# Sample Standard Deviation Formula

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. |

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.

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 .

The normal distribution is a continuous probability distribution that appears naturally in applications of statistics and probability. The shape of the normal distribution forms a "bell curve".