What is Standard Deviation?

In short

The standard deviation is a measure of how spread out the values in a data set are around their mean. A small value means the data are close together.

In simple words

For a population, $\sigma = \sqrt{\dfrac{\sum (x - \mu)^2}{N}}$ . For a sample, divide by $n - 1$ instead of $n$ , and call it $s$ . It is in the same unit as the data. About $68\%$ of values in a bell-shaped distribution lie within one standard deviation of the mean, and about $95\%$ within two. In Python, statistics.stdev gives the sample value and statistics.pstdev the population value.

Example

For $2, 4, 4, 4, 5, 5, 7, 9$ the mean is $5$ , and the population standard deviation is $\sqrt{\dfrac{32}{8}} = 2$ .