{"id":47,"date":"2023-01-31T00:46:02","date_gmt":"2023-01-31T00:46:02","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/applications-of-bar-graphs-dig-deeper\/"},"modified":"2025-05-11T19:36:38","modified_gmt":"2025-05-11T19:36:38","slug":"applications-of-bar-graphs-fresh-take","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/applications-of-bar-graphs-fresh-take\/","title":{"raw":"Applications of Bar Graphs: Fresh Take","rendered":"Applications of Bar Graphs: Fresh Take"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Create side-by-side and stacked bar graphs using technology<\/li>\r\n\t<li>Use side-by-side and stacked bar graphs to compare different groups<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Interpreting Side-by-Side and Stacked Bar Graphs<\/h2>\r\n<section class=\"textbox recall\" aria-label=\"Recall\">\r\n<h3><strong>The Main Idea<\/strong><\/h3>\r\n<p><strong>Side-by-side bar graphs<\/strong> are bar graphs that create two bars in the chart for each group to represent data for two categorical variables from more than one group. Side-by-side bar graphs are most efficient when presenting data counts (not percentages).<\/p>\r\n<p><strong>Stacked bar graphs<\/strong> also represent data for two categorical variables from more than one group, but stacked rather than side-by-side. Stacked bar graphs are most efficient when presenting percentages of the data in each group (not counts).<\/p>\r\n<p>The example problem below presents the same data displayed four different ways: as a contingency table (counts), as a conditional distribution (percentages), as side-by-side bar graphs (counts), and as stacked bar graphs (percentages). This won't always be the case; sometimes a bar graph will display percentages, but these examples represent efficient uses of these displays. Also note that these bars are vertical, but some side-by-side and stacked graphs are displayed horizontally.<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">The following displays present alcohol consumption by students at a college. Counts are given for four categories (abstaining, light consumption, moderate consumption, and heavy consumption) for first-year, second-year, third-year, and fourth-year students. The Contingency Table shows the level of alcohol consumption self-reported by 253 students. We can see, for example, that of the 95 second-year students who responded, 27 identified themselves as light drinkers.<br \/>\r\n<br \/>\r\n<img class=\"aligncenter wp-image-1889\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5826\/2022\/11\/09035253\/Contingency-Table.jpg\" alt=\"A contingency table showing the counts of alcohol consumption based on class year.\" width=\"549\" height=\"193\" \/>\r\n<ol>\r\n\t<li>How many third-year students identified themselves as heavy drinkers?<br \/>\r\n<p class=\"p1\">[reveal-answer q=\"190834\"]Show Answer[\/reveal-answer]<\/p>\r\n<p class=\"p1\">[hidden-answer a=\"190834\"]<\/p>\r\n<p class=\"p1\">5 [\/hidden-answer]<\/p>\r\n<\/li>\r\n<\/ol>\r\n<p>Now let's look at the data as percentages rather than counts.<\/p>\r\n<p><img class=\"aligncenter wp-image-1890\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5826\/2022\/11\/09040027\/Conditional-Distribution.jpg\" alt=\"A conditional distribution of alcohol consumption given class year using the same data as the previous table.\" width=\"550\" height=\"181\" \/><\/p>\r\n<p>Note that the percentages are given in decimal form. Multiply by 100 to convert to percentages. Each row adds up to 1 (100%) of all responses for each class year. We can see that the 27 of 95 second-year students we located in the table above is represented in this table as [latex]\\dfrac{27}{95}\\approx0.284[\/latex], which is about 28.4%.<\/p>\r\n<p style=\"padding-left: 40px;\">2. What percentage of third-year students identified themselves as heavy drinkers?<\/p>\r\n<p class=\"p1\" style=\"padding-left: 40px;\">[reveal-answer q=\"8877562\"]Show Answer[\/reveal-answer]<\/p>\r\n<p class=\"p1\" style=\"padding-left: 40px;\">[hidden-answer a=\"8877562\"] 5\/54 = 9.3%<\/p>\r\n<p class=\"p1\" style=\"padding-left: 40px;\">[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">\r\n<h4><strong>Side-by-Side Bar Graphs<\/strong><\/h4>\r\n<p>&nbsp;<\/p>\r\n<p><img class=\"aligncenter wp-image-1891 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5826\/2022\/11\/09040633\/newplot-4.png\" alt=\"A bar graph shows the alcohol consumption by year with different bar colors illustrating abstaining from alcohol, light consumption, moderate consumption, and heavy consumption.\" width=\"711\" height=\"360\" \/><\/p>\r\n<p>Here, we see the data from the contingency table displayed as side-by-side bar graphs. The horizontal axis contains the four class years of students while the vertical axis indicates the height of each bar in numbers of students. The differently colored bars each represent an alcohol consumption category.<\/p>\r\n<p>1. Try to locate the 27 second-year students who identified as light drinkers. What color is the bar and where is it located along the horizontal axis?<\/p>\r\n<p class=\"p1\">[reveal-answer q=\"908234\"]Show Answer[\/reveal-answer]<\/p>\r\n<p class=\"p1\">[hidden-answer a=\"908234\"]The green bar above 2 on the horizontal axis.<\/p>\r\n<p class=\"p1\">[\/hidden-answer]<\/p>\r\n<p>2. Which class year reports the most moderate drinking?<\/p>\r\n<p class=\"p1\">[reveal-answer q=\"266144\"]Show Answer[\/reveal-answer]<\/p>\r\n<p class=\"p1\">[hidden-answer a=\"266144\"] Year 2<\/p>\r\n<p class=\"p1\">[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">\r\n<h4><strong>Stacked Bar Graphs<\/strong><\/h4>\r\n<p>&nbsp;<\/p>\r\n<p><img class=\"aligncenter wp-image-1892 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5826\/2022\/11\/09041316\/newplot-3.png\" alt=\"A stacked bar graph of alcohol consumption by year, using the same bar colors and data as the above bar graph.\" width=\"711\" height=\"360\" \/><\/p>\r\n<p>Finally, we see the information from the conditional distribution displayed as stacked bar graphs.<\/p>\r\n<p>1. Which class year reported the lowest proportion of heavy drinkers?<\/p>\r\n<p class=\"p1\">[reveal-answer q=\"835577\"]Show Answer[\/reveal-answer]<\/p>\r\n<p class=\"p1\">[hidden-answer a=\"835577\"]First-year: the red section at the top of the stacked bar above 1 on the horizontal axis represents 2.1% of all first-year students who reported drinking heavily.<\/p>\r\n<p class=\"p1\">[\/hidden-answer]<\/p>\r\n<p>2. How did alcohol consumption change from class year to class year?<\/p>\r\n<p class=\"p1\">[reveal-answer q=\"800399\"]Show Answer[\/reveal-answer]<\/p>\r\n<p class=\"p1\">[hidden-answer a=\"800399\"](answers vary)<\/p>\r\n<p class=\"p1\">[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]754[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]755[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]756[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Create side-by-side and stacked bar graphs using technology<\/li>\n<li>Use side-by-side and stacked bar graphs to compare different groups<\/li>\n<\/ul>\n<\/section>\n<h2>Interpreting Side-by-Side and Stacked Bar Graphs<\/h2>\n<section class=\"textbox recall\" aria-label=\"Recall\">\n<h3><strong>The Main Idea<\/strong><\/h3>\n<p><strong>Side-by-side bar graphs<\/strong> are bar graphs that create two bars in the chart for each group to represent data for two categorical variables from more than one group. Side-by-side bar graphs are most efficient when presenting data counts (not percentages).<\/p>\n<p><strong>Stacked bar graphs<\/strong> also represent data for two categorical variables from more than one group, but stacked rather than side-by-side. Stacked bar graphs are most efficient when presenting percentages of the data in each group (not counts).<\/p>\n<p>The example problem below presents the same data displayed four different ways: as a contingency table (counts), as a conditional distribution (percentages), as side-by-side bar graphs (counts), and as stacked bar graphs (percentages). This won&#8217;t always be the case; sometimes a bar graph will display percentages, but these examples represent efficient uses of these displays. Also note that these bars are vertical, but some side-by-side and stacked graphs are displayed horizontally.<\/p>\n<\/section>\n<section class=\"textbox tryIt\">The following displays present alcohol consumption by students at a college. Counts are given for four categories (abstaining, light consumption, moderate consumption, and heavy consumption) for first-year, second-year, third-year, and fourth-year students. The Contingency Table shows the level of alcohol consumption self-reported by 253 students. We can see, for example, that of the 95 second-year students who responded, 27 identified themselves as light drinkers.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1889\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5826\/2022\/11\/09035253\/Contingency-Table.jpg\" alt=\"A contingency table showing the counts of alcohol consumption based on class year.\" width=\"549\" height=\"193\" \/><\/p>\n<ol>\n<li>How many third-year students identified themselves as heavy drinkers?\n<p class=\"p1\">\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q190834\">Show Answer<\/button><\/p>\n<p class=\"p1\">\n<div id=\"q190834\" class=\"hidden-answer\" style=\"display: none\">\n<p class=\"p1\">5 <\/div>\n<\/div>\n<\/li>\n<\/ol>\n<p>Now let&#8217;s look at the data as percentages rather than counts.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1890\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5826\/2022\/11\/09040027\/Conditional-Distribution.jpg\" alt=\"A conditional distribution of alcohol consumption given class year using the same data as the previous table.\" width=\"550\" height=\"181\" \/><\/p>\n<p>Note that the percentages are given in decimal form. Multiply by 100 to convert to percentages. Each row adds up to 1 (100%) of all responses for each class year. We can see that the 27 of 95 second-year students we located in the table above is represented in this table as [latex]\\dfrac{27}{95}\\approx0.284[\/latex], which is about 28.4%.<\/p>\n<p style=\"padding-left: 40px;\">2. What percentage of third-year students identified themselves as heavy drinkers?<\/p>\n<p class=\"p1\" style=\"padding-left: 40px;\">\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q8877562\">Show Answer<\/button><\/p>\n<p class=\"p1\" style=\"padding-left: 40px;\">\n<div id=\"q8877562\" class=\"hidden-answer\" style=\"display: none\"> 5\/54 = 9.3%<\/p>\n<p class=\"p1\" style=\"padding-left: 40px;\"><\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\">\n<h4><strong>Side-by-Side Bar Graphs<\/strong><\/h4>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1891 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5826\/2022\/11\/09040633\/newplot-4.png\" alt=\"A bar graph shows the alcohol consumption by year with different bar colors illustrating abstaining from alcohol, light consumption, moderate consumption, and heavy consumption.\" width=\"711\" height=\"360\" \/><\/p>\n<p>Here, we see the data from the contingency table displayed as side-by-side bar graphs. The horizontal axis contains the four class years of students while the vertical axis indicates the height of each bar in numbers of students. The differently colored bars each represent an alcohol consumption category.<\/p>\n<p>1. Try to locate the 27 second-year students who identified as light drinkers. What color is the bar and where is it located along the horizontal axis?<\/p>\n<p class=\"p1\">\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q908234\">Show Answer<\/button><\/p>\n<p class=\"p1\">\n<div id=\"q908234\" class=\"hidden-answer\" style=\"display: none\">The green bar above 2 on the horizontal axis.<\/p>\n<p class=\"p1\"><\/div>\n<\/div>\n<p>2. Which class year reports the most moderate drinking?<\/p>\n<p class=\"p1\">\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q266144\">Show Answer<\/button><\/p>\n<p class=\"p1\">\n<div id=\"q266144\" class=\"hidden-answer\" style=\"display: none\"> Year 2<\/p>\n<p class=\"p1\"><\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\">\n<h4><strong>Stacked Bar Graphs<\/strong><\/h4>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1892 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5826\/2022\/11\/09041316\/newplot-3.png\" alt=\"A stacked bar graph of alcohol consumption by year, using the same bar colors and data as the above bar graph.\" width=\"711\" height=\"360\" \/><\/p>\n<p>Finally, we see the information from the conditional distribution displayed as stacked bar graphs.<\/p>\n<p>1. Which class year reported the lowest proportion of heavy drinkers?<\/p>\n<p class=\"p1\">\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q835577\">Show Answer<\/button><\/p>\n<p class=\"p1\">\n<div id=\"q835577\" class=\"hidden-answer\" style=\"display: none\">First-year: the red section at the top of the stacked bar above 1 on the horizontal axis represents 2.1% of all first-year students who reported drinking heavily.<\/p>\n<p class=\"p1\"><\/div>\n<\/div>\n<p>2. How did alcohol consumption change from class year to class year?<\/p>\n<p class=\"p1\">\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q800399\">Show Answer<\/button><\/p>\n<p class=\"p1\">\n<div id=\"q800399\" class=\"hidden-answer\" style=\"display: none\">(answers vary)<\/p>\n<p class=\"p1\"><\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm754\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=754&theme=lumen&iframe_resize_id=ohm754&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm755\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=755&theme=lumen&iframe_resize_id=ohm755&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm756\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=756&theme=lumen&iframe_resize_id=ohm756&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":6,"menu_order":15,"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\/47"}],"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":13,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/47\/revisions"}],"predecessor-version":[{"id":7132,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/47\/revisions\/7132"}],"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\/47\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=47"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=47"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=47"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=47"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}