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Question

Listed below are annual salaries (in thousands of dollars) for a simple random sample of NCAA Division 1-A head football coaches (based on data from the New York Times).

$\begin{array}{llllllllll} 235 & 159 & 492 & 530 & 138 & 125 & 128 & 900 & 360 & 212 \end{array}$

d. Find the variance $s^2$ and express the result in appropriate units.

Solution

VerifiedStep 1

1 of 2The mean is the sum of all values divided by the number of values:

$\overline{x}=\dfrac{235+159+...+360+212}{10}=327.9$

The variance is the sum of squared deviations from the mean divided by $n-1$:

$s^2=\dfrac{(235-327.9)^2+...+(212-327.9)^2}{10-1}\approx 62,653.6$

The data values are all given in thousands of dollars:

$62,653.6(\text{ thousands of dollars})^2=62,653,600,000 \text{ dollars}^2$

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