variable are the <b>shape,<\/b>\u00a0<b>center,<\/b>\u00a0<b>spread,<\/b>\u00a0and\u00a0<b>presence of outliers<\/b>.<\/p>\r\n<section class=\"textbox proTip\">How do we decide when to use a dotplot and when to use a histogram? There are no rules here. Each type of graph can highlight different aspects of the data.\r\n\r\n<ul>\r\n\t<li>Here are some observations about <strong>dotplots<\/strong><em>:<\/em>\r\n<ul>\r\n\t<li>Individual variable values are visible, particularly when the data set is small.<\/li>\r\n\t<li>Descriptions of shape, center, and spread are not affected by how the dotplot is constructed.<\/li>\r\n\t<li>We can accurately calculate the overall range (largest value \u2013 smallest value).<\/li>\r\n<\/ul>\r\n<\/li>\r\n\t<li>Here are some observations about <strong>histograms<\/strong><em>:<\/em>\r\n<ul>\r\n\t<li>Individual variable values are not visible.<\/li>\r\n\t<li>Grouping individuals into bins of equal-sized intervals is particularly useful when analyzing large data sets.<\/li>\r\n\t<li>We can easily use percentages, also called relative frequencies, to describe the distribution.<\/li>\r\n\t<li>Descriptions of shape, center, and spread are affected by how the bins are defined.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/section>\r\n<section class=\"textbox interact\">Create the dotplots or histograms for the data set \"<strong>Recent Grads - Salary<\/strong>\" using the Describing and Exploring Quantitative Data tool to answer additional questions.[reveal-answer q=\"958968\"]Steps to create side-by-side dotplots[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"958968\"]\r\n\r\n<p style=\"padding-left: 30px;\"><strong>STEP 1:<\/strong> Click the \"Several Groups\" tab at the top of the page.<\/p>\r\n<p style=\"padding-left: 30px;\"><strong>STEP 2:<\/strong> Select data set \"Recent Grads - Salary.\"<\/p>\r\n<p style=\"padding-left: 30px;\"><strong>STEP 3:<\/strong> Select \"Histogram\" or \u201cDotplot\u201d and adjust the \"binwidth\" or \"dot size\" appropriately.<\/p>\r\n<p><em>Note: The dotplots will display their horizontal axes in scientific notation. For example: \"2e+04\" = 20,000.<\/em><\/p>\r\n<p>[\/hidden-answer]<\/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]823[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]824[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]825[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]826[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]827[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals focusable\" tabindex=\"-1\">\n<ul>\n<li>Compare data sets by describing their shapes, centers, spreads, and outliers<\/li>\n<\/ul>\n<\/section>\n<p>Let&#8217;s analyze the salary data set in the statistical tool and create side-by-side dotplots or histograms.<\/p>\n<p>By displaying the data set in side-by-side dotplots or histograms, we can describe and compare features of the distribution of the quantitative variable. The features used to describe the distribution of a quantitative variable are the <b>shape,<\/b>\u00a0<b>center,<\/b>\u00a0<b>spread,<\/b>\u00a0and\u00a0<b>presence of outliers<\/b>.<\/p>\n<section class=\"textbox proTip\">How do we decide when to use a dotplot and when to use a histogram? There are no rules here. Each type of graph can highlight different aspects of the data.<\/p>\n<ul>\n<li>Here are some observations about <strong>dotplots<\/strong><em>:<\/em>\n<ul>\n<li>Individual variable values are visible, particularly when the data set is small.<\/li>\n<li>Descriptions of shape, center, and spread are not affected by how the dotplot is constructed.<\/li>\n<li>We can accurately calculate the overall range (largest value \u2013 smallest value).<\/li>\n<\/ul>\n<\/li>\n<li>Here are some observations about <strong>histograms<\/strong><em>:<\/em>\n<ul>\n<li>Individual variable values are not visible.<\/li>\n<li>Grouping individuals into bins of equal-sized intervals is particularly useful when analyzing large data sets.<\/li>\n<li>We can easily use percentages, also called relative frequencies, to describe the distribution.<\/li>\n<li>Descriptions of shape, center, and spread are affected by how the bins are defined.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox interact\">Create the dotplots or histograms for the data set &#8220;<strong>Recent Grads &#8211; Salary<\/strong>&#8221; using the Describing and Exploring Quantitative Data tool to answer additional questions.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q958968\">Steps to create side-by-side dotplots<\/button><\/p>\n<div id=\"q958968\" class=\"hidden-answer\" style=\"display: none\">\n<p style=\"padding-left: 30px;\"><strong>STEP 1:<\/strong> Click the &#8220;Several Groups&#8221; tab at the top of the page.<\/p>\n<p style=\"padding-left: 30px;\"><strong>STEP 2:<\/strong> Select data set &#8220;Recent Grads &#8211; Salary.&#8221;<\/p>\n<p style=\"padding-left: 30px;\"><strong>STEP 3:<\/strong> Select &#8220;Histogram&#8221; or \u201cDotplot\u201d and adjust the &#8220;binwidth&#8221; or &#8220;dot size&#8221; appropriately.<\/p>\n<p><em>Note: The dotplots will display their horizontal axes in scientific notation. For example: &#8220;2e+04&#8221; = 20,000.<\/em><\/p>\n<\/div>\n<\/div>\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=\"ohm823\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=823&theme=lumen&iframe_resize_id=ohm823&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm824\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=824&theme=lumen&iframe_resize_id=ohm824&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm825\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=825&theme=lumen&iframe_resize_id=ohm825&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm826\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=826&theme=lumen&iframe_resize_id=ohm826&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm827\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=827&theme=lumen&iframe_resize_id=ohm827&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":6,"menu_order":30,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":20,"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\/75"}],"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\/6"}],"version-history":[{"count":14,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/75\/revisions"}],"predecessor-version":[{"id":5303,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/75\/revisions\/5303"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/20"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/75\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=75"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=75"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=75"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=75"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}