Standard deviation

As mentioned in the variance page, variance is just the standard deviation squared. So, to get the standard deviation, we just need to take the square root of the variance.

Standard deviation symbol

The symbol for standard deviation is \sigma (sigma).

\text{standard deviation:}\quad\sigma

Calculating standard deviation

1. Find the variance of the set of numbers.
2. Take the square root of the variance.

Formula

\sigma = \sqrt{\sigma^2}

\text{standard deviation} = \sqrt{\text{variance}}

If we want to substitute our formulae for variance into this, we can get any of:

\sigma = \sqrt{\overline{x^2} - \overline{x}^2}

\sigma = \sqrt{\frac{\sum(x-\overline{x})^2}{n}}

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