Answer to Question #339298 in Statistics and Probability for Lay

Question

A group of students got the following scores in a test; 5, 10, 15, and 25. Consider samples of size 2 that can be selected from the population. What is the mean of the population?

Answer 1

We have population values 5,9,10, 8, population size N=4.

Mean of population $(\mu)$ = $\dfrac{5+10+15+20}{4}=12.5$

Variance of population 

$$\sigma^2=\dfrac{\Sigma(x_i-\bar{x})^2}{n}=\dfrac{1}{4}(56.25+6.25+6.25+56.25)$$

$$=31.25$$

$$\sigma=\sqrt{\sigma^2}=\sqrt{31.25}\approx5.59017$$