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.

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So it stands Degree of freedom less available because information has been withdrawn from the sample. -> (n-1)

See also the note below Degree of freedom.



Output dataAverageStandard deviation
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 discreetDistribution functions comes.


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