For given sample of salaries of four employees, the variance of their salaries is: 26 thousands of dollars
The formula for the variance is,
![S^2=\frac{\sum (x_i - \bar{x})^2}{n-1}](https://tex.z-dn.net/?f=S%5E2%3D%5Cfrac%7B%5Csum%20%28x_i%20-%20%5Cbar%7Bx%7D%29%5E2%7D%7Bn-1%7D)
where,
= sample variance
= the value of the one observation
= the mean value of all observations
n = the number of observations
For given question,
n = 4
First we find the mean of their salaries.
(33 + 31 + 24 + 36 ) / 4 = 31
So, ![\bar{x}=31](https://tex.z-dn.net/?f=%5Cbar%7Bx%7D%3D31)
Using the formula for variance ,
![S^2=\frac{(33-31)^2}{4-1}+\frac{(31-31)^2}{4-1}+\frac{(24-31)^2}{4-1}+\frac{(36-31)^2}{4-1}\\\\ S^2=\frac{4}{3} + \frac{0}{3} + \frac{49}{3} + \frac{25}{3} \\\\S^2= \frac{4+49+25}{3}\\\\S^2=\frac{78}{3} \\\\S^2=26](https://tex.z-dn.net/?f=S%5E2%3D%5Cfrac%7B%2833-31%29%5E2%7D%7B4-1%7D%2B%5Cfrac%7B%2831-31%29%5E2%7D%7B4-1%7D%2B%5Cfrac%7B%2824-31%29%5E2%7D%7B4-1%7D%2B%5Cfrac%7B%2836-31%29%5E2%7D%7B4-1%7D%5C%5C%5C%5C%20S%5E2%3D%5Cfrac%7B4%7D%7B3%7D%20%20%2B%20%5Cfrac%7B0%7D%7B3%7D%20%2B%20%5Cfrac%7B49%7D%7B3%7D%20%2B%20%5Cfrac%7B25%7D%7B3%7D%20%5C%5C%5C%5CS%5E2%3D%20%5Cfrac%7B4%2B49%2B25%7D%7B3%7D%5C%5C%5C%5CS%5E2%3D%5Cfrac%7B78%7D%7B3%7D%20%20%5C%5C%5C%5CS%5E2%3D26)
Therefore, for given sample of salaries of four employees, the variance of their salaries is: 26 thousands of dollars
Learn more about the variance here:
brainly.com/question/13673183
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