The mean deviation (also called the mean absolute deviation) is the mean of the absolute deviations of a set of data about the data's mean. For a sample size N, the mean deviation is defined by MD congruent 1/N sum_(i = 1)^N left bracketing bar x_i - x^_ right bracketing bar , where x^_ is the mean of the distribution. The mean deviation of a list of numbers is implemented in the Wolfram Language as MeanDeviation[data]. The mean deviation for a discrete distribution P_i defined for i = 1, 2, ..., N is given by MD = sum_(i = 1)^N P_i left bracketing bar x_i - x^_ right bracketing bar .
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