Question

Consider a population consisting of 2,6,8,0 and 1. Suppose samples of size 2 are drawn from this population. Find the Mean and Variance of the sampling distribution of sample means.

Answer 1

Since there are 5 elements and 2 of them are taken to form a sample, then there will be ${5 \choose 2}=10$ samples(without replacement). They are listed below

(2,6); (2,8); (2,0); (2,1); (6,8); (6,0); (6,1); (8,0); (8,1); (0,1)

Sample means: 4, 5, 1, 1.5, 6, 3, 3.5, 4, 4.5, 0.5

Mean of sampling distribution of means: ${\frac {4+...+0.5} {10}}={\frac {33} {10}}=3.3$

Variance of sampling distribution of means: ${\frac {(4-3.3)^2+...+(0.5-3.3)^2} {10}}={\frac {28.55} {10}}=2.855$