# Standard Deviation

- Standard deviation is the square root of the variance, i.e. the square root of the mean of the squares of the deviations from the mean value of a vibrating quantity. The square of the standard deviation is the variance. An expression of the so-called "second moment," which describes the "dispersion" or variability around the mean.

- In noise data, the standard deviation should be approximately the same as the rms.

- for the data series:
*x*_{1},*x*_{2},*x*_{3},....,*x*_{n}the standard deviation of a sample,*σ*is:

- The standard deviation of the entire population,
*σ*_{p}

3σ | Represents about the same likelihood of tossing a coin and getting more than eight heads in a row. |

5σ | The level of certainty required in Particle Physics for a "discovery". |

5σ | Corresponds to tossing a coin and getting more than 20 heads in a row. |

**See also: **Average Deviation, Mean, Normal Distribution, Relative Standard Deviation, Standard Error, Statistic, Variance.

**Subjects: ** Statistics