Question

Consider a population consisting of 2,6,8,0 and 1. Suppose a sample size of 3 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 ${5 \choose 3}=10$ samples(without replacement). They are listed below

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

Sample means: 8, 4, 4.5, 5, 5.5, 1.5, 7, 7.5, 3.5, 4.5

Mean of sampling distribution of means: ${\frac {8+...+4.5} {10}}={\frac {51} {10}}=5.1$

Variance of sampling distribution of means: ${\frac {(8-5.1)^2+...+(4.5-5.1)^2} {10}}={\frac {35.39} {10}}=3.539$