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.

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

$\mathrm{data}≔\left[1\,3\,5\right]$

$\mathrm{data}≔\left[1\,3\,5\right]$

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

$51=51$

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

$\frac{272}{3}=\frac{272}{3}$

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

$0=0$