Question

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

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:

$77,500$