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Concept
Valeur absolue des écarts
Résumé
The average absolute deviation (AAD) of a data set is the average of the absolute deviations from a central point. It is a summary statistic of statistical dispersion or variability. In the general form, the central point can be a mean, median, mode, or the result of any other measure of central tendency or any reference value related to the given data set.
AAD includes the mean absolute deviation and the median absolute deviation (both abbreviated as MAD).
Several measures of statistical dispersion are defined in terms of the absolute deviation.
The term "average absolute deviation" does not uniquely identify a measure of statistical dispersion, as there are several measures that can be used to measure absolute deviations, and there are several measures of central tendency that can be used as well. Thus, to uniquely identify the absolute deviation it is necessary to specify both the measure of deviation and the measure of central tendency. The statistical literature has not yet adopted a standard notation, as both the mean absolute deviation around the mean and the median absolute deviation around the median have been denoted by their initials "MAD" in the literature, which may lead to confusion, since in general, they may have values considerably different from each other.
The mean absolute deviation of a set {x1, x2, ..., xn} is
The choice of measure of central tendency, , has a marked effect on the value of the mean deviation. For example, for the data set {2, 2, 3, 4, 14}:
The mean absolute deviation (MAD), also referred to as the "mean deviation" or sometimes "average absolute deviation", is the mean of the data's absolute deviations around the data's mean: the average (absolute) distance from the mean. "Average absolute deviation" can refer to either this usage, or to the general form with respect to a specified central point (see above).
MAD has been proposed to be used in place of standard deviation since it corresponds better to real life. Because the MAD is a simpler measure of variability than the standard deviation, it can be useful in school teaching.
Source officielle
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