Standard deviation

The standard deviation gives us an average of the distance between each data point and the arithmetic mean. It’s given by:

$$\sigma =\sqrt{\frac{\Sigma (x-\mu {)}^2}{n}}=\sqrt{\text{Var}(x)}$$

When we square this value (i.e., ${\sigma }^2$), we get the population variance.

The standard deviation intuitively represents the average distance of data members, while the variance describes the spread. One benefit is that it’s in the same unit as $x$.