Question

the table presents detailed tax data for 10 individuals, including their respective incomes, taxes paid, deductions, and tax refunds.

what is the standard deviation of the incomes in the sample tax data? round your answer to the nearest whole number.

enter your answer in the box.

Explanation:

Step1: Calculate sample mean

First, sum all incomes then divide by sample size $n=10$.
Sum of incomes:
$78340 + 51270 + 114950 + 88560 + 47380 + 104870 + 67490 + 83240 + 91760 + 57210 = 785070$
Mean $\bar{x} = \frac{785070}{10} = 78507$

Step2: Compute squared deviations

For each income $x_i$, calculate $(x_i - \bar{x})^2$:
$(78340-78507)^2 = (-167)^2 = 27889$
$(51270-78507)^2 = (-27237)^2 = 741854169$
$(114950-78507)^2 = (36443)^2 = 1328092249$
$(88560-78507)^2 = (10053)^2 = 101062809$
$(47380-78507)^2 = (-31127)^2 = 968889129$
$(104870-78507)^2 = (26363)^2 = 694907769$
$(67490-78507)^2 = (-11017)^2 = 121374289$
$(83240-78507)^2 = (4733)^2 = 22401289$
$(91760-78507)^2 = (13253)^2 = 175642009$
$(57210-78507)^2 = (-21297)^2 = 453562209$

Step3: Sum squared deviations

Add all the squared deviations:
$27889 + 741854169 + 1328092249 + 101062809 + 968889129 + 694907769 + 121374289 + 22401289 + 175642009 + 453562209 = 4607813810$

Step4: Calculate sample variance

Divide the sum by $n-1=9$:
$s^2 = \frac{4607813810}{9} \approx 511979312.22$

Step5: Find sample standard deviation

Take the square root of the variance:
$s = \sqrt{511979312.22} \approx 22627$

Answer:

22627