Absolute deviation

Encyclopedia : A : AB : ABS : Absolute deviation

The absolute deviation of an element of a data set is the absolute difference between that element and a given point. Typically the point from which the deviation is measured is the value of either the median or the mean of the data set.

[|D| = |x_i-\overline| ]

where

|D| is the absolute deviation,

x_i is the data element

and [\overline] is the chosen measure of central tendency of the data set.

The average absolute deviation (or simply average deviation) of a data set is the average (or expected value) of the absolute deviations and is a summary statistic of statistical dispersion or variability.

The average absolute deviation of a set is

[\frac\sum_^n |x_i-\overline|.]

The type of central tendency chosen has a significant effect on the value of the average deviation. For example, for the set , the median is 2 while the mean is 3. The average absolute deviation from the median is (1 + 0 + 0 + 2 + 4)/5 = 1.4 while the average absolute deviation from the mean (sometimes called the mean deviation) is (2 + 1 + 1 + 1 + 3)/5 = 1.6.

In general, the average absolute deviation from the mean is between one and two times the average absolute deviation from the median; it is also less than or equal to the standard deviation.

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