{"id":343,"date":"2022-06-17T15:36:53","date_gmt":"2022-06-17T15:36:53","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/alphamodule\/chapter\/comparing-quantitative-distributions-forming-connections\/"},"modified":"2022-06-17T15:53:17","modified_gmt":"2022-06-17T15:53:17","slug":"comparing-quantitative-distributions-forming-connections","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/alphamodule\/chapter\/comparing-quantitative-distributions-forming-connections\/","title":{"raw":"Comparing Quantitative Distributions: Apply It 1","rendered":"Comparing Quantitative Distributions: Apply It 1"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Goals<\/h3>\r\nDeepen your understanding and form connections within these skills:\r\n<ul>\r\n \t<li>Summarize a comparison of quantitative distributions across groups.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Decisions, Decisions, Decisions<\/h2>\r\n<img class=\"aligncenter wp-image-982\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11185526\/Picture20-215x300.jpg\" alt=\"A woman in a wheelchair holding a diploma in one hand and raising a graduation cap in the other. \" width=\"231\" height=\"322\" \/>\r\n\r\nNow that you've had a chance to practice using technology to create graphs and compare distributions of quantitative variables, let's put it all together to see how histograms and dotplots can be used to compare distributions of a quantitative variable across groups.\r\n\r\nTo do so, we'll consider median salary levels for recent college graduates. Before we get started, think for a moment about the reasons why a college student might choose a particular major. Some may choose a major based primarily on interests, and others choose a major based on its job prospects.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 1<\/h3>\r\n[ohm_question hide_question_numbers=1]240905[\/ohm_question]\r\n\r\n[reveal-answer q=\"606835\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"606835\"]What do <em>you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox tryit\">\r\n<h3>video placement<\/h3>\r\n<span style=\"background-color: #e6daf7;\">[<strong>Intro<\/strong>: \"What variables may play a role in a student's choice of major? Maybe what percent of students get a job in their major? Starting salary? Think about how we might be able to visualize data collected from students with different majors who answer these questions.\u00a0 In this activity, we'll see how stacked histograms and side-by-side dotplots can be used to compare distributions of a quantitative variable like median salary levels across several groups, in this case: college majors. You will be able to compare the center, shape, and spread of the quantitative variable across the groups using the graphical displays. Before we begin, let's take a look at the data set together. [display image of the data set Salary Levels of College Majors as show in the page below] These are a few lines from the data set. You can see that each major category, like Business, contains several college majors, like Accounting, Actuarial science, Finance, and so on. And each of those majors has a median salary associated with it. What do you think the observational units are in this data set? That is, on what entities are we collecting the information about the major category and the median salary? It may be tempting to put yourself in this picture and think the entities are college graduates who have received their first job. But the observational unit is not a person. You'll give your answer to that question below. \"]<\/span>\r\n\r\n<\/div>\r\nIn this activity, you will explore the distribution of median salary levels of college majors across different major categories for recent college graduates in 2011. For each college major in the table, the median salary and major category is listed. A small part of the data is shown in a table below. For example, the Business major category includes college majors such as actuarial science, finance, and business economics. The major categories (<em>Major_category<\/em>) included in the complete data set are: Agriculture &amp; Natural Resources, Arts, Biology &amp; Life Sciences, Business, Communications &amp; Journalism, Computers &amp; Mathematics, Education, Engineering, Health, Humanities &amp; Liberal Arts, Industrial Arts &amp; Consumer Services, Law &amp; Public Policy, Physical Sciences, Psychology &amp; Social Work, and Social Science.[footnote]American Community Survey 2010-2012 Public Use Microdata Series. n.d.). <em>College majors<\/em>. Github. https:\/\/github.com\/fivethirtyeight\/data\/tree\/master\/college-majors.[\/footnote]\r\n\r\nThe following table displays a subset (a few rows) of the data.\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td style=\"text-align: center;\" colspan=\"3\"><strong>Salary Levels of College Majors<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>Major<\/strong><\/td>\r\n<td style=\"text-align: center;\"><strong>Major_category<\/strong><\/td>\r\n<td style=\"text-align: center;\"><strong>Median_salary<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>ACCOUNTING<\/strong><\/td>\r\n<td style=\"text-align: center;\">Business<\/td>\r\n<td style=\"text-align: center;\">[latex]45000[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>ACTUARIAL SCIENCE<\/strong><\/td>\r\n<td style=\"text-align: center;\">Business<\/td>\r\n<td style=\"text-align: center;\">[latex]62000[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>FINANCE<\/strong><\/td>\r\n<td style=\"text-align: center;\">Business<\/td>\r\n<td style=\"text-align: center;\">[latex]47000[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>GENERAL BUSINESS<\/strong><\/td>\r\n<td style=\"text-align: center;\">Business<\/td>\r\n<td style=\"text-align: center;\">[latex]40000[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>HOSPITALITY MANAGEMENT<\/strong><\/td>\r\n<td style=\"text-align: center;\">Business<\/td>\r\n<td style=\"text-align: center;\">[latex]33000[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>MARKETING AND MARKETING RESEARCH<\/strong><\/td>\r\n<td style=\"text-align: center;\">Business<\/td>\r\n<td style=\"text-align: center;\">[latex]38000[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>MISCELLANEOUS BUSINESS AND MEDICAL ADMINISTRATION<\/strong><\/td>\r\n<td style=\"text-align: center;\">Business<\/td>\r\n<td style=\"text-align: center;\">[latex]40000[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>OPERATIONS LOGISTICS AND E-COMMERCE<\/strong><\/td>\r\n<td style=\"text-align: center;\">Business<\/td>\r\n<td style=\"text-align: center;\">[latex]50000[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\"><strong>AEROSPACE ENGINEERING<\/strong><\/td>\r\n<td style=\"text-align: center;\">Engineering<\/td>\r\n<td style=\"text-align: center;\">[latex]60000[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div style=\"text-align: left;\"><\/div>\r\n<div class=\"textbox examples\">\r\n<h3>recall<\/h3>\r\nRecall from [Forming Connections: 1C] that we record information about variables of interest\u00a0on each observational unit to form the data set.\r\n\r\nCore skill:\r\n[reveal-answer q=\"407851\"]Define the terms\u00a0<em>observational unit<\/em> and\u00a0<em>variable<\/em>[\/reveal-answer]\r\n[hidden-answer a=\"407851\"]\r\n\r\n<strong>Observational Units<\/strong>: individuals or items whose characteristics we are interested in.\r\n\r\n<strong>Variables<\/strong>: The characteristics we record on the observational units. These may be quantitative or categorical variables.[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 2<\/h3>\r\n[ohm_question hide_question_numbers=1]240906[\/ohm_question]\r\n\r\n[reveal-answer q=\"416000\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"416000\"]Note that there are two characteristics noted for each of the observational units in the data set.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 3<\/h3>\r\n[ohm_question hide_question_numbers=1]240908[\/ohm_question]\r\n\r\n[reveal-answer q=\"850781\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"850781\"]See 1C, <a href=\"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/summary-of\/\">3A<\/a>, and <a href=\"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/summary-of-exploring-the-influence-of-outliers-on-measures-of-center\/\">3C<\/a> for definitions of these types of variables.<span style=\"background-color: #ffff00;\">[This hint can link to the summary pages for 1C, 3A, and 3C]<\/span> [\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 4<\/h3>\r\n[ohm_question hide_question_numbers=1]240909[\/ohm_question]\r\n\r\n[reveal-answer q=\"773626\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"773626\"]See 1C, <a href=\"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/summary-of\/\">3A<\/a>, and <a href=\"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/summary-of-exploring-the-influence-of-outliers-on-measures-of-center\/\">3C<\/a> for definitions of these types of variables. <span style=\"background-color: #ffff00;\">[This hint can link to the summary pages for 1C, 3A, and 3C]<\/span>[\/hidden-answer]\r\n\r\n<\/div>\r\n<h2 id=\"Comparing Distributions Across Groups\">Comparing Distributions Across Groups<\/h2>\r\nNext, let's go to the data set in the data analysis tool and create side-by-side dotplots for all the median salaries for each of the major categories. We'll start with a comparison of median salaries for just Business, Engineering, and Education.\r\n<div class=\"textbox\">\r\n\r\nGo to the <em>Describing and Exploring Quantitative Variables<\/em> tool at <a href=\"https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/\">https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/<\/a>. <span style=\"background-color: #00ffff;\">&lt;-- there is a problem with the horizontal axis labels on the dotplot. They are displaying in scientific notation -- e.g., \"2e+04\" (2x10^4) instead of 20,000.\u00a0<\/span>\r\n<p style=\"padding-left: 30px;\">Step 1) Click the Several Groups tab at the top of the page.<\/p>\r\n<p style=\"padding-left: 30px;\">Step 2) Select data set \"Recent Grads - Salary.\"<\/p>\r\n<p style=\"padding-left: 30px;\">Step 3) Select \u201cDotplot\u201d and adjust the dot size appropriately.<\/p>\r\n\r\n<\/div>\r\nThis process will create a comparative dotplot of the median salaries for each major: Business, Engineering, and Education. Use the dotplot to approximate the typical median salary for majors in the Business major category, and the typical median salary for majors in the Engineering major category (we'll look at the Education category a little later).\r\n\r\nFor each of the plots, examine just the dotplot (not the descriptive statistics) to answer the questions below.\r\n<div class=\"textbox examples\">\r\n<h3>recall<\/h3>\r\nWhat does a dot on a dotplot represent? In particular, what does each dot on the Business dotplot represent?\r\n\r\nCore skill:[reveal-answer q=\"962558\"]Understand the how data is represented on a dotplot[\/reveal-answer]\r\n[hidden-answer a=\"962558\"]The dots on a dotplot represent individual observations made on the variable.\r\n\r\nFor example, each dot on the Business dotplot represents a particular median salary for a college major in the Business major category. For example, the $[latex]33,000[\/latex] median salary for Hospitality Management is at the far left of the plot while $[latex]62,000[\/latex] for Actuarial Science is at the far right. [\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 5<\/h3>\r\n[ohm_question hide_question_numbers=1]240910[\/ohm_question]\r\n\r\n[reveal-answer q=\"303985\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"303985\"] Use the dotplot itself, not the descriptive statistics, to answer.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 6<\/h3>\r\n[ohm_question hide_question_numbers=1]240912[\/ohm_question]\r\n\r\n[reveal-answer q=\"988555\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"988555\"] Do there appear to be any unusual dots lying to the far right or far left in either distribution?\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 7<\/h3>\r\n[ohm_question hide_question_numbers=1]240913[\/ohm_question]\r\n\r\n[reveal-answer q=\"981781\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"981781\"]Recall that a symmetric shape has roughly equal amounts of data to the right and left of the center.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 8<\/h3>\r\n[ohm_question hide_question_numbers=1]240916[\/ohm_question]\r\n\r\n[reveal-answer q=\"47630\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"47630\"] Use just the dotplot and not the descriptive statistics to answer this.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNow let's include Education majors in the comparison.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 9<\/h3>\r\n[ohm_question hide_question_numbers=1]240917[\/ohm_question]\r\n\r\n[reveal-answer q=\"496859\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"496859\"]Use just the dotplot and not the descriptive statistics to answer this.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 10<\/h3>\r\n[ohm_question hide_question_numbers=1]240918[\/ohm_question]\r\n\r\n[reveal-answer q=\"336155\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"336155\"] Look at the graphs to answer this fairly quickly.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNow switch the view in the tool from dotplots to histograms.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 11<\/h3>\r\n[ohm_question hide_question_numbers=1]240919[\/ohm_question]\r\n\r\n[reveal-answer q=\"620535\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"620535\"]What do <em>you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 12<\/h3>\r\n[ohm_question hide_question_numbers=1]240920[\/ohm_question]\r\n\r\n[reveal-answer q=\"853144\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"853144\"]What do <em>you<\/em> think?\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox tryit\">\r\n<h3>video placement<\/h3>\r\n<span style=\"background-color: #e6daf7;\">\u00a0[insert a sub-summary: How are you doing so far? The types of questions you've been answering should feel familiar. We recently described distributions in histograms using shape, center, variability (spread) and outliers. The main difference is that now we are comparing the same variable for more than one group at a time. Displaying the groups side by side over the same scale makes it easy to make these quick comparisons. ]<\/span>\r\n\r\n<\/div>\r\nNow let's look at the other major categories. Select the data set \u201cRecent Grads - Salary Many Majors.\u201d This data set includes the median salaries for recent graduates in Arts, Biology &amp; Life Sciences, Computers &amp; Mathematics, and\u00a0Humanities &amp; Liberal Arts.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 13<\/h3>\r\n[ohm_question hide_question_numbers=1]240921[\/ohm_question]\r\n\r\n[reveal-answer q=\"685421\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"685421\"]What do <em>you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 14<\/h3>\r\n[ohm_question hide_question_numbers=1]240922[\/ohm_question]\r\n\r\n[reveal-answer q=\"466380\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"466380\"]What do <em>you<\/em> think?[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox tryit\">\r\n<h3>video placement<\/h3>\r\n<span style=\"background-color: #e6daf7;\">[wrap-up: \"What did you chose based solely on median salary in the last question? Of course, there are many other considerations that go into making a choice of major. You do want to have an interest in your field of choice and feel that you could persist in your future career! But answering questions like that helps you to realize how nicely the side-by-side graphical displays enable comparisons of a quantitative variable across groups. In the next part of the course, we'll cover summary statistics for quantitative data. We'll learn about numerical measures for spread, mean and median, and how they relate in differently shaped distributions. We'll also learn how to use standard deviation as a measure of spread.\"]<\/span>\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Goals<\/h3>\n<p>Deepen your understanding and form connections within these skills:<\/p>\n<ul>\n<li>Summarize a comparison of quantitative distributions across groups.<\/li>\n<\/ul>\n<\/div>\n<h2>Decisions, Decisions, Decisions<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-982\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/11185526\/Picture20-215x300.jpg\" alt=\"A woman in a wheelchair holding a diploma in one hand and raising a graduation cap in the other.\" width=\"231\" height=\"322\" \/><\/p>\n<p>Now that you&#8217;ve had a chance to practice using technology to create graphs and compare distributions of quantitative variables, let&#8217;s put it all together to see how histograms and dotplots can be used to compare distributions of a quantitative variable across groups.<\/p>\n<p>To do so, we&#8217;ll consider median salary levels for recent college graduates. Before we get started, think for a moment about the reasons why a college student might choose a particular major. Some may choose a major based primarily on interests, and others choose a major based on its job prospects.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 1<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240905\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240905&theme=oea&iframe_resize_id=ohm240905\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q606835\">Hint<\/span><\/p>\n<div id=\"q606835\" class=\"hidden-answer\" style=\"display: none\">What do <em>you<\/em> think?<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>video placement<\/h3>\n<p><span style=\"background-color: #e6daf7;\">[<strong>Intro<\/strong>: &#8220;What variables may play a role in a student&#8217;s choice of major? Maybe what percent of students get a job in their major? Starting salary? Think about how we might be able to visualize data collected from students with different majors who answer these questions.\u00a0 In this activity, we&#8217;ll see how stacked histograms and side-by-side dotplots can be used to compare distributions of a quantitative variable like median salary levels across several groups, in this case: college majors. You will be able to compare the center, shape, and spread of the quantitative variable across the groups using the graphical displays. Before we begin, let&#8217;s take a look at the data set together. [display image of the data set Salary Levels of College Majors as show in the page below] These are a few lines from the data set. You can see that each major category, like Business, contains several college majors, like Accounting, Actuarial science, Finance, and so on. And each of those majors has a median salary associated with it. What do you think the observational units are in this data set? That is, on what entities are we collecting the information about the major category and the median salary? It may be tempting to put yourself in this picture and think the entities are college graduates who have received their first job. But the observational unit is not a person. You&#8217;ll give your answer to that question below. &#8220;]<\/span><\/p>\n<\/div>\n<p>In this activity, you will explore the distribution of median salary levels of college majors across different major categories for recent college graduates in 2011. For each college major in the table, the median salary and major category is listed. A small part of the data is shown in a table below. For example, the Business major category includes college majors such as actuarial science, finance, and business economics. The major categories (<em>Major_category<\/em>) included in the complete data set are: Agriculture &amp; Natural Resources, Arts, Biology &amp; Life Sciences, Business, Communications &amp; Journalism, Computers &amp; Mathematics, Education, Engineering, Health, Humanities &amp; Liberal Arts, Industrial Arts &amp; Consumer Services, Law &amp; Public Policy, Physical Sciences, Psychology &amp; Social Work, and Social Science.<a class=\"footnote\" title=\"American Community Survey 2010-2012 Public Use Microdata Series. n.d.). College majors. Github. https:\/\/github.com\/fivethirtyeight\/data\/tree\/master\/college-majors.\" id=\"return-footnote-343-1\" href=\"#footnote-343-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a><\/p>\n<p>The following table displays a subset (a few rows) of the data.<\/p>\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center;\" colspan=\"3\"><strong>Salary Levels of College Majors<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>Major<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>Major_category<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>Median_salary<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>ACCOUNTING<\/strong><\/td>\n<td style=\"text-align: center;\">Business<\/td>\n<td style=\"text-align: center;\">[latex]45000[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>ACTUARIAL SCIENCE<\/strong><\/td>\n<td style=\"text-align: center;\">Business<\/td>\n<td style=\"text-align: center;\">[latex]62000[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>FINANCE<\/strong><\/td>\n<td style=\"text-align: center;\">Business<\/td>\n<td style=\"text-align: center;\">[latex]47000[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>GENERAL BUSINESS<\/strong><\/td>\n<td style=\"text-align: center;\">Business<\/td>\n<td style=\"text-align: center;\">[latex]40000[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>HOSPITALITY MANAGEMENT<\/strong><\/td>\n<td style=\"text-align: center;\">Business<\/td>\n<td style=\"text-align: center;\">[latex]33000[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>MARKETING AND MARKETING RESEARCH<\/strong><\/td>\n<td style=\"text-align: center;\">Business<\/td>\n<td style=\"text-align: center;\">[latex]38000[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>MISCELLANEOUS BUSINESS AND MEDICAL ADMINISTRATION<\/strong><\/td>\n<td style=\"text-align: center;\">Business<\/td>\n<td style=\"text-align: center;\">[latex]40000[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>OPERATIONS LOGISTICS AND E-COMMERCE<\/strong><\/td>\n<td style=\"text-align: center;\">Business<\/td>\n<td style=\"text-align: center;\">[latex]50000[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>AEROSPACE ENGINEERING<\/strong><\/td>\n<td style=\"text-align: center;\">Engineering<\/td>\n<td style=\"text-align: center;\">[latex]60000[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div style=\"text-align: left;\"><\/div>\n<div class=\"textbox examples\">\n<h3>recall<\/h3>\n<p>Recall from [Forming Connections: 1C] that we record information about variables of interest\u00a0on each observational unit to form the data set.<\/p>\n<p>Core skill:<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q407851\">Define the terms\u00a0<em>observational unit<\/em> and\u00a0<em>variable<\/em><\/span><\/p>\n<div id=\"q407851\" class=\"hidden-answer\" style=\"display: none\">\n<p><strong>Observational Units<\/strong>: individuals or items whose characteristics we are interested in.<\/p>\n<p><strong>Variables<\/strong>: The characteristics we record on the observational units. These may be quantitative or categorical variables.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 2<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240906\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240906&theme=oea&iframe_resize_id=ohm240906\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q416000\">Hint<\/span><\/p>\n<div id=\"q416000\" class=\"hidden-answer\" style=\"display: none\">Note that there are two characteristics noted for each of the observational units in the data set.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 3<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240908\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240908&theme=oea&iframe_resize_id=ohm240908\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q850781\">Hint<\/span><\/p>\n<div id=\"q850781\" class=\"hidden-answer\" style=\"display: none\">See 1C, <a href=\"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/summary-of\/\">3A<\/a>, and <a href=\"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/summary-of-exploring-the-influence-of-outliers-on-measures-of-center\/\">3C<\/a> for definitions of these types of variables.<span style=\"background-color: #ffff00;\">[This hint can link to the summary pages for 1C, 3A, and 3C]<\/span> <\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 4<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240909\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240909&theme=oea&iframe_resize_id=ohm240909\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q773626\">Hint<\/span><\/p>\n<div id=\"q773626\" class=\"hidden-answer\" style=\"display: none\">See 1C, <a href=\"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/summary-of\/\">3A<\/a>, and <a href=\"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/summary-of-exploring-the-influence-of-outliers-on-measures-of-center\/\">3C<\/a> for definitions of these types of variables. <span style=\"background-color: #ffff00;\">[This hint can link to the summary pages for 1C, 3A, and 3C]<\/span><\/div>\n<\/div>\n<\/div>\n<h2 id=\"Comparing Distributions Across Groups\">Comparing Distributions Across Groups<\/h2>\n<p>Next, let&#8217;s go to the data set in the data analysis tool and create side-by-side dotplots for all the median salaries for each of the major categories. We&#8217;ll start with a comparison of median salaries for just Business, Engineering, and Education.<\/p>\n<div class=\"textbox\">\n<p>Go to the <em>Describing and Exploring Quantitative Variables<\/em> tool at <a href=\"https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/\">https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/<\/a>. <span style=\"background-color: #00ffff;\">&lt;&#8211; there is a problem with the horizontal axis labels on the dotplot. They are displaying in scientific notation &#8212; e.g., &#8220;2e+04&#8221; (2&#215;10^4) instead of 20,000.\u00a0<\/span><\/p>\n<p style=\"padding-left: 30px;\">Step 1) Click the Several Groups tab at the top of the page.<\/p>\n<p style=\"padding-left: 30px;\">Step 2) Select data set &#8220;Recent Grads &#8211; Salary.&#8221;<\/p>\n<p style=\"padding-left: 30px;\">Step 3) Select \u201cDotplot\u201d and adjust the dot size appropriately.<\/p>\n<\/div>\n<p>This process will create a comparative dotplot of the median salaries for each major: Business, Engineering, and Education. Use the dotplot to approximate the typical median salary for majors in the Business major category, and the typical median salary for majors in the Engineering major category (we&#8217;ll look at the Education category a little later).<\/p>\n<p>For each of the plots, examine just the dotplot (not the descriptive statistics) to answer the questions below.<\/p>\n<div class=\"textbox examples\">\n<h3>recall<\/h3>\n<p>What does a dot on a dotplot represent? In particular, what does each dot on the Business dotplot represent?<\/p>\n<p>Core skill:<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q962558\">Understand the how data is represented on a dotplot<\/span><\/p>\n<div id=\"q962558\" class=\"hidden-answer\" style=\"display: none\">The dots on a dotplot represent individual observations made on the variable.<\/p>\n<p>For example, each dot on the Business dotplot represents a particular median salary for a college major in the Business major category. For example, the $[latex]33,000[\/latex] median salary for Hospitality Management is at the far left of the plot while $[latex]62,000[\/latex] for Actuarial Science is at the far right. <\/p><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 5<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240910\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240910&theme=oea&iframe_resize_id=ohm240910\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q303985\">Hint<\/span><\/p>\n<div id=\"q303985\" class=\"hidden-answer\" style=\"display: none\"> Use the dotplot itself, not the descriptive statistics, to answer.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 6<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240912\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240912&theme=oea&iframe_resize_id=ohm240912\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q988555\">Hint<\/span><\/p>\n<div id=\"q988555\" class=\"hidden-answer\" style=\"display: none\"> Do there appear to be any unusual dots lying to the far right or far left in either distribution?<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 7<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240913\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240913&theme=oea&iframe_resize_id=ohm240913\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q981781\">Hint<\/span><\/p>\n<div id=\"q981781\" class=\"hidden-answer\" style=\"display: none\">Recall that a symmetric shape has roughly equal amounts of data to the right and left of the center.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 8<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240916\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240916&theme=oea&iframe_resize_id=ohm240916\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q47630\">Hint<\/span><\/p>\n<div id=\"q47630\" class=\"hidden-answer\" style=\"display: none\"> Use just the dotplot and not the descriptive statistics to answer this.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>Now let&#8217;s include Education majors in the comparison.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 9<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240917\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240917&theme=oea&iframe_resize_id=ohm240917\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q496859\">Hint<\/span><\/p>\n<div id=\"q496859\" class=\"hidden-answer\" style=\"display: none\">Use just the dotplot and not the descriptive statistics to answer this.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 10<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240918\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240918&theme=oea&iframe_resize_id=ohm240918\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q336155\">Hint<\/span><\/p>\n<div id=\"q336155\" class=\"hidden-answer\" style=\"display: none\"> Look at the graphs to answer this fairly quickly.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>Now switch the view in the tool from dotplots to histograms.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 11<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240919\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240919&theme=oea&iframe_resize_id=ohm240919\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q620535\">Hint<\/span><\/p>\n<div id=\"q620535\" class=\"hidden-answer\" style=\"display: none\">What do <em>you<\/em> think?<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 12<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240920\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240920&theme=oea&iframe_resize_id=ohm240920\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q853144\">Hint<\/span><\/p>\n<div id=\"q853144\" class=\"hidden-answer\" style=\"display: none\">What do <em>you<\/em> think?<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>video placement<\/h3>\n<p><span style=\"background-color: #e6daf7;\">\u00a0[insert a sub-summary: How are you doing so far? The types of questions you&#8217;ve been answering should feel familiar. We recently described distributions in histograms using shape, center, variability (spread) and outliers. The main difference is that now we are comparing the same variable for more than one group at a time. Displaying the groups side by side over the same scale makes it easy to make these quick comparisons. ]<\/span><\/p>\n<\/div>\n<p>Now let&#8217;s look at the other major categories. Select the data set \u201cRecent Grads &#8211; Salary Many Majors.\u201d This data set includes the median salaries for recent graduates in Arts, Biology &amp; Life Sciences, Computers &amp; Mathematics, and\u00a0Humanities &amp; Liberal Arts.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 13<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240921\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240921&theme=oea&iframe_resize_id=ohm240921\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q685421\">Hint<\/span><\/p>\n<div id=\"q685421\" class=\"hidden-answer\" style=\"display: none\">What do <em>you<\/em> think?<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 14<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm240922\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=240922&theme=oea&iframe_resize_id=ohm240922\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q466380\">Hint<\/span><\/p>\n<div id=\"q466380\" class=\"hidden-answer\" style=\"display: none\">What do <em>you<\/em> think?<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>video placement<\/h3>\n<p><span style=\"background-color: #e6daf7;\">[wrap-up: &#8220;What did you chose based solely on median salary in the last question? Of course, there are many other considerations that go into making a choice of major. You do want to have an interest in your field of choice and feel that you could persist in your future career! But answering questions like that helps you to realize how nicely the side-by-side graphical displays enable comparisons of a quantitative variable across groups. In the next part of the course, we&#8217;ll cover summary statistics for quantitative data. We&#8217;ll learn about numerical measures for spread, mean and median, and how they relate in differently shaped distributions. We&#8217;ll also learn how to use standard deviation as a measure of spread.&#8221;]<\/span><\/p>\n<\/div>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-343-1\">American Community Survey 2010-2012 Public Use Microdata Series. n.d.). <em>College majors<\/em>. Github. https:\/\/github.com\/fivethirtyeight\/data\/tree\/master\/college-majors. <a href=\"#return-footnote-343-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":17533,"menu_order":23,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-343","chapter","type-chapter","status-publish","hentry"],"part":160,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/343","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":4,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/343\/revisions"}],"predecessor-version":[{"id":622,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/343\/revisions\/622"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/parts\/160"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/343\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/media?parent=343"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapter-type?post=343"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/contributor?post=343"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/license?post=343"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}