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

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

The quantile can be describe as follows. Given a fraction `r` between 0 and 1. Sort the data. The r-th-quantile is a value that separates the data into 2 parts. One having the portion `r` of the sorted data which is less than the quantile value, the other have the 1-`r` portion of the data which is greater than the quantile value.

The precise position is computed as followed:  r*n+offset, where n is the total weight of the data list.

The quantile generalizes the concept of median, quartile, percentile etc.

To obtain the median, one has to use an offset of 1/2. This is because the median of two numbers is situated  midway between these numbers.

NOTE: the quantile and the quartile have similar spelling.

Missing data are ignored.

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

The data must be numeric.

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

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

$\mathrm{data}≔\left[\mathrm{seq}\left(\frac{i}{7}\,i=1..60\right)\right]\:$

$\mathrm{describe}\left[\mathrm{quantile}\left[\frac{1}{3}\right]\right]\left(\mathrm{data}\right)$

$\frac{20}{7}$

$\mathrm{somequantiles}≔\left[\mathrm{seq}\left(\mathrm{describe}\left[\mathrm{quantile}\left[\frac{i}{20}\right]\right]\,i=8..15\right)\right]\:$

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

$\left[\frac{24}{7}\,\frac{27}{7}\,\frac{30}{7}\,\frac{33}{7}\,\frac{36}{7}\,\frac{39}{7}\,6\,\frac{45}{7}\right]$

$\mathrm{describe}\left[\mathrm{median}\right]\left(\left[10\,20\,30\right]\right)$

$20$

$\mathrm{describe}\left[\mathrm{quantile}\left[\frac{1}{2},\frac{1}{2}\right]\right]\left(\left[10\,20\,30\right]\right)$

$20$

$\mathrm{describe}\left[\mathrm{median}\right]\left(\left[10\,20\,30\,40\right]\right)$

$25$

$\mathrm{describe}\left[\mathrm{quantile}\left[\frac{1}{2},\frac{1}{2}\right]\right]\left(\left[10\,20\,30\,40\right]\right)$

$25$

$\mathrm{describe}\left[\mathrm{quantile}\left[\frac{1}{2}\right]\right]\left(\left[10\,20\,30\,40\right]\right)$

$20$