{"id":3929,"date":"2022-03-16T18:01:26","date_gmt":"2022-03-16T18:01:26","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=3929"},"modified":"2022-03-17T03:45:39","modified_gmt":"2022-03-17T03:45:39","slug":"five-number-summary-in-boxplots-and-datasets","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/five-number-summary-in-boxplots-and-datasets\/","title":{"raw":"Instructor Guide Five Number Summary in Boxplots and Datasets: Forming Connections","rendered":"Instructor Guide Five Number Summary in Boxplots and Datasets: Forming Connections"},"content":{"raw":"<h2>Overview<\/h2>\r\n<ul>\r\n \t<li>Students will compare boxplots to assess the effectiveness of\u00a0public policy.<\/li>\r\n \t<li>This activity connects back to calculations of measures of center and spread, and prepares students to perform analyses of univariate data.<\/li>\r\n \t<li>Additional context: The dataset used in this activity comes from the independent Tax Policy Center, which is a non-partisan group. Specifically, students will look at their distributional tables of tax cuts by income levels, which were constructed in February 2018. You can view these directly at this link: https:\/\/www.taxpolicycenter.org\/model-estimates\/individual-income-tax-provisions-tax-cuts-and-jobs-act-tcja-february-2018\/t18-0025.<\/li>\r\n \t<li><span style=\"background-color: #ffff99;\">V3, S4, V4, C3, C5, S2, C4, O2, C2 \u2190 Link to EBTP descriptions\u00a0<\/span><\/li>\r\n<\/ul>\r\n<h3>Prerequisite assumptions<\/h3>\r\nStudents should be able to do each of the following after completing the <em>What to Know<\/em> assignment.\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Identity and interpret the features of a boxplot.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Identify outliers in a dataset.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Relate a boxplot of a quantitative variable to its distribution.<\/li>\r\n<\/ul>\r\n<h3>Intended goals for this activity<\/h3>\r\nAfter completing this activity, students should understand that boxplots provide visual summaries of quantitative variables, and can\u00a0be used to compare the distributions of multiple populations. They should be able to compare and draw inferences from boxplots.\r\n<h2>Synchronous Delivery and Activity Flow<\/h2>\r\nThe sample activity delivery below assumes a face-to-face class meeting but can be adapted to a fully online or hybrid delivery by using break-out rooms for pairs and small groups.\r\n<h3>Frame the activity (3 minutes)<\/h3>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Note that this activity aims to sharpen students\u2019 skills in public policy\u00a0analysis. As a class, they will undertake this goal in a non-partisan\u00a0and analytical framework. However, there will be room for discussion. V3<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Have students read and answer Question 1 independently. Then,\u00a0have students discuss their answers in pairs before sharing with the\u00a0full group. S4<\/li>\r\n \t<li aria-level=\"1\">Transition to the in-class activity by briefly discussing the objectives\u00a0for the activity.<\/li>\r\n<\/ul>\r\n<h3>Activity Flow (18 minutes)<\/h3>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Students may answer Questions 2 - 8 in pairs or small groups. V4\r\n<ul>\r\n \t<li aria-level=\"1\">As you hear student conversations, remind them that these are\u00a0possible distributions of the tax cuts\u2014not income levels. Remind\u00a0students of the scale (thousands of $). C3<\/li>\r\n \t<li aria-level=\"1\">Have at least one group share with the full class how they\u00a0answered Questions 7 and 8. S4<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Students continue in groups to answer Questions 9 and 10. Guiding questions include:\r\n<ul>\r\n \t<li aria-level=\"1\">\u201cWhat does a quartile mean? Ok, so now think: what do\u00a0you think a quintile is?\u201d<\/li>\r\n \t<li aria-level=\"1\">\u201cWhat pattern do you notice in the tax cut amounts as the\u00a0incomes tend to climb? How might this inform where you\u00a0think the median tax cut amount is?\u201d<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Use a whole-class discussion for Questions 11 and 12.\u00a0Have students first independently write their own answers in\r\ncomplete sentences. Optionally, give them a chance to share with\u00a0other pairs before starting the\u00a0 whole-class discussion. C5\r\n<ul>\r\n \t<li>To help keep the conversation focused and productive, as needed, encourage students who try to tackle the complex relationships between tax cuts, economic growth, and the national debt to answer only the questions for which they are given data (the questions on the page).<\/li>\r\n \t<li>The data are provided in terms of dollar amounts. However, some\u00a0students may want to know about tax cuts in terms of the percent of\u00a0peoples\u2019 incomes. The Tax Policy Center also provides this\u00a0information. It is linked at the bottom of the activity page.\r\n<ul>\r\n \t<li>[reveal-answer q=\"825052\"]Percent Change in After-Tax Income by Income Group[\/reveal-answer]\r\n[hidden-answer a=\"825052\"]\r\n<table style=\"border-collapse: collapse; width: 49.3841%; height: 112px;\" border=\"1\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%; text-align: center;\" colspan=\"2\"><strong>After-Tax Income by Income Group<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 50%; height: 14px; text-align: center;\"><strong>Income Group<\/strong><\/td>\r\n<td style=\"width: 50%; height: 14px; text-align: center;\"><strong>Percent Change in After-Tax Income<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 50%; height: 14px; text-align: center;\"><strong>Lowest Quintile<\/strong><\/td>\r\n<td style=\"width: 50%; height: 14px; text-align: center;\">[latex]0.3[\/latex]%<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 50%; height: 14px; text-align: center;\"><strong>Second Quintile<\/strong><\/td>\r\n<td style=\"width: 50%; height: 14px; text-align: center;\">[latex]1.0[\/latex]%<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 50%; height: 14px; text-align: center;\"><strong>Middle Quintile<\/strong><\/td>\r\n<td style=\"width: 50%; height: 14px; text-align: center;\">[latex]1.4[\/latex]%<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 50%; height: 14px; text-align: center;\"><strong>Fourth Quintile<\/strong><\/td>\r\n<td style=\"width: 50%; height: 14px; text-align: center;\">[latex]1.6[\/latex]%<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 50%; height: 14px; text-align: center;\"><strong>Top Quintile<\/strong><\/td>\r\n<td style=\"width: 50%; height: 14px; text-align: center;\">[latex]2.2[\/latex]%<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 50%; height: 14px; text-align: center;\"><strong>Top 1 Percent<\/strong><\/td>\r\n<td style=\"width: 50%; height: 14px; text-align: center;\">[latex]2.2[\/latex]%<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 50%; height: 14px; text-align: center;\"><strong>Top 0.1 Percent<\/strong><\/td>\r\n<td style=\"width: 50%; height: 14px; text-align: center;\">[latex]1.3[\/latex]%<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\nImportantly, the top income groups not only tended to receive higher tax\u00a0cuts in dollar amounts, but they also tended to receive the largest\u00a0percent growth in after-tax income as a result of the bill. However, the\r\ntop 0.1 percent of income earners do not fit this trend.[\/hidden-answer]<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h3>Wrap-up\/transition (5 minutes)<\/h3>\r\n<ul>\r\n \t<li>As a final formative assessment, consider giving students various\u00a0five-number summaries and have them draw boxplots. Have\u00a0students compare their distributions. C3<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Have students refer back to the Objectives for the activity and identify ones they recognized completing. S2, C4, O2<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Assign the homework or\u00a0<em>Practice<\/em>\u00a0and any <em>What to Know<\/em> pages for the <em>Forming Connections<\/em> activities you plan to complete in the next class meeting. C2<\/li>\r\n<\/ul>","rendered":"<h2>Overview<\/h2>\n<ul>\n<li>Students will compare boxplots to assess the effectiveness of\u00a0public policy.<\/li>\n<li>This activity connects back to calculations of measures of center and spread, and prepares students to perform analyses of univariate data.<\/li>\n<li>Additional context: The dataset used in this activity comes from the independent Tax Policy Center, which is a non-partisan group. Specifically, students will look at their distributional tables of tax cuts by income levels, which were constructed in February 2018. You can view these directly at this link: https:\/\/www.taxpolicycenter.org\/model-estimates\/individual-income-tax-provisions-tax-cuts-and-jobs-act-tcja-february-2018\/t18-0025.<\/li>\n<li><span style=\"background-color: #ffff99;\">V3, S4, V4, C3, C5, S2, C4, O2, C2 \u2190 Link to EBTP descriptions\u00a0<\/span><\/li>\n<\/ul>\n<h3>Prerequisite assumptions<\/h3>\n<p>Students should be able to do each of the following after completing the <em>What to Know<\/em> assignment.<\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Identity and interpret the features of a boxplot.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Identify outliers in a dataset.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Relate a boxplot of a quantitative variable to its distribution.<\/li>\n<\/ul>\n<h3>Intended goals for this activity<\/h3>\n<p>After completing this activity, students should understand that boxplots provide visual summaries of quantitative variables, and can\u00a0be used to compare the distributions of multiple populations. They should be able to compare and draw inferences from boxplots.<\/p>\n<h2>Synchronous Delivery and Activity Flow<\/h2>\n<p>The sample activity delivery below assumes a face-to-face class meeting but can be adapted to a fully online or hybrid delivery by using break-out rooms for pairs and small groups.<\/p>\n<h3>Frame the activity (3 minutes)<\/h3>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Note that this activity aims to sharpen students\u2019 skills in public policy\u00a0analysis. As a class, they will undertake this goal in a non-partisan\u00a0and analytical framework. However, there will be room for discussion. V3<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Have students read and answer Question 1 independently. Then,\u00a0have students discuss their answers in pairs before sharing with the\u00a0full group. S4<\/li>\n<li aria-level=\"1\">Transition to the in-class activity by briefly discussing the objectives\u00a0for the activity.<\/li>\n<\/ul>\n<h3>Activity Flow (18 minutes)<\/h3>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Students may answer Questions 2 &#8211; 8 in pairs or small groups. V4\n<ul>\n<li aria-level=\"1\">As you hear student conversations, remind them that these are\u00a0possible distributions of the tax cuts\u2014not income levels. Remind\u00a0students of the scale (thousands of $). C3<\/li>\n<li aria-level=\"1\">Have at least one group share with the full class how they\u00a0answered Questions 7 and 8. S4<\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Students continue in groups to answer Questions 9 and 10. Guiding questions include:\n<ul>\n<li aria-level=\"1\">\u201cWhat does a quartile mean? Ok, so now think: what do\u00a0you think a quintile is?\u201d<\/li>\n<li aria-level=\"1\">\u201cWhat pattern do you notice in the tax cut amounts as the\u00a0incomes tend to climb? How might this inform where you\u00a0think the median tax cut amount is?\u201d<\/li>\n<\/ul>\n<\/li>\n<li>Use a whole-class discussion for Questions 11 and 12.\u00a0Have students first independently write their own answers in<br \/>\ncomplete sentences. Optionally, give them a chance to share with\u00a0other pairs before starting the\u00a0 whole-class discussion. C5<\/p>\n<ul>\n<li>To help keep the conversation focused and productive, as needed, encourage students who try to tackle the complex relationships between tax cuts, economic growth, and the national debt to answer only the questions for which they are given data (the questions on the page).<\/li>\n<li>The data are provided in terms of dollar amounts. However, some\u00a0students may want to know about tax cuts in terms of the percent of\u00a0peoples\u2019 incomes. The Tax Policy Center also provides this\u00a0information. It is linked at the bottom of the activity page.\n<ul>\n<li>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q825052\">Percent Change in After-Tax Income by Income Group<\/span><\/p>\n<div id=\"q825052\" class=\"hidden-answer\" style=\"display: none\">\n<table style=\"border-collapse: collapse; width: 49.3841%; height: 112px;\">\n<tbody>\n<tr>\n<td style=\"width: 50%; text-align: center;\" colspan=\"2\"><strong>After-Tax Income by Income Group<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px; text-align: center;\"><strong>Income Group<\/strong><\/td>\n<td style=\"width: 50%; height: 14px; text-align: center;\"><strong>Percent Change in After-Tax Income<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px; text-align: center;\"><strong>Lowest Quintile<\/strong><\/td>\n<td style=\"width: 50%; height: 14px; text-align: center;\">[latex]0.3[\/latex]%<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px; text-align: center;\"><strong>Second Quintile<\/strong><\/td>\n<td style=\"width: 50%; height: 14px; text-align: center;\">[latex]1.0[\/latex]%<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px; text-align: center;\"><strong>Middle Quintile<\/strong><\/td>\n<td style=\"width: 50%; height: 14px; text-align: center;\">[latex]1.4[\/latex]%<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px; text-align: center;\"><strong>Fourth Quintile<\/strong><\/td>\n<td style=\"width: 50%; height: 14px; text-align: center;\">[latex]1.6[\/latex]%<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px; text-align: center;\"><strong>Top Quintile<\/strong><\/td>\n<td style=\"width: 50%; height: 14px; text-align: center;\">[latex]2.2[\/latex]%<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px; text-align: center;\"><strong>Top 1 Percent<\/strong><\/td>\n<td style=\"width: 50%; height: 14px; text-align: center;\">[latex]2.2[\/latex]%<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px; text-align: center;\"><strong>Top 0.1 Percent<\/strong><\/td>\n<td style=\"width: 50%; height: 14px; text-align: center;\">[latex]1.3[\/latex]%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>Importantly, the top income groups not only tended to receive higher tax\u00a0cuts in dollar amounts, but they also tended to receive the largest\u00a0percent growth in after-tax income as a result of the bill. However, the<br \/>\ntop 0.1 percent of income earners do not fit this trend.<\/p><\/div>\n<\/div>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3>Wrap-up\/transition (5 minutes)<\/h3>\n<ul>\n<li>As a final formative assessment, consider giving students various\u00a0five-number summaries and have them draw boxplots. Have\u00a0students compare their distributions. C3<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Have students refer back to the Objectives for the activity and identify ones they recognized completing. S2, C4, O2<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Assign the homework or\u00a0<em>Practice<\/em>\u00a0and any <em>What to Know<\/em> pages for the <em>Forming Connections<\/em> activities you plan to complete in the next class meeting. C2<\/li>\n<\/ul>\n","protected":false},"author":25777,"menu_order":18,"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-3929","chapter","type-chapter","status-publish","hentry"],"part":3890,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3929","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/25777"}],"version-history":[{"count":7,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3929\/revisions"}],"predecessor-version":[{"id":4064,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3929\/revisions\/4064"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/3890"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3929\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=3929"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=3929"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=3929"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=3929"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}