# What is the variance of {15, 9, -3, 8, 0}?

Variance ${\sigma}^{2} = \frac{1054}{25} = 42.16$

#### Explanation:

We compute the arithmetic mean first

$\mu = \frac{15 + 9 + \left(- 3\right) + 8 + 0}{5}$

$\mu = \frac{29}{5}$

To compute for variance ${\sigma}^{2}$ use the formula

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

${\sigma}^{2} = \frac{{\left(15 - \frac{29}{5}\right)}^{2} + {\left(9 - \frac{29}{5}\right)}^{2} + {\left(- 3 - \frac{29}{5}\right)}^{2} + {\left(8 - \frac{29}{5}\right)}^{2} + {\left(0 - \frac{29}{5}\right)}^{2}}{5}$

${\sigma}^{2} = \frac{1054}{25} = 42.16$

God bless...I hope the explanation is useful.