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In statistics, the median absolute deviation (or "MAD") is a resistant measure of the variability of a univariate sample. It is useful for describing the variability of data with outliers.
For a univariate data set X1, X2, ..., Xn, the MAD is defined as
Relation to standard deviation Edit
As an estimate for the standard deviation σ, one takes
where K is a constant. For normally distributed data K is taken to be 1 / Φ-1(3/4) (where Φ-1 is the inverse of the cumulative distribution function for the standard normal distribution), or 1.4826... , because the MAD is given by:
In this case, its expectation for large samples of normally distributed Xi is approximately equal to the standard deviation of the normal distribution.
- Hoaglin, David C.; Frederick Mosteller and John W. Tukey (1983). Understanding Robust and Exploratory Data Analysis, 404-414, John Wiley & Sons.
- Venables, W.N.; B.D. Ripley (1999). Modern Applied Statistics with S-PLUS, 128, Springer.