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# Chapter 3 - Chapter 3 3.1 a The most interesting aspect of...

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Chapter 3 3.1 a The most interesting aspect of the table is the small number of taxpayers who pay a large amount of income tax and the large number of taxpayers who pay little. Additionally, the table tells us that the results are stable over the eight-year period. b There are several ways to graphically display the numbers. The figure shown next is a two-dimensional bar chart that shows are five years and displays the average return and the numbers of taxpayers in each category. Returns Average 0 500,000 1,000,000 1,500,000 1 3 5 7 9 11 13 15 17 19 21 N um b e ro fre tu rn s (1 , 0 ) Taxable Income categories Bar Chart Returns Average Returns Average Returns Average Returns Average Returns We can also show each year separately. Here is the most recent years, 2002. 0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1 2 3 4 5 6 7 8 9 101112131415161718192021 Taxable income categories Bar Chart 2002 Returns 2002 Average 77

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c The drawback is that it is difficult to interpret. The cause of the problem is that there are very large and very small numbers. Moreover there are too many categories. We can solve the latter problem by grouping some categories. 3.2 We can draw a bar chart showing number of returns and the average paid by taxpayers for each of the five taxable income categories for all five years. 0 20,000 40,000 60,000 80,000 N um b e r A ve ra g e N um b e r A ve ra g e N um b e r A ve ra g e N um b e r A ve ra g e N um b e r A ve ra g e 1995 1995 1997 1997 1999 1999 2000 2000 2002 2002 Bar Chart However the problem of the difficulty of interpretation remains. Here is another way of representing the numbers. The table below converts the number of taxpayers in each category to the proportion of the total number of taxpayers. It also converts the average tax in each category to the proportion of the total amount of income tax. 1 2 3 4 5 6 7 A B C D E F G H I J K 1995 1995 1997 1997 1999 1999 2000 2000 2002 2002 Taxable Inc Prop Prop Prop Prop Prop Prop Prop Prop Prop Prop < 25,000 0.546 0.067 0.513 0.064 0.483 0.044 0.468 0.048 0.457 0.046 25,000-49,999 0.248 0.148 0.252 0.146 0.248 0.114 0.250 0.107 0.255 0.112 50,000-74,999 0.116 0.157 0.124 0.148 0.132 0.128 0.132 0.116 0.134 0.125 75,000-00,000 0.045 0.120 0.053 0.107 0.061 0.104 0.066 0.099 0.071 0.113 Over 100,000 0.045 0.508 0.059 0.534 0.075 0.611 0.084 0.630 0.083 0.603 The graph that follows depicts these numbers.
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Chapter 3 - Chapter 3 3.1 a The most interesting aspect of...

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