The following data are from a random sample: 5, 8, 10, 7, 10, 14, the…

The correct answer is Option (4) → 3.1

The point estimate of the population standard deviation is the sample standard deviation with divisor n − 1:

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

Here n = 6 and

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

The deviations from 9 are −4, −1, 1, −2, 1, 5, so

    \(\sum (x - \bar{x})^2 = 16 + 1 + 1 + 4 + 1 + 25 = 48\)

    \( \displaystyle s = \sqrt{\frac{48}{5}} = \sqrt{9.6} \approx 3.1 \)

With divisor n = 6 the result would be \(\sqrt{8} \approx 2.83\), which is not an option.