The following data are from a simple random sample: 5, 8, 10, 7, 10,…

The correct answer is Option (1) → 9.6

The point estimate of the population variance is the sample variance \(s^2\), whose divisor is n − 1:

    \( \displaystyle s^2 = \frac{\sum (x_i - \overline{x})^2}{n-1} \)

Here n = 6 and the mean is

    \( \displaystyle \overline{x} = \frac{5+8+10+7+10+14}{6} = \frac{54}{6} = 9 \)

The squared deviations from the mean:

    \( (5-9)^2 + (8-9)^2 + (10-9)^2 + (7-9)^2 + (10-9)^2 + (14-9)^2 \)

    \( = 16 + 1 + 1 + 4 + 1 + 25 = 48 \)

    \( \displaystyle s^2 = \frac{48}{6-1} = \frac{48}{5} = 9.6 \)

Tip: Dividing by n instead of n − 1 gives \(\frac{48}{6} = 8\), Option (3). That is the variance of the six sample values themselves, not the estimate of the population variance.