Question

Random samples of size n=2 are drawn from a finite population consisting of the numbers 5,67,8 and 9. Compute the mean, variance and standard deviation of the population, and the me a variance and standard deviation of the sample means. Showtablr with complete solutions

Answer 1

We have given the population,

$5,6,7,8 \hspace{2mm}and \hspace{2mm}9$

Population mean = $\dfrac{5+6+7+8+9}{5} = 7$

Variance $= \dfrac{(5-7)^2+(6-7)^2+(7-7)^2+(8-7)^2+(9-7)^2}{5}\\$

$= \dfrac{4+1+0+1+4}{5} = 2$

Standard Deviation $= \sqrt{2} = 1.41$

Table for sampling distribution can be formed as

Variance of sampling distribution =

$\dfrac{(5.5-7)^2+(6-7)^2+2(6.5-7)^2+2(7-7)^2+2(7.5-7)^2+(8-7)^2+(8.5-7)^2}{10}\\ = \dfrac{2.25+1+0.5+0+0.5+1+2.25}{10} \\ = 0.75$

Sample standard deviation $= \sqrt{0.75} = 0.86$