## Standard deviation $\sigma $

The standard deviation $\sigma $
is the square root of the variance.

### Variance ${\sigma}^{2}$

$${\sigma}^{2}=\frac{\underset{i=1}{\overset{n}{\u2140}}{\left({x}_{i}-\overline{x}\right)}^{2}}{n}$$

### Standard deviation $\sigma $

$$\sigma =\sqrt{{\sigma}^{2}}$$

$$\sigma =\sqrt{\frac{\underset{i=1}{\overset{n}{\u2140}}{\left({x}_{i}-\overline{x}\right)}^{2}}{n}}$$

- $\sigma $
- standard deviation;
- ${\sigma}^{2}$
- variance;
- $n$
- a number of elements of the statistical set;
- ${x}_{i}$
- an element of the statistical set with index
*i*;
- $\overline{x}$
- a simple arithmetic mean.

The standard deviation is an indicator of variability.