# How do you find the variance and standard deviation of {2,3,4,6,8,9}?

Oct 12, 2017

${\sigma}^{2} = \frac{118}{15} \cong 7.867$

$\sigma = \sqrt{7.8666} = 2.80475786$

#### Explanation:

Variance of a sample is given by the following equation:

${\sigma}^{2} = \frac{\sum {\left(x - \overline{x}\right)}^{2}}{n - 1}$

It can be rearranged to:

${\sigma}^{2} = \frac{\Sigma {x}^{2} - {\left(\Sigma x\right)}^{2} / n}{n - 1}$

$\Sigma \left({x}^{2}\right) = {2}^{2} + {3}^{2} + {4}^{2} + {6}^{2} + {8}^{2} + {9}^{2} = 210$

$\Sigma \left(x\right) = 2 + 3 + 4 + 6 + 8 + 9 = 32$

$n = 6$

${\sigma}^{2} = \frac{210 - \left({32}^{2} / 6\right)}{6 - 1} = \frac{118}{15} \cong 7.867$

Standard deviation is the square root of variance.

$\sigma = \sqrt{7.8666} = 2.80475786$