# What is the variance of {5, 3, 6, 14, 8, 10, 3, 17, 19, 9}?

Apr 5, 2016

${\sigma}^{2} = 28.64$

#### Explanation:

There are 10 numbers, so $N = 10$.

First find the mean

$\mu = \frac{\sum X}{N}$

$= 9.4$

The variance is calculated as follows

${\sigma}^{2} = \frac{\sum \left({\left(X - \mu\right)}^{2}\right)}{N}$

$= 28.64$



Alternatively, use the equivalent formula

${\sigma}^{2} = \frac{1}{N} \left(\sum {X}^{2} - {\left(\sum X\right)}^{2} / N\right)$

$= 28.64$