# Standard Deviation

## Standard Deviation

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.