Question

The following are numbers obtained from the population samples: 2, 4, 7, 12, 15. Find the standard deviation of the sample.

Answer 1

n=5

Mean

$\bar{x} = \frac{2+4+7+12+15}{5}= 8$

Sample standard deviation

$s = \sqrt{\frac{(2-8)^2+(4-8)^2+(7-8)^2 +(12-8)^2 +(15-8)^2}{5-1}} \\ = \sqrt{\frac{36 + 16 + 1 + 16 + 49}{4}} \\ = \sqrt{29.5} \\ = 5.43$