describe(deprecated)/meandeviation - Help

stats[describe, meandeviation]

Mean Deviation of a Statistical List

 Calling Sequence stats[describe, meandeviation](data) describe[meandeviation](data)

Parameters

 data - statistical list

Description

 • Important: The stats package has been deprecated. Use the superseding package Statistics instead.
 • The function meandeviation of the subpackage stats[describe, ...] computes the  mean deviation of the given data.
 • The mean deviation is defined as follows:  the mean is first removed from the data, then the absolute value is taken for each item. The mean deviation is the mean  of the resulting list.
 • The mean deviation is a measure of the dispersion of the data. For more information about such measures, refer to describe[standarddeviation].
 • When the arithmetic mean is not a suitable measure of the central tendency of the data, then neither is the mean deviation a suitable measure of the dispersion of the data. For more information please refer to the various measures of central tendency, such as describe[mean].
 • Classes are assumed to be represented by the class mark, for example 10..12 has the value 11. Missing data are ignored.
 • The command with(stats[describe],meandeviation) allows the use of the abbreviated form of this command.

Examples

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

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

The data 1,3,7 is more dispersed than the data 2,3,5, as can be seen as follows:

 > $\mathrm{describe}[\mathrm{meandeviation}]\left(\left[1,3,7\right]\right),\mathrm{describe}[\mathrm{meandeviation}]\left(\left[2,3,5\right]\right)$
 $\frac{{20}}{{9}}{,}\frac{{10}}{{9}}$ (1)

Here is an example where the mean deviation is not a suitable measure of dispersion. The data consists of 100 copies of the value 1, and 1 copy of the value 100000. This last value really has too much of an influence (it is likely that it was a bad reading of an instrument).

 > $\mathrm{describe}[\mathrm{meandeviation}]\left(\left[\mathrm{Weight}\left(1,100\right),\mathrm{Weight}\left(100000,1\right)\right]\right)$
 $\frac{{19999800}}{{10201}}$ (2)
 > $\mathrm{evalf}\left(\right)$
 ${1960.572493}$ (3)