# What is the variance of {12, 6, -2, 9, 5, -1}?

Jul 6, 2017

Variance is $25.14$

#### Explanation:

Data ; $D = \left\{12 , 6 , - 2 , 9 , 5 , - 1\right\}$

Variance $\left({\sigma}^{2}\right)$ is the average of squared difference from mean.

Mean is $\frac{\sum D}{6} = \frac{29}{6} \approx 4.83 \left(2 \mathrm{dp}\right)$

${\sigma}^{2} =$
$\frac{{\left(12 - 4.83\right)}^{2} + {\left(6 - 4.83\right)}^{2} + {\left(- 2 - 4.83\right)}^{2} + {\left(9 - 4.83\right)}^{2} + {\left(5 - 4.83\right)}^{2} + {\left(- 1 - 4.83\right)}^{2}}{6} = \frac{150.83}{6} \approx 25.14 \left(2 \mathrm{dp}\right)$

Variance is $25.14$ [Ans]