# What is the variance of {9, -4, 7, 10, 3, -2}?

Mar 27, 2016

Variance is 28.472

#### Explanation:

Mean of $\left\{9 , - 4 , 7 , 10 , 3 , - 2\right\}$ is

$\frac{9 + \left(- 4\right) + 7 + 10 + 3 + \left(- 2\right)}{6} = \frac{23}{6}$

For Variance of a series $\left\{{x}_{1.} {x}_{2} , \ldots , {x}_{6}\right\}$, whose mean is $\overline{x}$is given by

$\frac{\Sigma {\left(x - \overline{x}\right)}^{2}}{6}$ and hence it is

$\frac{1}{6} \cdot \left\{{\left(\frac{23}{6} - 9\right)}^{2} + {\left(\frac{23}{6} - \left(- 4\right)\right)}^{2} + {\left(\frac{23}{6} - 7\right)}^{2} + {\left(\frac{23}{6} - 10\right)}^{2} + {\left(\frac{23}{6} - 3\right)}^{2} + {\left(\frac{23}{6} - \left(- 2\right)\right)}^{2}\right\}$ or

$\frac{1}{6} \cdot \left\{{\left(- \frac{31}{6}\right)}^{2} + {\left(\frac{47}{6}\right)}^{2} + {\left(- \frac{19}{6}\right)}^{2} + {\left(- \frac{37}{6}\right)}^{2} + {\left(\frac{5}{6}\right)}^{2} + {\left(\frac{35}{6}\right)}^{2}\right\}$

= $\frac{1}{6} \cdot \left\{\frac{961}{36} + \frac{2209}{36} + \frac{361}{36} + \frac{1369}{36} + \frac{25}{36} + \frac{1225}{36}\right\}$

= $\frac{1}{6} \cdot \left(\frac{6150}{36}\right) = 28.472$