The point estimate of the population standard deviation as per the below mentioned data from a simple random sample 6, 10, 15, 12, 9, 8 will be:-
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 3.162
The point estimate of the population standard deviation is the sample standard deviation with divisor n − 1 (the unbiased estimate of the variance).
\( \displaystyle \bar{x} = \frac{6 + 10 + 15 + 12 + 9 + 8}{6} = \frac{60}{6} = 10 \)
The deviations from 10 are −4, 0, 5, 2, −1, −2:
\( \sum (x - \bar{x})^2 = 16 + 0 + 25 + 4 + 1 + 4 = 50 \)
\( \displaystyle s^2 = \frac{\sum (x - \bar{x})^2}{n - 1} = \frac{50}{5} = 10 \)
\( \displaystyle s = \sqrt{10} \approx 3.162 \)
Dividing by n = 6 instead would give \(\sqrt{50/6} \approx 2.887\), which is not an option.