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) - $\sqrt{2}$
$\text{Data: } 7, 8, 10, 7$
$\bar{x} = \frac{7+8+10+7}{4} = 8$
$\sum (x-\bar{x})^2 = (7-8)^2+(8-8)^2+(10-8)^2+(7-8)^2$
$=1+0+4+1=6$
$s = \sqrt{\frac{6}{4-1}} = \sqrt{\frac{6}{3}} = \sqrt{2}$
The point estimate of population standard deviation is $\sqrt{2}$.