Square root of the variance of a statistical variable.

### Symbols

In the case of an entire population the standard deviation is noted as “σ”.

In the case of a sample population, the standard deviation is generally noted as “s”.

### Formula

In the case of an entire population, the standard deviation is found by applying this formula:

σ = \(\sqrt{\dfrac{∑(x_i − μ)^2}{n}}\)

In which μ represents the arithmetic mean of the distribution and *n* represents the number of results in the population.

In the case of a sample of this distribution, the standard deviation is found by applying this formula:

s = \(\sqrt{\dfrac{∑(x_i − \overline {x})^2}{n-1}}\)

In which \(\overline {x}\) represents the mean of the results of the sample and *n* represents the number of results considered.