The mean absolute deviation is defined as

 mad = mean (abs (x - mean (x)))
 

The median absolute deviation is defined as

 mad = median (abs (x - median (x)))
 

If x is a vector, compute mad for each element in x. If x is an array the calculation is performed over the first non-singleton dimension.

mad excludes NaN values from calculation similar to using the omitnan option in var, mean, and median.

The optional argument opt determines whether mean or median absolute deviation is calculated. The default is 0 which corresponds to mean absolute deviation; a value of 1 corresponds to median absolute deviation. Passing an empty input [] defaults to mean absolute deviation (opt = 0).

The optional argument dim forces mad to operate along the specified dimension. Specifying any singleton dimension in x, including any dimension exceeding ndims (x), will result in an output of 0.

Specifying the dimension as vecdim, a vector of non-repeating dimensions, will return the mad over the array slice defined by vecdim. If vecdim indexes all dimensions of x, then it is equivalent to the option "all". Any dimension included in vecdim greater than ndims (x) is ignored.

Specifying the dimension as "all" will force mad to operate on all elements of x, and is equivalent to mad (x(:)).

As a measure of dispersion, mad is less affected by outliers than std. See also: bounds, range, iqr, std, mean, median

Source Code: mad