# What is the variance of {-7, 12, 14, 8, -10, 0, 14}?

Dec 29, 2016

$2.55 \left(3 s . f .\right)$

#### Explanation:

$\left\{- 7 , 12 , 14 , 8 , - 10 , 0 , 14\right\}$

mean:

$\frac{- 7 + 12 + 14 + 8 + - 10 + 0 + 14}{7}$

$= \frac{31}{7}$

find deviations of each number ($n$-mean):

$- 7 - \frac{31}{7} = - \frac{49}{7} - \frac{31}{7} = \frac{80}{7}$

$12 - \frac{31}{7} = \frac{84}{7} - \frac{31}{7} = \frac{53}{7}$

$14 - \frac{31}{7} = \frac{98}{7} - \frac{31}{7} = \frac{67}{7}$

$8 - \frac{31}{7} = \frac{56}{7} - \frac{31}{7} = \frac{25}{7}$

$- 10 - \frac{31}{7} = - \frac{70}{7} - \frac{31}{7} = - \frac{101}{7}$

$0 - \frac{31}{7} = - \frac{31}{7}$

$14 - \frac{31}{7} = \frac{98}{7} - \frac{67}{7} = \frac{32}{7}$

variance = mean of deviations:

$\frac{\frac{80}{7} + \frac{53}{7} + \frac{67}{7} + \frac{25}{7} - \frac{101}{7} - \frac{31}{7} + \frac{32}{7}}{7}$

$= \frac{125}{49}$

$= 2.55 \left(3 s . f .\right)$