Median absolute deviation
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
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. (1983). Understanding Robust and Exploratory Data Analysis. John Wiley & Sons. pp. 404–414. ISBN 0-471-09777-2. Unknown parameter
- Venables, W.N. (1999). Modern Applied Statistics with S-PLUS. Springer. p. 128. ISBN 0-387-98825-4. Unknown parameter