# Sample Standard Deviation Formula

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:

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.

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.