mad {stats}R Documentation

Median Absolute Deviation


Compute the median absolute deviation, i.e., the (lo-/hi-) median of the absolute deviations from the median, and (by default) adjust by a factor for asymptotically normal consistency.


mad(x, center = median(x), constant = 1.4826, na.rm = FALSE,
    low = FALSE, high = FALSE)



a numeric vector.


Optionally, the centre: defaults to the median.


scale factor.


if TRUE then NA values are stripped from x before computation takes place.


if TRUE, compute the ‘lo-median’, i.e., for even sample size, do not average the two middle values, but take the smaller one.


if TRUE, compute the ‘hi-median’, i.e., take the larger of the two middle values for even sample size.


The actual value calculated is constant * cMedian(abs(x - center)) with the default value of center being median(x), and cMedian being the usual, the ‘low’ or ‘high’ median, see the arguments description for low and high above.

In the case of n = 1 non-missing values and default center, the result is 0, consistent with “no deviation from the center”.

The default constant = 1.4826 (approximately 1/\Phi^{-1}(\frac 3 4) = 1/qnorm(3/4)) ensures consistency, i.e.,

E[mad(X_1,\dots,X_n)] = \sigma

for X_i distributed as N(\mu, \sigma^2) and large n.

If na.rm is TRUE then NA values are stripped from x before computation takes place. If this is not done then an NA value in x will cause mad to return NA.

See Also

IQR which is simpler but less robust, median, var.


print(mad(c(1:9),     constant = 1)) ==
      mad(c(1:8, 100), constant = 1)       # = 2 ; TRUE
x <- c(1,2,3,5,7,8)
sort(abs(x - median(x)))
c(mad(x, constant = 1),
  mad(x, constant = 1, low = TRUE),
  mad(x, constant = 1, high = TRUE))

[Package stats version 4.3.0 Index]