A simple random sample consists of five observations: 4, 5, 9, 10 & 12. What is the point estimate of population standard deviation?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 3.4
The sample mean is \( \bar{x}=\frac{40}{5}=8 \). The point estimate of the population standard deviation is the sample standard deviation with divisor n − 1:
\( \displaystyle s=\sqrt{\frac{(4-8)^2+(5-8)^2+(9-8)^2+(10-8)^2+(12-8)^2}{5-1}} \)
\( \displaystyle =\sqrt{\frac{46}{4}} \)
\( \displaystyle =\sqrt{11.5}\approx 3.4 \)