 Because the MAD is a more robust estimator of scale than the sample variance or standard deviation, it works better with distributions without a mean or variance, such as the Cauchy distribution.The MAD may be used similarly to how one would use the deviation for the average.In order to use the MAD as a consistent estimator for the estimation of the standard deviation formula_3, one takes

where formula_5 is a constant scale factor, which depends on the distribution.