MAD

Description

The MAD function returns the median absolute deviation from the median; like the IQR it is a robust estimator of scale. And like the IQR function, the MAD optionally returns a corrected form instead of the uncorrected value (which is the default).

Syntax

MAD(data, [corrected=FALSE]) where

• data is the univariate data (any shape), filtering out non-numeric values
• corrected is a boolean that determines whether to divide by a correcting factor

The syntax and philosophy are similar to the IQR function: “correction” means dividing by the MAD of the standard normal distribution (which is also the value of the third quartile, $Q_3 = 0.6745$).

Example

Usage is straightforward: pass in the data as the first argument, and if the corrected value is desired pass in a value of TRUE for the second argument. Note that Excel interprets any nonzero number as TRUE and it is common to use syntax like =MAD(data,1) to obtain the corrected MAD for the data.

Source Code

MAD = LAMBDA(
    X, // input data (any shape)
    [corrected], // apply correction? Default is FALSE.
    LET(
        corrected, IF(ISOMITTED(corrected), FALSE, corrected),
        Xc, TOCOL(X),
        Xn, FILTER(Xc, ISNUMBER(Xc)),
        MAD, MEDIAN(ABS(Xn - MEDIAN(Xn))),
        IF(corrected, MAD / NORM.S.INV(0.75), MAD)
    )
);