Question

Random samples of size 2 are taken from a finite population which consist of measurements 6,7,8,9,10 and 11. Show that the mean of the population is 2.5 and its standard deviation is 0.493

Answer 1

$N=6 \\ n=2 \\ Number \;of \; samples = \frac{6!}{2!(6-2)!}= 15$

The mean of the population

$\mu = \frac{6+7+8+9+10+ 11}{6}=8.5$

The standard deviation

$\sigma = \sqrt{ \frac{\sum (x- \mu)^2}{n} } \\ \sigma = \sqrt{ \frac{1}{6} ( (6-8.5)^2+(7-8.5)^2+(8-8.5)^2+(9-8.5)^2+(10-8.5)^2+(11-8.5)^2 ) } = 1.70$