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)


x a numeric vector.
center Optionally, the centre: defaults to the median.
constant scale factor.
na.rm if TRUE then NA values are stripped from x before computation takes place.
low if TRUE, compute the “lo-median”, i.e., for even sample size, do not average the two middle values, but take the smaller one.
high 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.

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

E[mad(X_1,...,X_n)] = σ

for X_i distributed as N(μ,σ^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, co=1), mad(x, co=1, lo = TRUE), mad(x, co=1, hi = TRUE))

[Package stats version 2.5.0 Index]