describe(deprecated)/moment - Help

stats[describe]

 moment
 Moments of a Statistical List

 Calling Sequence stats[describe, moment[which, origin, Nconstraint]](data) describe[moment[which, origin, Nconstraint]](data)

Parameters

 data - statistical list which - integer that specifies the required moment origin - (optional, default=0) the quantity about which the moment is computed. Nconstraint - (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 moment of the subpackage stats[describe, ...] computes the various moments  of the given data about any origin.
 • The r-th moment about an origin R is computed as follows: M_R:=(1/(N-Nconstraints))*sum( (X-R)^r ), where N is the total weight of the data.
 • The value of origin can be either a number, or the various descriptive statistic functions that can be specified via stats[describe, descriptive statistic function].
 • The function moment is closely related to the function sumdata.
 • 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 the moment varies according to whether it is computed for the whole population, or only for a sample. The parameter Nconstraint provides for this. Refer to describe[standarddeviation] for more information about this.
 • The command with(stats[describe],moment) allows the use of the abbreviated form of this command.

Examples

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

 > $\mathrm{with}\left(\mathrm{stats}\right):$
 > $\mathrm{data}≔\left[1,3,5\right]$
 ${\mathrm{data}}{:=}\left[{1}{,}{3}{,}{5}\right]$ (1)

 > $\mathrm{describe}[\mathrm{moment}[3]]\left(\mathrm{data}\right)=\frac{1\left({1}^{3}+{3}^{3}+{5}^{3}\right)}{3}$
 ${51}{=}{51}$ (2)

 > $\mathrm{describe}[\mathrm{moment}[4,1]]\left(\mathrm{data}\right)=\frac{1\left({\left(1-1\right)}^{4}+{\left(3-1\right)}^{4}+{\left(5-1\right)}^{4}\right)}{3}$
 $\frac{{272}}{{3}}{=}\frac{{272}}{{3}}$ (3)

Fifth moment about the mean, for a sample population:

 > $\mathrm{describe}[\mathrm{moment}[5,\mathrm{mean},1]]\left(\mathrm{data}\right)=\frac{1\left({\left(1-3\right)}^{5}+{\left(3-3\right)}^{5}+{\left(5-3\right)}^{5}\right)}{2}$
 ${0}{=}{0}$ (4)