Important: The stats package has been deprecated. Use the superseding package Statistics instead.

The function standarddeviation of the subpackage stats[describe, ...] computes the standard deviation of the given data.

The standard deviation  is defined to be the square root of the mean of the square of the deviations from the mean.

Classes are assumed to be represented by the class mark, for example 10..12 has the value 11. Missing data are ignored.

The standard deviation is a measure of the dispersion of the given data. There are various other dispersion measure, such as the mean deviation (see describe[meandev]), the range (see describe[range]) and the variance (see describe[variance]). Refer to describe[quartile] and describe[percentile] on how to use these function to construct other measures of dispersion. The various measures of dispersion are affected to various degrees by extreme values. For instance, the standard deviation is affected more strongly than the mean deviation. This varying dependence on extreme values is one major reason why there are many  measures of dispersion in use.

A related function, describe[coefficientofvariation], measures the relative dispersion of the data. The standard deviation measures the absolute dispersion.

The definition of standard deviation varies according to whether the data is the whole population, or if it just a random selection (a sample) of the whole population and we are trying what the standard deviation would be had we had the complete set of data. The parameter Nconstraint provides for this. If one desires the sample standard deviation, the appropriate value for this parameter is 1. The reason for this is technical, but providing this parameter allows the standard deviation of a sample to be an unbiased (closer) estimator for the standard deviation of the full population. For more than about 30 items of data, the effect is small, anyway.

The command with(stats[describe],standarddeviation) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{stats}\right)\:$

$\mathrm{data1}≔\left[3\,4\,7\right]$

$\mathrm{data1}≔\left[3\,4\,7\right]$

$\mathrm{data2}≔\left[1\,4\,9\right]$

$\mathrm{data2}≔\left[1\,4\,9\right]$

$\left[\mathrm{describe}\left[\mathrm{standarddeviation}\right]\left(\mathrm{data1}\right)\,\mathrm{describe}\left[\mathrm{standarddeviation}\right]\left(\mathrm{data2}\right)\right]$

$\left[\frac{\sqrt{26}}{3}\,\frac{7\sqrt{2}}{3}\right]$

$\mathrm{map}\left(\mathrm{evalf}\,\right)$

$\left[1.699673171\,3.299831644\right]$

$\mathrm{data3}≔\left[34\,93\,39\,49\right]$

$\mathrm{data3}≔\left[34\,93\,39\,49\right]$

$\mathrm{data4}≔\left[12\,59\,93\,39\right]$

$\mathrm{data4}≔\left[12\,59\,93\,39\right]$

$\left[\mathrm{describe}\left[\mathrm{standarddeviation}\left[1\right]\right]\left(\mathrm{data3}\right)\,\mathrm{describe}\left[\mathrm{standarddeviation}\left[1\right]\right]\left(\mathrm{data4}\right)\right]$

$\left[\frac{\sqrt{26049}}{6}\,\frac{\sqrt{4657}}{2}\right]$

$\mathrm{map}\left(\mathrm{evalf}\,\right)$

$\left[26.89950434\,34.12110784\right]$