# What is the variance of {-2, 5, 18, -8, -10, 14, -12, 4}?

Variance ${\sigma}^{2} = \frac{6903}{64} = 107.8593$

#### Explanation:

compute the arithmetic mean $\mu$ first

$n = 8$

$\mu = \frac{- 2 + 5 + 18 + \left(- 8\right) + \left(- 10\right) + 14 + \left(- 12\right) + 4}{8}$

$\mu = \frac{- 32 + 41}{8}$

$\mu = \frac{9}{8}$

compute the variance ${\sigma}^{2}$ using the variance formula for population

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

${\sigma}^{2} = \frac{{\left(- 2 - \frac{9}{8}\right)}^{2} + {\left(5 - \frac{9}{8}\right)}^{2} + {\left(18 - \frac{9}{8}\right)}^{2} + {\left(- 8 - \frac{9}{8}\right)}^{2} + {\left(- 10 - \frac{9}{8}\right)}^{2} + {\left(14 - \frac{9}{8}\right)}^{2} + {\left(- 12 - \frac{9}{8}\right)}^{2} + {\left(4 - \frac{9}{8}\right)}^{2}}{8}$

${\sigma}^{2} = \frac{6903}{64}$

${\sigma}^{2} = 107.8593$

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