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.

The average absolute deviation of a data set is the average of the absolute deviations and is a summary statistic of statistical dispersion or variability.

The average absolute deviation of a set {x₀, x₁, ..., x_n−1} is:

where is the selected value of central tendency of the set about which the average absolute deviation is being measured.

The median is the point which minimises the average absolute deviation of a data set. For example, for the set {1,2,2,4,6}, 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.