Question

Calculate

SS,

variance, and standard deviation for the following population of

N

= 5 scores:

2, 13, 4, 10, 6.

Answer 1

The mean is

$$\mu=\bar{x}=\dfrac{2+13+4+10+6}{5}=7$$

Then

$$SS(sum\ of\ squares)=(2-7)^2+(13-7)^2$$

$$+(4-7)^2+(10-7)^2+(6-7)^2=80$$

Variance

$$Var(X)=\sigma^2=\dfrac{SS}{n}=\dfrac{80}{5}=16$$

Standard deviation

$$\sigma=\sqrt{\sigma^2}=\sqrt{16}=4$$