Question

tax data calculating variance
refunds for various taxpayers.
what is the variance of the income in the sample tax data? round answer to the nearest whole number. enter your answer in the box.

tax id	income ($)	tax paid ($)	deductions ($)	tax refund ($)
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
id009	95,000	16,000	10,500	900
id010	55,000	8,000	5,500	700

Explanation:

Step1: Calculate the mean

Let the incomes be $x_1 = 75000,x_2 = 50000,\cdots,x_{10}=55000$. The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$, where $n = 10$.
$\sum_{i=1}^{10}x_i=75000 + 50000+90000+120000+45000+110000+65000+80000+95000+55000 = 880000$
$\bar{x}=\frac{880000}{10}=88000$

Step2: Calculate the squared - differences

The formula for the squared - difference is $(x_i-\bar{x})^2$.
For $x_1 = 75000$, $(x_1 - \bar{x})^2=(75000 - 88000)^2=(- 13000)^2 = 169000000$
For $x_2 = 50000$, $(x_2-\bar{x})^2=(50000 - 88000)^2=(-38000)^2 = 1444000000$
And so on for all $i$ from $1$ to $10$.

Step3: Calculate the variance

The formula for the sample variance $s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}$.
$\sum_{i=1}^{10}(x_i - \bar{x})^2=169000000+1444000000+\cdots$
After calculating all the squared - differences and summing them up, $\sum_{i=1}^{10}(x_i - \bar{x})^2 = 7924000000$
$s^2=\frac{7924000000}{9}\approx880444444$

Answer:

$880444444$