# what are the standard deviation and coefficient of variation of {5,6,7,9,8}?

Jun 28, 2016

Standard Deviation is $1.4142$ and Coefficient of variation is 20.2%

#### Explanation:

The mean $\left(\mu\right)$ of data set is given by the sum of data divided by their number i.e. $\frac{\Sigma x}{N}$

Hence mean is $\frac{1}{5} \left(5 + 6 + 7 + 9 + 8\right) = 7$

Standard Deviation $\left(\sigma\right)$ is given by sqrt[(Sigmax^2)/N-((Sigmax)/N)^2

$\frac{\Sigma {x}^{2}}{N} = \frac{1}{5} \left({5}^{2} + {6}^{2} + {7}^{2} + {9}^{2} + {8}^{2}\right)$

= $\frac{1}{5} \left(25 + 36 + 49 + 81 + 64\right) = \frac{255}{5} = 51$

Hence Standard Deviation is $\sqrt{51 - {\left(7\right)}^{2}} = \sqrt{2} = 1.4142$

Coefficient of variation is $\frac{\sigma}{\mu} \times 100$ = 1.4142/7xx100=20.2%