A simple random sample consists of four observations 7, 8, 10, 7. The point estimate of population standard deviation is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\sqrt{2}\)
The point estimate of the population standard deviation is the sample standard deviation with divisor n − 1:
\( \displaystyle s = \sqrt{\frac{\sum (x - \bar{x})^2}{n - 1}} \)
Sample mean:
\( \displaystyle \bar{x} = \frac{7 + 8 + 10 + 7}{4} = \frac{32}{4} = 8 \)
Squared deviations from 8:
\((-1)^2 + 0^2 + 2^2 + (-1)^2 = 1 + 0 + 4 + 1 = 6\)
Then
\( \displaystyle s = \sqrt{\frac{6}{4 - 1}} = \sqrt{2} \)