# What is a sample in standard deviation

**Standard deviation**

The standard deviation is the best known measure of dispersion, but it is not easy to explain. Standard deviation is the zwide root of the *Variance*.

The term standard deviation has grown unfortunate historically; it should actually be called standard error.

The designation standard deviation would actually correspond to the formula expression below without the factor 1 / N or 1 / (N-1). See explanations under Standard Error.

The standard deviation is not very clear and difficult to interpret. *Variance* on the other hand, it can be interpreted directly as unexplained information.

On the other hand, the standard deviation has the same physical dimension as the original variable itself, which is probably the real reason for its popularity.

The standard deviation is the most commonly used *Spread*.

When calculating the standard deviation, a distinction must be made between one * sample* and one *Population*.

sample | Population |

The reason for choosing (n-1) instead of n for the sample is that one must have determined the mean value beforehand when calculating the sample standard deviation. When the mean value is mentioned, however, all n individual values are no longer freely selectable, but only (n-1); the nth value results clearly from the (n-1) values and the mean value. So it stands Degree of freedom. |

**example**

Output data | Average | Standard deviation (Sample) |

1, 4, 3, 8 | (1+4+3+8)/4= 4 | = =2,944 |

For tests that test for differences in standard deviations, see below *Variance*.

See also * Chebyshev's inequality*.

In the indentations of the rubrics *Characteristic function* and *Hypergeometric distribution*

ways are described how to contribute to standard deviations *discreet**Distribution functions* comes.

For confidence intervals of the standard deviation in normally distributed samples see *Confidence intervals*.

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