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.^[1]

For a univariate data set X₁, X₂, ..., X_n, the MAD is defined as the median of the absolute deviations from the data's median ${\displaystyle {\tilde {X}}=\operatorname {median} (X)}$:

${\displaystyle \operatorname {MAD} =\operatorname {median} (|X_{i}-{\tilde {X}}|)}$

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