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

The function percentile of the subpackage stats[describe, ...] finds the item in data that corresponds to the percentile specified by which. If the requested percentile falls between entries, it is interpolated.

The percentiles are values that partition the data, once sorted, into 100 equal parts.

Using percentiles, one can compute various measures of dispersion. For example, the 10-90 percentile range is the value of the 90th percentile minus that of the 10th percentile. Other similar dispersion measures constructed with the percentiles are the 20-80 and the 25-75 percentile range. For more information related to measures of dispersion, refer to describe[standarddeviation].

Missing data are ignored.

For information about the parameter gap, see describe[gaps].

The data must be numeric.

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

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

$\mathrm{data}≔\left[\mathrm{seq}\left(\frac{i}{3}+\frac{1}{2}\,i=1..300\right)\right]\:$

$\mathrm{describe}\left[\mathrm{percentile}\left[15\right]\right]\left(\mathrm{data}\right)$

$\frac{31}{2}$

$\mathrm{somepercentiles}≔\left[\mathrm{seq}\left(\mathrm{describe}\left[\mathrm{percentile}\left[9i\right]\right]\,i=1..9\right)\right]$

$\mathrm{somepercentiles}≔\left[{\mathrm{describe}}_{{\mathrm{percentile}}_9}\,{\mathrm{describe}}_{{\mathrm{percentile}}_{18}}\,{\mathrm{describe}}_{{\mathrm{percentile}}_{27}}\,{\mathrm{describe}}_{{\mathrm{percentile}}_{36}}\,{\mathrm{describe}}_{{\mathrm{percentile}}_{45}}\,{\mathrm{describe}}_{{\mathrm{percentile}}_{54}}\,{\mathrm{describe}}_{{\mathrm{percentile}}_{63}}\,{\mathrm{describe}}_{{\mathrm{percentile}}_{72}}\,{\mathrm{describe}}_{{\mathrm{percentile}}_{81}}\right]$

$\mathrm{somepercentiles}\left(\mathrm{data}\right)$

$\left[\frac{19}{2}\,\frac{37}{2}\,\frac{55}{2}\,\frac{73}{2}\,\frac{91}{2}\,\frac{109}{2}\,\frac{127}{2}\,\frac{145}{2}\,\frac{163}{2}\right]$

$\mathrm{range\_1090}≔x\mapsto \mathrm{describe}\left[\mathrm{percentile}\left[90\right]\right]\left(x\right)-\mathrm{describe}\left[\mathrm{percentile}\left[10\right]\right]\left(x\right)\:$

$\mathrm{range\_1090}\left(\mathrm{data}\right)$

$80$