The following data are from a simple random sample : 1, 4, 7
The point estimate of the population standard deviation is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 3
The point estimate of the population standard deviation is the sample standard deviation s, worked out with the divisor n − 1:
\( \displaystyle s = \sqrt{\frac{\sum (x - \bar{x})^2}{n - 1}} \)
Sample mean:
\( \displaystyle \bar{x} = \frac{1 + 4 + 7}{3} = 4 \)
Squared deviations from the mean:
\((1 - 4)^2 = 9,\quad (4 - 4)^2 = 0,\quad (7 - 4)^2 = 9\)
\(\sum (x - \bar{x})^2 = 18\)
With n − 1 = 2:
\( \displaystyle s^2 = \frac{18}{2} = 9 \)
\(s = 3\)
(Dividing by n = 3 instead would give \(\sqrt{6} \approx 2.45\), which is not among the options.)