{"id":507,"date":"2022-07-11T20:40:46","date_gmt":"2022-07-11T20:40:46","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/alphamodule\/?post_type=chapter&p=507"},"modified":"2022-07-29T00:16:40","modified_gmt":"2022-07-29T00:16:40","slug":"five-number-summary-in-boxplots-and-data-sets-apply-it-3","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/alphamodule\/chapter\/five-number-summary-in-boxplots-and-data-sets-apply-it-3\/","title":{"raw":"Five Number Summary in Boxplots and Data Sets: Apply It 4","rendered":"Five Number Summary in Boxplots and Data Sets: Apply It 4"},"content":{"raw":"

Drawing inferences from boxplots<\/h3>\r\nNow let's look at the data from the 2017 Tax Reform bill.\r\n\r\nThe 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\u00a0[latex]20[\/latex]% of values up to the highest\u00a0[latex]20[\/latex]% of values.\r\n\r\nThe Tax Policy Center released the following data about the actual tax cuts households experienced because of the 2017 Tax Reform bill.[footnote]\u00a0Tax Policy Center. (2018, February 16). T18-0025 - The Tax Cuts and Jobs Act (TCJA): All provisions\u00a0<\/em>and individual income tax provisions; distribution of federal tax change by expanded cash income\u00a0<\/em>percentile, 2018.<\/em> https:\/\/www.taxpolicycenter.org\/model-estimates\/individual-income-tax-provisions-tax-cuts-and-jobs-act-tcja-february-2018\/t18-0025[\/footnote]\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Household Tax Cuts<\/strong><\/td>\r\n<\/tr>\r\n
Income Group<\/strong><\/td>\r\nMean Tax Cut<\/strong><\/td>\r\n<\/tr>\r\n
Lowest Quintile<\/strong><\/td>\r\n$[latex]40[\/latex]<\/td>\r\n<\/tr>\r\n
Second Quintile<\/strong><\/td>\r\n$[latex]320[\/latex]<\/td>\r\n<\/tr>\r\n
Middle Quintile<\/strong><\/td>\r\n$[latex]780[\/latex]<\/td>\r\n<\/tr>\r\n
Fourth Quintile<\/strong><\/td>\r\n$[latex]1,480[\/latex]<\/td>\r\n<\/tr>\r\n
Top Quintile<\/strong><\/td>\r\n$[latex]5,790[\/latex]<\/td>\r\n<\/tr>\r\n
Top 1 Percent<\/strong><\/td>\r\n$[latex]32,650[\/latex]<\/td>\r\n<\/tr>\r\n
Top 0.1 Percent<\/strong><\/td>\r\n$[latex]89,060[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nCompare the 2017 Tax Reform data with the hypothetical data displayed in boxplots A and B below:\"Two<\/strong>\r\n\r\n<\/div>\r\n
\r\n

question 9<\/h3>\r\n[ohm_question hide_question_numbers=1]241184[\/ohm_question]\r\n\r\n[reveal-answer q=\"566117\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"566117\"]What pattern do you notice in the tax cut amounts as the incomes tend to climb? Which quintile do you assume represents the median of the five quintiles? [\/hidden-answer]\r\n\r\n<\/div>\r\n
\r\n

question 10<\/h3>\r\n[ohm_question hide_question_numbers=1]241185[\/ohm_question]\r\n\r\n[reveal-answer q=\"359334\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"359334\"]Compare the maximum listed in the data table to the maximum shown on the graph for Boxplot B.[\/hidden-answer]\r\n\r\n<\/div>\r\n
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question 11<\/h3>\r\n[ohm_question hide_question_numbers=1]241186[\/ohm_question]\r\n\r\n[reveal-answer q=\"942338\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"942338\"]In other words, is the statement factual?[\/hidden-answer]\r\n\r\n<\/div>\r\n
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question 12<\/h3>\r\n[ohm_question hide_question_numbers=1]241187[\/ohm_question]\r\n\r\n[reveal-answer q=\"194601\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"194601\"]If you consider possible skew due to outliers in the data set, how do you think the value $[latex]1,260[\/latex] was generated? How does that number compare with what you understand from the data table to be the \"typical\" American household?[\/hidden-answer]\r\n\r\n<\/div>\r\n
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video placement<\/h3>\r\nWrap 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<\/em>. [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.\"<\/span>\r\n\r\n<\/div>\r\n[reveal-answer q=\"825052\"]Percent Change in After-Tax Income by Income Group[\/reveal-answer]\r\n[hidden-answer a=\"825052\"]\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
After-Tax Income by Income Group<\/strong><\/td>\r\n<\/tr>\r\n
Income Group<\/strong><\/td>\r\nPercent Change in After-Tax Income<\/strong><\/td>\r\n<\/tr>\r\n
Lowest Quintile<\/strong><\/td>\r\n[latex]0.3[\/latex]%<\/td>\r\n<\/tr>\r\n
Second Quintile<\/strong><\/td>\r\n[latex]1.0[\/latex]%<\/td>\r\n<\/tr>\r\n
Middle Quintile<\/strong><\/td>\r\n[latex]1.4[\/latex]%<\/td>\r\n<\/tr>\r\n
Fourth Quintile<\/strong><\/td>\r\n[latex]1.6[\/latex]%<\/td>\r\n<\/tr>\r\n
Top Quintile<\/strong><\/td>\r\n[latex]2.2[\/latex]%<\/td>\r\n<\/tr>\r\n
Top 1 Percent<\/strong><\/td>\r\n[latex]2.2[\/latex]%<\/td>\r\n<\/tr>\r\n
Top 0.1 Percent<\/strong><\/td>\r\n[latex]1.3[\/latex]%<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n ","rendered":"

Drawing inferences from boxplots<\/h3>\n

Now let’s look at the data from the 2017 Tax Reform bill.<\/p>\n

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\u00a0[latex]20[\/latex]% of values up to the highest\u00a0[latex]20[\/latex]% of values.<\/p>\n

The Tax Policy Center released the following data about the actual tax cuts households experienced because of the 2017 Tax Reform bill.[1]<\/sup><\/a><\/p>\n

\n\n\n\n\n\n\n\n\n\n\n\n
Household Tax Cuts<\/strong><\/td>\n<\/tr>\n
Income Group<\/strong><\/td>\nMean Tax Cut<\/strong><\/td>\n<\/tr>\n
Lowest Quintile<\/strong><\/td>\n$[latex]40[\/latex]<\/td>\n<\/tr>\n
Second Quintile<\/strong><\/td>\n$[latex]320[\/latex]<\/td>\n<\/tr>\n
Middle Quintile<\/strong><\/td>\n$[latex]780[\/latex]<\/td>\n<\/tr>\n
Fourth Quintile<\/strong><\/td>\n$[latex]1,480[\/latex]<\/td>\n<\/tr>\n
Top Quintile<\/strong><\/td>\n$[latex]5,790[\/latex]<\/td>\n<\/tr>\n
Top 1 Percent<\/strong><\/td>\n$[latex]32,650[\/latex]<\/td>\n<\/tr>\n
Top 0.1 Percent<\/strong><\/td>\n$[latex]89,060[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Compare the 2017 Tax Reform data with the hypothetical data displayed in boxplots A and B below:\"Two<\/strong><\/p>\n<\/div>\n

\n

question 9<\/h3>\n