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.
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"
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