Question

A population consists of three numbers (3,5,9).Consider all possible samples of size n=2 which can be drawn WITHOUT REPLACEMENT from the population.

Questions to be answered:

Population mean

Population variance

Population standard deviation

Mean of the samples and mean of the sampling distribution of the means

Answer 1

Given population = 3,5,9

Population mean $\mu =\dfrac{3+5+9}{3}=\dfrac{17}{3}=5.66$

Population variance

$\sigma^2= \sum \dfrac{ (x-\mu)^2}{n}=\dfrac{(3-5.66)^2+(5-5.66)^2+(9-5.66)^2}{3}=\dfrac{18.6}{3}=6.2$

Population standard deviation $\sigma=\sqrt{ Variance}=\sqrt{6.2}=2.49$

The mean of the samples are shown in the given table-

Total samples=3

mean of the sampling distribution of the means$=\dfrac{ \sum \text{sample mean}}{\text{total sample}}=\dfrac{17}{3}=5.66$