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In statistics, the median absolute deviation is a robust measure of the variability of a univariate sample of quantitative data. It can also refer to the population parameter that is estimated by the MAD calculated from a sample.
For a univariate data set X1, X2, ..., Xn, the MAD is defined as the median of the absolute deviations from the data's median X ~ = median {\displaystyle {\tilde {X}}=\operatorname {median} } :
that is, starting with the residuals from the data's median, the MAD is the median of their absolute values.
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