Question

Given a population consists of three numbers (2,5,9). Consider all possible samples of size 2 which can be drawn from the population. Find the standard deviation of the sampling distribution of the sample means. 

Answer 1

possible samples mean

2,5 3.5

2,9 5.5

5,9 7

mean of the sample means:

$\mu=\frac{3.5+5.5+7}{3}=5.33$

standard deviation of the sample means:

$\sigma=\sqrt{\frac{\sum(\overline{x_i}-\mu)^2}{n}}=\sqrt{\frac{(3.5-5.33)^2+(5.5-5.33)^2+(7-5.33)^2}{3}}=1.43$