Overview

• Students will compare boxplots to assess the effectiveness of public policy.
• This activity connects back to calculations of measures of center and spread, and prepares students to perform analyses of univariate data.
• 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.
• V3, S4, V4, C3, C5, S2, C4, O2, C2 ← Link to EBTP descriptions 

Prerequisite assumptions

Students should be able to do each of the following after completing the What to Know assignment.

• Identity and interpret the features of a boxplot.
• Identify outliers in a dataset.
• Relate a boxplot of a quantitative variable to its distribution.

Intended goals for this activity

After completing this activity, students should understand that boxplots provide visual summaries of quantitative variables, and can be used to compare the distributions of multiple populations. They should be able to compare and draw inferences from boxplots.

Synchronous Delivery and Activity Flow

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.

Frame the activity (3 minutes)

• Note that this activity aims to sharpen students’ skills in public policy analysis. As a class, they will undertake this goal in a non-partisan and analytical framework. However, there will be room for discussion. V3
• Have students read and answer Question 1 independently. Then, have students discuss their answers in pairs before sharing with the full group. S4
• Transition to the in-class activity by briefly discussing the objectives for the activity.

Activity Flow (18 minutes)

• Students may answer Questions 2 – 8 in pairs or small groups. V4
  • As you hear student conversations, remind them that these are possible distributions of the tax cuts—not income levels. Remind students of the scale (thousands of $). C3
  • Have at least one group share with the full class how they answered Questions 7 and 8. S4
• Students continue in groups to answer Questions 9 and 10. Guiding questions include:
  • “What does a quartile mean? Ok, so now think: what do you think a quintile is?”
  • “What pattern do you notice in the tax cut amounts as the incomes tend to climb? How might this inform where you think the median tax cut amount is?”
• Use a whole-class discussion for Questions 11 and 12. Have students first independently write their own answers in
  complete sentences. Optionally, give them a chance to share with other pairs before starting the  whole-class discussion. C5
  • 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).
  • The data are provided in terms of dollar amounts. However, some students may want to know about tax cuts in terms of the percent of peoples’ incomes. The Tax Policy Center also provides this information. It is linked at the bottom of the activity page.
    • Percent Change in After-Tax Income by Income Group

      After-Tax Income by Income Group
      Income Group	Percent Change in After-Tax Income
      Lowest Quintile	[latex]0.3[/latex]%
      Second Quintile	[latex]1.0[/latex]%
      Middle Quintile	[latex]1.4[/latex]%
      Fourth Quintile	[latex]1.6[/latex]%
      Top Quintile	[latex]2.2[/latex]%
      Top 1 Percent	[latex]2.2[/latex]%
      Top 0.1 Percent	[latex]1.3[/latex]%

       

      Importantly, the top income groups not only tended to receive higher tax cuts in dollar amounts, but they also tended to receive the largest percent growth in after-tax income as a result of the bill. However, the
      top 0.1 percent of income earners do not fit this trend.

Wrap-up/transition (5 minutes)

• As a final formative assessment, consider giving students various five-number summaries and have them draw boxplots. Have students compare their distributions. C3
• Have students refer back to the Objectives for the activity and identify ones they recognized completing. S2, C4, O2
• Assign the homework or Practice and any What to Know pages for the Forming Connections activities you plan to complete in the next class meeting. C2