Question

this table shows historical tax bracket data for the u.s. comparing historical tax rates tax data historical tax data years a 1987 1997 mean standard deviation taxable income: single b $0 to $1,800 $1,801 to $16,800 $16,801 to $27,000 $27,001 to $54,000 $54,001 and up $0 to $24,650 $24,651 to $59,750 $59,751 to $124,650 rate c 11 15 28 35 38.5 22.5 12.103718 15 28 31 which statement is true about the tax rates in the periods 1987 and 1997? the tax rates in 1987 have a greater mean than the rates in 1997. the tax rates in 1997 have a greater mean than the rates in 1987. the tax rates in 1987 and 1997 have the same mean and standard deviation. the tax rates in 1997 have a greater standard deviation than the rates in 1987.

Explanation:

Step1: Identify tax - rate data for 1987 and 1997

For 1987: 11, 15, 28, 35, 38.5
For 1997: 15, 28, 31, 12.103718, 22.5

Step2: Calculate the mean for 1987

Mean of 1987 rates = $\frac{11 + 15+28+35+38.5}{5}=\frac{127.5}{5}=25.5$

Step3: Calculate the mean for 1997

Mean of 1997 rates = $\frac{15 + 28+31+12.103718+22.5}{5}=\frac{108.603718}{5}=21.7207436$

Step4: Compare the means

Since $25.5>21.7207436$, the tax - rates in 1987 have a greater mean than the rates in 1997.

Answer:

The tax rates in 1987 have a greater mean than the rates in 1997.