Five Number Summary in Boxplots and Data Sets: Apply It 4

Drawing inferences from boxplots

Now let’s look at the data from the 2017 Tax Reform bill.

The data from the Tax Policy Center in the table below separates income groups into quintiles. Quintiles divide data sets into five parts, from the lowest [latex]20[/latex]% of values up to the highest [latex]20[/latex]% of values.

The Tax Policy Center released the following data about the actual tax cuts households experienced because of the 2017 Tax Reform bill.[1]

Household Tax Cuts
Income Group Mean Tax Cut
Lowest Quintile $[latex]40[/latex]
Second Quintile $[latex]320[/latex]
Middle Quintile $[latex]780[/latex]
Fourth Quintile $[latex]1,480[/latex]
Top Quintile $[latex]5,790[/latex]
Top 1 Percent $[latex]32,650[/latex]
Top 0.1 Percent $[latex]89,060[/latex]

Compare the 2017 Tax Reform data with the hypothetical data displayed in boxplots A and B below:Two box plots. The horizontal axis is labeled "Household Tax Costs ($ thousands) and is numbered in increments of one. The top is labeled A and has its lowest point at zero and its highest at approximately 2.3. The lower end of the box is at approximately 0.5 while the upper end is at approximately 2. The center line is at approximately 1.4. For plot B, the lowest point is at 0 and the highest point is at approximately 1.25. The low end of the box is at approximately 0.05 while the upper end is at approximately 0.5. The middle line is at approximately 0.1. Above the high point of plot B, there are lots of individual dots very close together all the way up the rest of the box plot.

question 9

question 10

question 11

question 12

video placement

Wrap up: “There are many perspectives to take and questions to answer when trying to sort out as complicated a situation as this one. We are only presented a small amount of information in this activity so we limited ourselves to questions we could answer using the data we had. It is of interest, though, to compare these tax cuts given in dollar amounts to their equivalencies in terms of percent of peoples’ incomes. [voice over the table given in the hidden text below]. The Tax Policy Center also provides this information. The top income groups received both the largest cuts in dollar amounts but also the largest percent growth in after-tax income as a result of the bill (the top 0.1 percent don’t follow this trend, however). But hopefully you’ve been able to understand from this activity how boxplots provide a quick glance, a summary, of the data to make comparisons based on median, skew, outliers, and percentiles. Let’s take a look at a few general five-number summaries to make sure you feel good about what you’ve learned here.” — Provide a few five-number summaries and ask students to sketch boxplots of them. Then show the answers for comparison. — “You’ve seen that boxplots provide visual summaries of quantitative variables that can be used to compare the distributions of multiple populations. Hopefully, you feel that you are now comfortable using boxplots to compare and draw inferences.”

 

  1.  Tax Policy Center. (2018, February 16). T18-0025 - The Tax Cuts and Jobs Act (TCJA): All provisions and individual income tax provisions; distribution of federal tax change by expanded cash income percentile, 2018. https://www.taxpolicycenter.org/model-estimates/individual-income-tax-provisions-tax-cuts-and-jobs-act-tcja-february-2018/t18-0025 ↵