In statistics, the standard deviation (also called the root mean square deviation or RMS for short) is a measure that is used to quantify how far data points are spread out from their average value.

The standard deviation of a set of numbers is the square root of their average squared deviation from their mean. The same concept applies to sets of real-valued functions and complex-valued functions. In general, it is a measure of how widely dispersed a set of data points are about their mean value, often taken as zero.

If the values are normally distributed with mean 0 and variance 1 (i.e., they form a bell curve), then 68% of the data points fall within one standard deviation of the mean; 95% within two standard deviations; and 99.7% within three standard deviations.

The term “standard deviation” can refer to either an individual result or an average: if each result has the same deviation from its own mean, then they all have the same standard deviation; likewise, if every individual result has precisely the same value as all other results, then they all have the same standard deviation too. In this case we talk about population.

Last modified: August 14, 2022