Question

Random sample of size N = 2 are drawn from a finite population consisting of the numbers 1, 3, 8, 9.

Find the following:

31 35. Mean, Variance and Standard deviation of the Population.

36-40. Mean, Variance and Standard deviation of the Sample means

Answer 1

$\mu =\frac{1+3+8+9}{4}=5.25\\\sigma ^2=\frac{\left( 1-5.25 \right) ^2+\left( 3-5.25 \right) ^2+\left( 8-5.25 \right) ^2+\left( 9-5.25 \right) ^2}{4}=11.1875\\\sigma =\sqrt{\sigma ^2}=\sqrt{11.1875}=3.34477\\\mu _{\bar{x}}=\mu =5.25\\{\sigma ^2}_{\bar{x}}=\frac{\sigma ^2}{n}=\frac{11.1875}{2}=5.59375\\\sigma _{\bar{x}}=\frac{\sigma}{\sqrt{n}}=\frac{3.34477}{\sqrt{2}}=2.36511\\$