Answer to Question #339363 in Statistics and Probability for Jean

Question

A population consists of the four measurements as follow:

5 9 10 8

What is the mean and standard deviation of the population?

Answer 1

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

Mean of population $(\mu)$ = $\dfrac{5+9+10+8}{4}=8$

Variance of population 

$$\sigma^2=\dfrac{\Sigma(x_i-\bar{x})^2}{n}=\dfrac{1}{4}(9+1+4+0)$$

$$=3.5$$

$$\sigma=\sqrt{\sigma^2}=\sqrt{3.5}\approx1.8708$$