overview of taxpayer data. the table shows the breakdown of income, taxes paid, deductions, and tax refunds…

overview of taxpayer data. the table shows the breakdown of income, taxes paid, deductions, and tax refunds for various taxpayers. tax id, income ($), tax paid ($), deductions ($), tax refund ($). id001, 75,000, 12,000, 8,000, 500. id002, 50,000, 7,500, 5,000, 700. id003, 90,000, 15,000, 10,000, 800. id004, 120,000, 24,000, 12,000, 1,200. id005, 45,000, 6,000, 4,500, 600. id006, 110,000, 22,000, 11,000, 1,100. id007, 65,000, 10,000, 7,000, 650. id008, 80,000, 13,000, 9,000, 750. what is the median income of the sample tax data? $75,000, $77,500, $78,500, $100,000

overview of taxpayer data. the table shows the breakdown of income, taxes paid, deductions, and tax refunds for various taxpayers. tax id, income ($), tax paid ($), deductions ($), tax refund ($). id001, 75,000, 12,000, 8,000, 500. id002, 50,000, 7,500, 5,000, 700. id003, 90,000, 15,000, 10,000, 800. id004, 120,000, 24,000, 12,000, 1,200. id005, 45,000, 6,000, 4,500, 600. id006, 110,000, 22,000, 11,000, 1,100. id007, 65,000, 10,000, 7,000, 650. id008, 80,000, 13,000, 9,000, 750. what is the median income of the sample tax data? $75,000, $77,500, $78,500, $100,000

Answer

Explanation:

Step1: List income values

$45000, 50000, 65000, 75000, 80000, 90000, 110000, 120000$

Step2: Determine number of values

There are $n = 8$ values. Since $n$ is even, the median is the average of the $\frac{n}{2}$-th and $(\frac{n}{2}+ 1)$-th ordered - values.

Step3: Find the two middle - values

$\frac{n}{2}=\frac{8}{2}=4$ and $\frac{n}{2}+1 = 5$. The 4th value is $75000$ and the 5th value is $80000$.

Step4: Calculate the median

Median=$\frac{75000 + 80000}{2}=\frac{155000}{2}=77500$

Answer:

$77,500$