# Sample Standard Deviation Formula ## Formula

### Summary

This formula calculates the sample standard deviation 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.
The sample mean, calculated with this formula.
The -th element of the samle data.

## Usage

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 corresponding to the data. 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 of the samples, two standard deviations contain approximately of the samples, and so on. Because this formula calculates an approximate value for the true standard deviation there will be some discrepancy between the actual normal distribution and the one modeled by the sample standard deviation. ### Population vs Sample Formula

The difference between the sample standard deviation formula and the population standard deviation formula is Bessel’s correction which corrects for bias in the sample data and, as a result, calculates a more accurate standard deviation value. The variable differentiates the sample standard deviation from the population standard deviation which is denoted using (sigma).

Comparing the two formulas, the sample standard deviation subtracts one from the sample size which can be seen in the expression .