Sample Standard Deviation Formula

Sample Standard Deviation



This formula calculates the sample standard devition of a normal distribution from sample data. See the population standard deviation formula for calculating the standard deviation from population data. The difference between population and sample data is that a sample represents a subset of the whole population.

Expression Description
The sample standard deviation
The size of the sample
Element of the data set
Average value of the data set


This formula calculates the sample standard deviation of a normal distribution. This approximate value for the standard deviation can be used to calculate probabilities and model the normal distribution of the data, pictured below:

This figure illustrates how the standard deviation corresponds to the distribution of data around the mean.
Figure 1: Normal Distribution Area

The value for the standard deviation describes how closely the data set is to the mean. One standard deviation away from the mean on either side contains approximately 68.3% of the samples, two standard deviations contains approximately 95.4% of the samples, and so on.


Population vs Sample

The variable is used to differentiate the sample standard deviation from the population standard deviation which is denoted using (sigma). The formulas are different in that the formula for a sample population uses Bessel’s Correction, which corrects for bias in the sample data.