# What is the variance of {-7, 8, -9, 10, 12, -14, 8}?

Mar 14, 2016

-140.714286

#### Explanation:

The variance is calculated using the formula $\frac{1}{N} {\sum}_{N = 1}^{N} \left({x}_{i} - \mu\right)$, and when you sub in the numbers, you get the following values:
$\mu = 8$
${\left(- 14 - 8\right)}^{2} = {\left(- 22\right)}^{2} = - 484$
${\left(- 9 - 8\right)}^{2} = {\left(- 17\right)}^{2} = - 289$
${\left(- 7 - 8\right)}^{2} = {\left(- 15\right)}^{2} = - 225$
${\left(8 - 8\right)}^{2} = 0$
${\left(8 - 8\right)}^{2} = 0$
${\left(10 - 8\right)}^{2} = {\left(2\right)}^{2} = 4$
${\left(12 - 8\right)}^{2} = {\left(3\right)}^{2} = 9$

$\frac{- 484 + \left(- 289\right) + \left(- 225\right) + 0 + 0 + 4 + 9}{7} = - 140.714286$