{"id":527,"date":"2022-07-11T20:40:44","date_gmt":"2022-07-11T20:40:44","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/alphamodule\/?post_type=chapter&p=527"},"modified":"2022-07-29T00:15:02","modified_gmt":"2022-07-29T00:15:02","slug":"five-number-summary-in-boxplots-and-data-sets-apply-it-2","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/alphamodule\/chapter\/five-number-summary-in-boxplots-and-data-sets-apply-it-2\/","title":{"raw":"Five Number Summary in Boxplots and Data Sets: Apply It 2","rendered":"Five Number Summary in Boxplots and Data Sets: Apply It 2"},"content":{"raw":"

Comparing Multiple Distributions<\/h3>\r\nSince we'll be using data from the Tax Policy Center to analyze the claims made in the two quotes above, let's first investigate a statement the Center made about the\u00a0average<\/em> tax cut experienced from the law.\r\n\r\nAccording to the independent Tax Policy Center, the average income tax cut as a result of the law was $[latex]1,260[\/latex].[footnote] Tax Policy Center. (2018, February 16).\u00a0T18-0025 - 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.\u00a0<\/em>htpps:\/\/www.taxpolicycenter.org\/model-estimates\/individual-income-tax-provisions-tax-cuts-and-jobs-act-tcja-february-2019\/t18-0025[\/footnote] However, as we\u2019ve seen before, averages can be misleading and uninformative.\r\n\r\nTwo boxplots are provided below, each displaying a hypothetical<\/em> distribution of\u00a0[latex]5,000[\/latex] tax cuts that would result in a mean tax cut of $[latex]1,260[\/latex].\r\n\r\n\"Two<\/strong>\r\n
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question 2<\/h3>\r\n[ohm_question hide_question_numbers=1]241161[\/ohm_question]\r\n\r\n[reveal-answer q=\"223883\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"223883\"]Remember that the scale of the graph shows tax cuts in thousands of dollars. Where is the value $[latex]500[\/latex] located on the graph?[\/hidden-answer]\r\n\r\n<\/div>\r\n
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question 3<\/h3>\r\n[ohm_question hide_question_numbers=1]241162[\/ohm_question]\r\n\r\n[reveal-answer q=\"539176\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"539176\"]Recall where to find Q1, Median, and Q3 on the boxplot. Which of these is located at the $[latex]500[\/latex] mark on the graph?[\/hidden-answer]\r\n\r\n<\/div>\r\nNow, let's compare these distributions.\r\n
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question 4<\/h3>\r\n[ohm_question hide_question_numbers=1]241163[\/ohm_question]\r\n\r\n[reveal-answer q=\"562548\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"562548\"]What measure of center is displayed in a boxplot?[\/hidden-answer]\r\n\r\n<\/div>\r\n
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question 5<\/h3>\r\n[ohm_question hide_question_numbers=1]241164[\/ohm_question]\r\n\r\n[reveal-answer q=\"39682\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"39682\"]Which IQR is wider? Which range is larger?[\/hidden-answer]\r\n\r\n<\/div>\r\n
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question 6<\/h3>\r\n[ohm_question hide_question_numbers=1]241165 [\/ohm_question]\r\n\r\n[reveal-answer q=\"348809\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"348809\"]Use the presence (or lack of) outliers to help identify the shapes.[\/hidden-answer]\r\n\r\n<\/div>\r\n","rendered":"

Comparing Multiple Distributions<\/h3>\n

Since we’ll be using data from the Tax Policy Center to analyze the claims made in the two quotes above, let’s first investigate a statement the Center made about the\u00a0average<\/em> tax cut experienced from the law.<\/p>\n

According to the independent Tax Policy Center, the average income tax cut as a result of the law was $[latex]1,260[\/latex].[1]<\/sup><\/a> However, as we\u2019ve seen before, averages can be misleading and uninformative.<\/p>\n

Two boxplots are provided below, each displaying a hypothetical<\/em> distribution of\u00a0[latex]5,000[\/latex] tax cuts that would result in a mean tax cut of $[latex]1,260[\/latex].<\/p>\n

\"Two<\/strong><\/p>\n

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question 2<\/h3>\n