{"id":2243,"date":"2021-10-07T18:38:49","date_gmt":"2021-10-07T18:38:49","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=2243"},"modified":"2022-04-21T23:35:42","modified_gmt":"2022-04-21T23:35:42","slug":"interpreting-two-way-tables","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/interpreting-two-way-tables\/","title":{"raw":"Interpreting Two-Way Tables","rendered":"Interpreting Two-Way Tables"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Read and interpret data from pie charts and bar charts as percents<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Two-Way Tables<\/h2>\r\nCategorical data is sometimes categorized by two attributes. For example, students at a college may be categorized by class standing as well as residential status. Each individual belongs to one class standing (freshman, sophomore, junior or senior) and either lives on campus or commutes.\r\n\r\nIn a <strong>two-way table,<\/strong>\u00a0or contingency table, counts are displayed by rows corresponding to categories for one attribute and by columns corresponding to categories for the other attribute. The intersection of a row and a column is called a cell, and it tells the number of data values with both characteristics.\r\n<div align=\"left\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>Residential<\/td>\r\n<td>Commuter<\/td>\r\n<td>Total<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Freshman<\/td>\r\n<td>650<\/td>\r\n<td>125<\/td>\r\n<td>775<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Sophomore<\/td>\r\n<td>300<\/td>\r\n<td>100<\/td>\r\n<td>400<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Junior<\/td>\r\n<td>350<\/td>\r\n<td>325<\/td>\r\n<td>675<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Senior<\/td>\r\n<td>310<\/td>\r\n<td>340<\/td>\r\n<td>650<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Total<\/td>\r\n<td>1610<\/td>\r\n<td>890<\/td>\r\n<td>2500<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe table above tells us there are 125 freshmen that commute, while the other 650 freshmen live on campus. The total for that row, 775, gives the total number of freshmen. Similarly, the total of the column \u201cResidential\u201d tells us that 1610 students live on campus.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nWhat percent of students at the college are seniors who commute?\r\n\r\n[reveal-answer q=\"449112\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"449112\"]\r\n\r\nFormulate the question as a percent problem.\r\n\r\nIdentify the percent, the base, and the amount.\r\n\r\nPercent: <em>p<\/em>\r\n\r\nBase: the total number of students is 2500\r\n\r\nAmount: the number of students who are seniors who commute is 340\r\n\r\nWrite the percent equation.\r\n<p style=\"text-align: center;\">[latex]\\mathrm{Percent} \\ \\cdot \\ \\mathrm{Base} \\ = \\ \\mathrm{Amount}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]p \\cdot 2500 = 340[\/latex]<\/p>\r\nDivide and convert to a percent.\r\n<p style=\"text-align: center;\">[latex]p=\\frac{340}{2500} = 0.136 = (0.136) \\cdot 100 \\% = 13.6 \\%[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]13.6 \\%[\/latex] of students are seniors who commute.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nWhat percent of juniors live on campus?\r\n\r\n[reveal-answer q=\"194742\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"194742\"]\r\n\r\nFormulate the question as a percent problem.\r\n\r\nIdentify the percent, the base, and the amount.\r\n\r\nPercent: <em>p<\/em>\r\n\r\nBase: the total number of juniors is 675\r\n\r\nAmount: the number of juniors who live on campus is 350\r\n\r\nWrite the percent equation.\r\n<p style=\"text-align: center;\">[latex]\\mathrm{Percent} \\ \\cdot \\ \\mathrm{Base} \\ = \\ \\mathrm{Amount}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]p \\cdot 675 = 350[\/latex]<\/p>\r\nDivide and convert to a percent.\r\n<p style=\"text-align: center;\">[latex]p=\\frac{350}{675} \\approx 0.519 = (0.519) \\cdot 100 \\% = 51.9 \\%[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]51.9 \\%[\/latex] of juniors live on campus.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]232420[\/ohm_question]\r\n\r\n<\/div>","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Read and interpret data from pie charts and bar charts as percents<\/li>\n<\/ul>\n<\/div>\n<h2>Two-Way Tables<\/h2>\n<p>Categorical data is sometimes categorized by two attributes. For example, students at a college may be categorized by class standing as well as residential status. Each individual belongs to one class standing (freshman, sophomore, junior or senior) and either lives on campus or commutes.<\/p>\n<p>In a <strong>two-way table,<\/strong>\u00a0or contingency table, counts are displayed by rows corresponding to categories for one attribute and by columns corresponding to categories for the other attribute. The intersection of a row and a column is called a cell, and it tells the number of data values with both characteristics.<\/p>\n<div style=\"text-align: left;\">\n<table>\n<tbody>\n<tr>\n<td><\/td>\n<td>Residential<\/td>\n<td>Commuter<\/td>\n<td>Total<\/td>\n<\/tr>\n<tr>\n<td>Freshman<\/td>\n<td>650<\/td>\n<td>125<\/td>\n<td>775<\/td>\n<\/tr>\n<tr>\n<td>Sophomore<\/td>\n<td>300<\/td>\n<td>100<\/td>\n<td>400<\/td>\n<\/tr>\n<tr>\n<td>Junior<\/td>\n<td>350<\/td>\n<td>325<\/td>\n<td>675<\/td>\n<\/tr>\n<tr>\n<td>Senior<\/td>\n<td>310<\/td>\n<td>340<\/td>\n<td>650<\/td>\n<\/tr>\n<tr>\n<td>Total<\/td>\n<td>1610<\/td>\n<td>890<\/td>\n<td>2500<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The table above tells us there are 125 freshmen that commute, while the other 650 freshmen live on campus. The total for that row, 775, gives the total number of freshmen. Similarly, the total of the column \u201cResidential\u201d tells us that 1610 students live on campus.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>What percent of students at the college are seniors who commute?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q449112\">Show Answer<\/span><\/p>\n<div id=\"q449112\" class=\"hidden-answer\" style=\"display: none\">\n<p>Formulate the question as a percent problem.<\/p>\n<p>Identify the percent, the base, and the amount.<\/p>\n<p>Percent: <em>p<\/em><\/p>\n<p>Base: the total number of students is 2500<\/p>\n<p>Amount: the number of students who are seniors who commute is 340<\/p>\n<p>Write the percent equation.<\/p>\n<p style=\"text-align: center;\">[latex]\\mathrm{Percent} \\ \\cdot \\ \\mathrm{Base} \\ = \\ \\mathrm{Amount}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]p \\cdot 2500 = 340[\/latex]<\/p>\n<p>Divide and convert to a percent.<\/p>\n<p style=\"text-align: center;\">[latex]p=\\frac{340}{2500} = 0.136 = (0.136) \\cdot 100 \\% = 13.6 \\%[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]13.6 \\%[\/latex] of students are seniors who commute.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>What percent of juniors live on campus?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q194742\">Show Answer<\/span><\/p>\n<div id=\"q194742\" class=\"hidden-answer\" style=\"display: none\">\n<p>Formulate the question as a percent problem.<\/p>\n<p>Identify the percent, the base, and the amount.<\/p>\n<p>Percent: <em>p<\/em><\/p>\n<p>Base: the total number of juniors is 675<\/p>\n<p>Amount: the number of juniors who live on campus is 350<\/p>\n<p>Write the percent equation.<\/p>\n<p style=\"text-align: center;\">[latex]\\mathrm{Percent} \\ \\cdot \\ \\mathrm{Base} \\ = \\ \\mathrm{Amount}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]p \\cdot 675 = 350[\/latex]<\/p>\n<p>Divide and convert to a percent.<\/p>\n<p style=\"text-align: center;\">[latex]p=\\frac{350}{675} \\approx 0.519 = (0.519) \\cdot 100 \\% = 51.9 \\%[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]51.9 \\%[\/latex] of juniors live on campus.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm232420\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=232420&theme=oea&iframe_resize_id=ohm232420&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-2243\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>QID 232420. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><li><strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":169134,"menu_order":4,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"QID 232420\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"},{\"type\":\"original\",\"description\":\"\",\"author\":\"\",\"organization\":\"Lumen 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