Median Absolute Deviation

Median Absolute Deviation

In statistics, the median absolute deviation (MAD) 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:

\operatorname{MAD} = \operatorname{median}_{i}\left(\ \left| X_{i} - \operatorname{median}_{j} (X_{j}) \right|\ \right), \,

that is, starting with the residuals (deviations) from the data's median, the MAD is the median of their absolute values.

Read more about Median Absolute Deviation:  Example, Uses, Relation To Standard Deviation, The Population MAD

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