{"id":851,"date":"2023-03-20T19:17:29","date_gmt":"2023-03-20T19:17:29","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/interpreting-the-mean-and-median-of-a-data-set-background-youll-need-2\/"},"modified":"2024-02-27T19:50:51","modified_gmt":"2024-02-27T19:50:51","slug":"interpreting-the-mean-and-median-of-a-data-set-background-youll-need-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/interpreting-the-mean-and-median-of-a-data-set-background-youll-need-2\/","title":{"raw":"Describing Data Numerically: Background You'll Need 4","rendered":"Describing Data Numerically: Background You&#8217;ll Need 4"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Calculate the mean of a data set by hand&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4608,&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Calculate the mean of a data set by hand<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2 id=\"CalcMean\">Calculating Mean<\/h2>\r\n<section class=\"textbox recall\">Do you recall how to calculate the mean of a data set?[reveal-answer q=\"574698\"]Recall the definition of the mean of a set of values.[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"574698\"]The <strong>mean<\/strong> is what we think of as the \"average\" of a set of numbers. It is the sum of the entire set divided by the number of values present. The formula to calculate the mean is [latex]\\bar{x}=\\dfrac{\\sum{x}}{n}[\/latex]<br \/>\r\n[\/hidden-answer]<\/section>\r\n<p>To try it, we'll use the data set below to find the mean.<\/p>\r\n<table>\r\n<tbody>\r\n<tr style=\"height: 65px;\">\r\n<td style=\"text-align: center; height: 65px; width: 82px;\"><strong>Employee<\/strong><\/td>\r\n<td style=\"height: 65px; width: 190px;\">\r\n<p style=\"text-align: center;\"><strong>Monthly Salary in January<\/strong><\/p>\r\n<p style=\"text-align: center;\"><strong>(in thousands of dollars)<\/strong><\/p>\r\n<\/td>\r\n<td style=\"height: 131px; width: 287px;\">\r\n<p style=\"text-align: center;\"><strong>Monthly Salary in February<\/strong><\/p>\r\n<p style=\"text-align: center;\"><strong>(in thousands of dollars)<\/strong><\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"text-align: center; height: 14px; width: 82px;\"><strong>Employee 1<\/strong><\/td>\r\n<td style=\"text-align: center; height: 14px; width: 190px;\">[latex]4[\/latex]<\/td>\r\n<td style=\"text-align: center; height: 14px; width: 287px;\">[latex]4[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"text-align: center; height: 14px; width: 82px;\"><strong>Employee 2<\/strong><\/td>\r\n<td style=\"text-align: center; height: 14px; width: 190px;\">[latex]6[\/latex]<\/td>\r\n<td style=\"text-align: center; height: 14px; width: 287px;\">[latex]8[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"text-align: center; height: 14px; width: 82px;\"><strong>Employee 3<\/strong><\/td>\r\n<td style=\"text-align: center; height: 14px; width: 190px;\">[latex]3[\/latex]<\/td>\r\n<td style=\"text-align: center; height: 14px; width: 287px;\">[latex]3[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"text-align: center; height: 14px; width: 82px;\"><strong>Employee 4<\/strong><\/td>\r\n<td style=\"text-align: center; height: 14px; width: 190px;\">[latex]5[\/latex]<\/td>\r\n<td style=\"text-align: center; height: 14px; width: 287px;\">[latex]5[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"text-align: center; height: 14px; width: 82px;\"><strong>Employee 5<\/strong><\/td>\r\n<td style=\"text-align: center; height: 14px; width: 190px;\">[latex]6[\/latex]<\/td>\r\n<td style=\"text-align: center; height: 14px; width: 287px;\">[latex]6[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"text-align: center; height: 14px; width: 82px;\"><strong>Employee 6<\/strong><\/td>\r\n<td style=\"text-align: center; height: 14px; width: 190px;\">[latex]3[\/latex]<\/td>\r\n<td style=\"text-align: center; height: 14px; width: 287px;\">[latex]3[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div>\r\n<section class=\"textbox tryIt\"><br \/>\r\n[ohm2_question hide_question_numbers=1]2061[\/ohm2_question]<\/section>\r\n<\/div>\r\n<p>The same steps we used to calculate the median with the statistics tool can be used to find the mean.<\/p>\r\n<section class=\"textbox interact\">[reveal-answer q=\"363540\"]How to obtain the descriptive statistics using the statistical tool:[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"363540\"]\r\n\r\n<p style=\"padding-left: 30px;\"><strong>Step 1:<\/strong> Select the <strong>Single Group<\/strong> tab.<\/p>\r\n<p style=\"padding-left: 30px;\"><strong>Step 2:<\/strong>\u00a0Locate the drop-down menu under <strong>Enter Data<\/strong> and select <strong>Your Own<\/strong>.<\/p>\r\n<p style=\"padding-left: 30px;\"><strong>Step 3:<\/strong>\u00a0Under\u00a0<strong>Do you have,\u00a0<\/strong>select\u00a0<strong>Individual Observations<\/strong>.<\/p>\r\n<p style=\"padding-left: 30px;\"><strong>Step 4:<\/strong>\u00a0Under <strong>Name of Variable<\/strong>, type \"January Salaries (in thousands $).\"<\/p>\r\n<p style=\"padding-left: 30px;\"><strong>Step 5:<\/strong>\u00a0Under <strong>Enter observations<\/strong>, enter the data list, separated by spaces: \u201c4 6 3 5 6 3.\u201d The median will be among the Descriptive Statistics listed in the tool.<\/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<p>Use the tool to find the mean of the January salaries and compare it to your by hand calculation. Did they match?\u200b<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2062[\/ohm2_question]<\/section>\r\n<p>Now, consider what the mean tells us about the data.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2063[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2064[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Calculate the mean of a data set by hand&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4608,&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Calculate the mean of a data set by hand<\/span><\/li>\n<\/ul>\n<\/section>\n<h2 id=\"CalcMean\">Calculating Mean<\/h2>\n<section class=\"textbox recall\">Do you recall how to calculate the mean of a data set?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q574698\">Recall the definition of the mean of a set of values.<\/button><\/p>\n<div id=\"q574698\" class=\"hidden-answer\" style=\"display: none\">The <strong>mean<\/strong> is what we think of as the &#8220;average&#8221; of a set of numbers. It is the sum of the entire set divided by the number of values present. The formula to calculate the mean is [latex]\\bar{x}=\\dfrac{\\sum{x}}{n}[\/latex]\n<\/div>\n<\/div>\n<\/section>\n<p>To try it, we&#8217;ll use the data set below to find the mean.<\/p>\n<table>\n<tbody>\n<tr style=\"height: 65px;\">\n<td style=\"text-align: center; height: 65px; width: 82px;\"><strong>Employee<\/strong><\/td>\n<td style=\"height: 65px; width: 190px;\">\n<p style=\"text-align: center;\"><strong>Monthly Salary in January<\/strong><\/p>\n<p style=\"text-align: center;\"><strong>(in thousands of dollars)<\/strong><\/p>\n<\/td>\n<td style=\"height: 131px; width: 287px;\">\n<p style=\"text-align: center;\"><strong>Monthly Salary in February<\/strong><\/p>\n<p style=\"text-align: center;\"><strong>(in thousands of dollars)<\/strong><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"text-align: center; height: 14px; width: 82px;\"><strong>Employee 1<\/strong><\/td>\n<td style=\"text-align: center; height: 14px; width: 190px;\">[latex]4[\/latex]<\/td>\n<td style=\"text-align: center; height: 14px; width: 287px;\">[latex]4[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"text-align: center; height: 14px; width: 82px;\"><strong>Employee 2<\/strong><\/td>\n<td style=\"text-align: center; height: 14px; width: 190px;\">[latex]6[\/latex]<\/td>\n<td style=\"text-align: center; height: 14px; width: 287px;\">[latex]8[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"text-align: center; height: 14px; width: 82px;\"><strong>Employee 3<\/strong><\/td>\n<td style=\"text-align: center; height: 14px; width: 190px;\">[latex]3[\/latex]<\/td>\n<td style=\"text-align: center; height: 14px; width: 287px;\">[latex]3[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"text-align: center; height: 14px; width: 82px;\"><strong>Employee 4<\/strong><\/td>\n<td style=\"text-align: center; height: 14px; width: 190px;\">[latex]5[\/latex]<\/td>\n<td style=\"text-align: center; height: 14px; width: 287px;\">[latex]5[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"text-align: center; height: 14px; width: 82px;\"><strong>Employee 5<\/strong><\/td>\n<td style=\"text-align: center; height: 14px; width: 190px;\">[latex]6[\/latex]<\/td>\n<td style=\"text-align: center; height: 14px; width: 287px;\">[latex]6[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"text-align: center; height: 14px; width: 82px;\"><strong>Employee 6<\/strong><\/td>\n<td style=\"text-align: center; height: 14px; width: 190px;\">[latex]3[\/latex]<\/td>\n<td style=\"text-align: center; height: 14px; width: 287px;\">[latex]3[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div>\n<section class=\"textbox tryIt\">\n<iframe loading=\"lazy\" id=\"ohm2061\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2061&theme=lumen&iframe_resize_id=ohm2061&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/div>\n<p>The same steps we used to calculate the median with the statistics tool can be used to find the mean.<\/p>\n<section class=\"textbox interact\">\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q363540\">How to obtain the descriptive statistics using the statistical tool:<\/button><\/p>\n<div id=\"q363540\" class=\"hidden-answer\" style=\"display: none\">\n<p style=\"padding-left: 30px;\"><strong>Step 1:<\/strong> Select the <strong>Single Group<\/strong> tab.<\/p>\n<p style=\"padding-left: 30px;\"><strong>Step 2:<\/strong>\u00a0Locate the drop-down menu under <strong>Enter Data<\/strong> and select <strong>Your Own<\/strong>.<\/p>\n<p style=\"padding-left: 30px;\"><strong>Step 3:<\/strong>\u00a0Under\u00a0<strong>Do you have,\u00a0<\/strong>select\u00a0<strong>Individual Observations<\/strong>.<\/p>\n<p style=\"padding-left: 30px;\"><strong>Step 4:<\/strong>\u00a0Under <strong>Name of Variable<\/strong>, type &#8220;January Salaries (in thousands $).&#8221;<\/p>\n<p style=\"padding-left: 30px;\"><strong>Step 5:<\/strong>\u00a0Under <strong>Enter observations<\/strong>, enter the data list, separated by spaces: \u201c4 6 3 5 6 3.\u201d The median will be among the Descriptive Statistics listed in the tool.<\/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<p>Use the tool to find the mean of the January salaries and compare it to your by hand calculation. Did they match?\u200b<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2062\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2062&theme=lumen&iframe_resize_id=ohm2062&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>Now, consider what the mean tells us about the data.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2063\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2063&theme=lumen&iframe_resize_id=ohm2063&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2064\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2064&theme=lumen&iframe_resize_id=ohm2064&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":13,"menu_order":5,"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":"background_you_need","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\/851"}],"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":7,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/851\/revisions"}],"predecessor-version":[{"id":5703,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/851\/revisions\/5703"}],"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\/851\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=851"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=851"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=851"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=851"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}