{"id":57,"date":"2023-01-31T00:46:10","date_gmt":"2023-01-31T00:46:10","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/visualizing-quantitative-data-dig-deeper\/"},"modified":"2025-05-11T19:39:52","modified_gmt":"2025-05-11T19:39:52","slug":"visualizing-quantitative-data-fresh-take","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/visualizing-quantitative-data-fresh-take\/","title":{"raw":"Visualizing Quantitative Data: Fresh Take","rendered":"Visualizing Quantitative Data: Fresh Take"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Create a graph that displays key information from numerical data<\/li>\r\n\t<li>Explain the differences between different graphs that display the same quantitative data<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Dotplots and Histograms<\/h2>\r\n<section class=\"textbox recall\" aria-label=\"Recall\">\r\n<h3>The Main Idea<\/h3>\r\n<p><span class=\"TextRun SCXW26391111 BCX0\" lang=\"EN-US\" xml:lang=\"EN-US\" data-contrast=\"auto\"><span class=\"NormalTextRun SCXW26391111 BCX0\">A <strong>dotplot<\/strong> takes a collection of quantitative data points and distributes them across a horizontal axis (a number line). Each value is represented by a single dot on the dotplot. Identical values get stacked up, so we can tell at a glance <\/span><span class=\"NormalTextRun SCXW26391111 BCX0\">which values showed up in <\/span><span class=\"NormalTextRun SCXW26391111 BCX0\">large quantities<\/span><span class=\"NormalTextRun SCXW26391111 BCX0\"> in the data set and which are <\/span><span class=\"NormalTextRun SCXW26391111 BCX0\">rarer<\/span><span class=\"NormalTextRun SCXW26391111 BCX0\">. From a <\/span><span class=\"NormalTextRun SpellingErrorV2Themed SCXW26391111 BCX0\">dotplot<\/span><span class=\"NormalTextRun SCXW26391111 BCX0\">, if there <\/span><span class=\"NormalTextRun SCXW26391111 BCX0\">aren\u2019t<\/span><span class=\"NormalTextRun SCXW26391111 BCX0\"> too many data points, we can count the number of\u00a0observations and <\/span><span class=\"NormalTextRun SCXW26391111 BCX0\">locate<\/span><span class=\"NormalTextRun SCXW26391111 BCX0\"> the exact median of the data.<\/span><\/span><span class=\"EOP SCXW26391111 BCX0\" data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> We can also discern the shape of the data distribution. (Is it symmetric or bunched up to one side or the other?).<\/span><\/p>\r\n<p><span class=\"TextRun SCXW125914864 BCX0\" lang=\"EN-US\" xml:lang=\"EN-US\" data-contrast=\"auto\"><span class=\"NormalTextRun SCXW125914864 BCX0\">A <strong>histogram<\/strong> is like a bar chart for quantitative variables. It takes all the data measurements collected and groups them into bins of equal width. The person creating the histogram, whether by technology or by hand, chooses the binwidth. The smaller the bin, the finer the detail. The opposite is true: large bin-width may hide detail by flattening out variation in the data. From a histogram, we can see summary information about the data set and discern the shape and center of the data. <\/span><\/span><span class=\"EOP SCXW125914864 BCX0\" data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\r\n<\/section>\r\n<p>The two videos below demonstrate how to read and interpret these quantitative graphs.<\/p>\r\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\r\n<p>[embed]https:\/\/www.youtube.com\/embed\/le8lFMyg0nk[\/embed]<\/p>\r\n<\/section>\r\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\r\n<p>[embed]https:\/\/www.youtube.com\/embed\/RZJ4qqQboHQ[\/embed]<\/p>\r\n<\/section>\r\n<section class=\"textbox example\">\r\n<h4>Hip measurements<\/h4>\r\n<p>Here we have three graphs of the same set of hip girth measurements (circumference\/distance around someone's hips) for 507 adults who exercise regularly.<\/p>\r\n<h4><strong>Dotplot:<\/strong><\/h4>\r\n<p>From the dotplot, we can see that the distribution of hip measurements has an overall range of 79 to 128 cm. For convenience, we started the axis at 75 and ended the axis at 130.<\/p>\r\n<p><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1729\/2017\/04\/15031543\/m2_summarizing_data_topic_2_1_Topic2_1Histograms1of4_image1.png\" alt=\"Dotplot showing distribution of hip measurements of 507 adults. Most of the data points are right-skewed\" width=\"650\" height=\"310\" \/><\/p>\r\n<h4><strong>Dotplot with Bins:<\/strong><\/h4>\r\n<p>To create a histogram, divide the variable values into equal-sized intervals called <strong>bins<\/strong>. In this graph, we chose bins with a width of 5 cm. Each bin contains a different number of individuals. For example, 48 adults have hip measurements between 85 and 90 cm and 97 adults have hip measurements between 100 and 105 cm.<\/p>\r\n<p><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1729\/2017\/04\/15031545\/m2_summarizing_data_topic_2_1_Topic2_1Histograms1of4_image2.png\" alt=\"Dotplot showing distribution of hip measurements of 507 adults, with white and gray bars overlaid on the dots every 5 cm.\" width=\"650\" height=\"310\" \/><\/p>\r\n<h4><strong>Histogram:<\/strong><\/h4>\r\n<p>Here is a histogram. Each bin is now a bar. The height of the bar indicates the number of individuals with hip measurements in the interval for that bin. As before, we can see that 48 adults have hip measurements between 85 and 90 cm and 97 adults have hip measurements between 100 and 105 cm.<\/p>\r\n<p><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1729\/2017\/04\/15031547\/m2_summarizing_data_topic_2_1_Topic2_1Histograms1of4_image3.png\" alt=\"Histogram showing distribution of hip measurements of 150 adults, with bars indicating number of adults in each interval. The highest proportion of hip girth is in the ninety to one hundred cm range.\" width=\"650\" height=\"310\" \/><\/p>\r\n<p><strong>Note:<\/strong> In the histogram, the count is the number of individuals in each bin. The count is also called the <strong>frequency<\/strong>. From these counts, we can determine a percentage of individuals with a given interval of variable values. This percentage is called a <strong>relative frequency<\/strong>.<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">Using the data and graphs above, approximately what percentage of the sample has hip measurements between 85 and 90 cm?[reveal-answer q=\"405449\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"405449\"] Of the 507 adults in the data set, 48 have hip measurements between 85 and 90 cm. 48 out of 507 is 48 \u00f7 507 \u2248 0.095 = 9.5%. So, approximately 9.5% of the adults in this sample have hip girths between 85 and 90 cm.[\/hidden-answer]<\/section>\r\n<section>\r\n<section class=\"textbox interact\" aria-label=\"Interact\">\r\n<p>Create a histogram for the data\u00a0\"<strong>Hours Watching TV (2018)<\/strong>\" using the Describing and Exploring Quantitative Variables tool below. Steps to create a histogram:<\/p>\r\n<p><strong>STEP 1:<\/strong> Select \"Single Group\"<br \/>\r\n<strong><br \/>\r\nSTEP 2:<\/strong> Select the Data Set \"Hours Watching TV (2018)\"<br \/>\r\n<strong><br \/>\r\nSTEP 3:<\/strong> Under \"Choose Type of Plot\", select \"Histogram\"<br \/>\r\n<strong><br \/>\r\nSTEP 4:<\/strong> Create three histograms with different binwidths \"2\", \"5\", and \"10.\"<\/p>\r\n<\/section>\r\n<\/section>\r\n<section><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/eda_quantitative\/\" width=\"100%\" height=\"850\"><\/iframe> <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>]\r\n\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]774[\/ohm2_question]<\/section>\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Create a graph that displays key information from numerical data<\/li>\n<li>Explain the differences between different graphs that display the same quantitative data<\/li>\n<\/ul>\n<\/section>\n<h2>Dotplots and Histograms<\/h2>\n<section class=\"textbox recall\" aria-label=\"Recall\">\n<h3>The Main Idea<\/h3>\n<p><span class=\"TextRun SCXW26391111 BCX0\" lang=\"EN-US\" xml:lang=\"EN-US\" data-contrast=\"auto\"><span class=\"NormalTextRun SCXW26391111 BCX0\">A <strong>dotplot<\/strong> takes a collection of quantitative data points and distributes them across a horizontal axis (a number line). Each value is represented by a single dot on the dotplot. Identical values get stacked up, so we can tell at a glance <\/span><span class=\"NormalTextRun SCXW26391111 BCX0\">which values showed up in <\/span><span class=\"NormalTextRun SCXW26391111 BCX0\">large quantities<\/span><span class=\"NormalTextRun SCXW26391111 BCX0\"> in the data set and which are <\/span><span class=\"NormalTextRun SCXW26391111 BCX0\">rarer<\/span><span class=\"NormalTextRun SCXW26391111 BCX0\">. From a <\/span><span class=\"NormalTextRun SpellingErrorV2Themed SCXW26391111 BCX0\">dotplot<\/span><span class=\"NormalTextRun SCXW26391111 BCX0\">, if there <\/span><span class=\"NormalTextRun SCXW26391111 BCX0\">aren\u2019t<\/span><span class=\"NormalTextRun SCXW26391111 BCX0\"> too many data points, we can count the number of\u00a0observations and <\/span><span class=\"NormalTextRun SCXW26391111 BCX0\">locate<\/span><span class=\"NormalTextRun SCXW26391111 BCX0\"> the exact median of the data.<\/span><\/span><span class=\"EOP SCXW26391111 BCX0\" data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> We can also discern the shape of the data distribution. (Is it symmetric or bunched up to one side or the other?).<\/span><\/p>\n<p><span class=\"TextRun SCXW125914864 BCX0\" lang=\"EN-US\" xml:lang=\"EN-US\" data-contrast=\"auto\"><span class=\"NormalTextRun SCXW125914864 BCX0\">A <strong>histogram<\/strong> is like a bar chart for quantitative variables. It takes all the data measurements collected and groups them into bins of equal width. The person creating the histogram, whether by technology or by hand, chooses the binwidth. The smaller the bin, the finer the detail. The opposite is true: large bin-width may hide detail by flattening out variation in the data. From a histogram, we can see summary information about the data set and discern the shape and center of the data. <\/span><\/span><span class=\"EOP SCXW125914864 BCX0\" data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<\/section>\n<p>The two videos below demonstrate how to read and interpret these quantitative graphs.<\/p>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Interpreting Dot Plots\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/le8lFMyg0nk?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/section>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Distributions and Their Shapes\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/RZJ4qqQboHQ?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/section>\n<section class=\"textbox example\">\n<h4>Hip measurements<\/h4>\n<p>Here we have three graphs of the same set of hip girth measurements (circumference\/distance around someone&#8217;s hips) for 507 adults who exercise regularly.<\/p>\n<h4><strong>Dotplot:<\/strong><\/h4>\n<p>From the dotplot, we can see that the distribution of hip measurements has an overall range of 79 to 128 cm. For convenience, we started the axis at 75 and ended the axis at 130.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1729\/2017\/04\/15031543\/m2_summarizing_data_topic_2_1_Topic2_1Histograms1of4_image1.png\" alt=\"Dotplot showing distribution of hip measurements of 507 adults. Most of the data points are right-skewed\" width=\"650\" height=\"310\" \/><\/p>\n<h4><strong>Dotplot with Bins:<\/strong><\/h4>\n<p>To create a histogram, divide the variable values into equal-sized intervals called <strong>bins<\/strong>. In this graph, we chose bins with a width of 5 cm. Each bin contains a different number of individuals. For example, 48 adults have hip measurements between 85 and 90 cm and 97 adults have hip measurements between 100 and 105 cm.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1729\/2017\/04\/15031545\/m2_summarizing_data_topic_2_1_Topic2_1Histograms1of4_image2.png\" alt=\"Dotplot showing distribution of hip measurements of 507 adults, with white and gray bars overlaid on the dots every 5 cm.\" width=\"650\" height=\"310\" \/><\/p>\n<h4><strong>Histogram:<\/strong><\/h4>\n<p>Here is a histogram. Each bin is now a bar. The height of the bar indicates the number of individuals with hip measurements in the interval for that bin. As before, we can see that 48 adults have hip measurements between 85 and 90 cm and 97 adults have hip measurements between 100 and 105 cm.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1729\/2017\/04\/15031547\/m2_summarizing_data_topic_2_1_Topic2_1Histograms1of4_image3.png\" alt=\"Histogram showing distribution of hip measurements of 150 adults, with bars indicating number of adults in each interval. The highest proportion of hip girth is in the ninety to one hundred cm range.\" width=\"650\" height=\"310\" \/><\/p>\n<p><strong>Note:<\/strong> In the histogram, the count is the number of individuals in each bin. The count is also called the <strong>frequency<\/strong>. From these counts, we can determine a percentage of individuals with a given interval of variable values. This percentage is called a <strong>relative frequency<\/strong>.<\/p>\n<\/section>\n<section class=\"textbox tryIt\">Using the data and graphs above, approximately what percentage of the sample has hip measurements between 85 and 90 cm?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q405449\">Show Solution<\/button><\/p>\n<div id=\"q405449\" class=\"hidden-answer\" style=\"display: none\"> Of the 507 adults in the data set, 48 have hip measurements between 85 and 90 cm. 48 out of 507 is 48 \u00f7 507 \u2248 0.095 = 9.5%. So, approximately 9.5% of the adults in this sample have hip girths between 85 and 90 cm.<\/div>\n<\/div>\n<\/section>\n<section>\n<section class=\"textbox interact\" aria-label=\"Interact\">\n<p>Create a histogram for the data\u00a0&#8220;<strong>Hours Watching TV (2018)<\/strong>&#8221; using the Describing and Exploring Quantitative Variables tool below. Steps to create a histogram:<\/p>\n<p><strong>STEP 1:<\/strong> Select &#8220;Single Group&#8221;<br \/>\n<strong><br \/>\nSTEP 2:<\/strong> Select the Data Set &#8220;Hours Watching TV (2018)&#8221;<br \/>\n<strong><br \/>\nSTEP 3:<\/strong> Under &#8220;Choose Type of Plot&#8221;, select &#8220;Histogram&#8221;<br \/>\n<strong><br \/>\nSTEP 4:<\/strong> Create three histograms with different binwidths &#8220;2&#8221;, &#8220;5&#8221;, and &#8220;10.&#8221;<\/p>\n<\/section>\n<\/section>\n<section><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/eda_quantitative\/\" width=\"100%\" height=\"850\"><\/iframe> <br \/>\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=\"ohm774\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=774&theme=lumen&iframe_resize_id=ohm774&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/section>\n","protected":false},"author":6,"menu_order":20,"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":"fresh_take","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\/57"}],"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":10,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/57\/revisions"}],"predecessor-version":[{"id":6607,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/57\/revisions\/6607"}],"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\/57\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=57"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=57"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=57"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=57"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}