MAD stands for the median absolute deviation.
It is one way to estimate the variability in a set of data, particularly when the data set has some extreme values as outliers. The general approach is to take the absolute values of deviations of individual values from a measure of their central tendency (i.e., the median of the data set).
Why do we choose to use the median instead of the arithmetic mean?
The median, by definition, is the middle value in an ordered sequence of data. Thus, it is unaffected by extreme values in the data set.
Therefore, we calculate the deviation of each data from the median of the original data set and then again find the median of the absolute values of these deviations, expressed as MAD. It is being used in the robust statistics.
We often use wish to use MAD as an estimator of the population standard deviation, but it cannot be adopted directly but has to be multiplied by a constant, 1.4826 first to become a consistent estimate of the population standard deviation.
It may be noted that an important desirable property of a statistic is consistency. A consistent statistic comes nearer to a population parameter when the size of the sample on which it is based gets larger. For example, analysis of 3 samples may give a sample mean which is much different from the expected population mean but when 30 samples are analyzed, the mean would be found much closer to the population parameter as the mean is known to be a consistent statistic.
You may wish to read our previous article https://consultglp.com/2015/02/02/robust-statistics-mad-method/ which demonstrates how the constant, 1.4826 is derived from.