tax data calculating variance\nrefunds for various taxpayers.\nwhat is the variance of the income in the…

tax data calculating variance\nrefunds for various taxpayers.\nwhat is the variance of the income in the sample tax data? round answer to the nearest whole number. enter your answer in the box.\n| tax id | income ($) | tax paid ($) | deductions ($) | tax refund ($) |\n| ---- | ---- | ---- | ---- | ---- |\n| id001 | 75,000 | 12,000 | 8,000 | 500 |\n| id002 | 50,000 | 7,500 | 5,000 | 700 |\n| id003 | 90,000 | 15,000 | 10,000 | 800 |\n| id004 | 120,000 | 24,000 | 12,000 | 1,200 |\n| id005 | 45,000 | 6,000 | 4,500 | 600 |\n| id006 | 110,000 | 22,000 | 11,000 | 1,100 |\n| id007 | 65,000 | 10,000 | 7,000 | 650 |\n| id008 | 80,000 | 13,000 | 9,000 | 750 |\n| id009 | 95,000 | 16,000 | 10,500 | 900 |\n| id010 | 55,000 | 8,000 | 5,500 | 700 |

tax data calculating variance\nrefunds for various taxpayers.\nwhat is the variance of the income in the sample tax data? round answer to the nearest whole number. enter your answer in the box.\n| tax id | income ($) | tax paid ($) | deductions ($) | tax refund ($) |\n| ---- | ---- | ---- | ---- | ---- |\n| id001 | 75,000 | 12,000 | 8,000 | 500 |\n| id002 | 50,000 | 7,500 | 5,000 | 700 |\n| id003 | 90,000 | 15,000 | 10,000 | 800 |\n| id004 | 120,000 | 24,000 | 12,000 | 1,200 |\n| id005 | 45,000 | 6,000 | 4,500 | 600 |\n| id006 | 110,000 | 22,000 | 11,000 | 1,100 |\n| id007 | 65,000 | 10,000 | 7,000 | 650 |\n| id008 | 80,000 | 13,000 | 9,000 | 750 |\n| id009 | 95,000 | 16,000 | 10,500 | 900 |\n| id010 | 55,000 | 8,000 | 5,500 | 700 |

Answer

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:

$880444444$