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 a summary statistic of statistical dispersion or variability.

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 is (2+1+1+1+3)/5=1.6.