describe(deprecated)/coefficientofvariation - Help

stats[describe]

 coefficientofvariation
 Coefficient of Variation

 Calling Sequence stats[describe, coefficientofvariation](data) stats[describe, coefficientofvariation[Nconstraints]](data) describe[coefficientofvariation](data) describe[coefficientofvariation[Nconstraints]](data)

Parameters

 data - statistical list Nconstraints - (optional, default=0) Number of constraints, 1 for sample, 0 for full population

Description

 • Important: The stats package has been deprecated. Use the superseding package Statistics instead.
 • The function coefficientofvariation of the subpackage stats[describe, ...] computes the coefficient of variation of the given data. It is defined to be the standard deviation divided by the mean.
 • The coefficient of variation is a measure of the relative dispersion of the data. The standard deviation is a measure of the absolute dispersion. Since the coefficient of variation is independent of the units it is useful in comparing distributions where differing units have been used. One disadvantage of using the coefficient of variation as a measure of relative dispersion is that its value is not very useful when the average is close to zero.
 • Classes are assumed to be represented by the class mark, for example 10..12 has the value 11. Missing data are ignored.
 • The definition of standard deviation varies according to whether it is computed for the whole population, or only for a sample. The parameter Nconstraints provides for this. Refer to describe[standarddeviation] for more information.
 • The command with(stats[describe],coefficientofvariation) allows the use of the abbreviated form of this command.

Examples

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

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

For the following two data sets

 > $\mathrm{data1}≔\left[3,4,5\right]$
 ${\mathrm{data1}}{≔}\left[{3}{,}{4}{,}{5}\right]$ (1)
 > $\mathrm{data2}≔\left[31,32,33\right]$
 ${\mathrm{data2}}{≔}\left[{31}{,}{32}{,}{33}\right]$ (2)

The standard deviation is the same

 > $\mathrm{describe}[\mathrm{standarddeviation}]\left(\mathrm{data1}\right)=\mathrm{describe}[\mathrm{standarddeviation}]\left(\mathrm{data2}\right)$
 $\frac{{1}}{{3}}{}\sqrt{{6}}{=}\frac{{1}}{{3}}{}\sqrt{{6}}$ (3)

However, the first distribution "varies more" than the second one.

This can be seen using the coefficient of variation.

 > $\mathrm{describe}[\mathrm{coefficientofvariation}]\left(\mathrm{data1}\right):$$\mathrm{evalf}\left(\right)$
 ${0.8164965809}{=}{0.8164965809}$ (4)
 > $\mathrm{describe}[\mathrm{coefficientofvariation}]\left(\mathrm{data2}\right):$$\mathrm{evalf}\left(\right)$
 ${0.8164965809}{=}{0.8164965809}$ (5)