Question

A group of students got the following scores in a test; 6, 9, 12, and 18. Consider samples of size 2 that can be selected from the population. What is the variance of the population?

Answer 1

We have population values 6,9,12,18, population size N=4.

Mean of population $(\mu)$ = $\dfrac{6+9+12+18}{4}=11.25$

Variance of population 

$$\sigma^2=\dfrac{\Sigma(x_i-\bar{x})^2}{N}=\dfrac{1}{4}(27.5625+5.0625$$ $$+0.5625+45.5625)=19.6875$$