Explain median absolute deviation (mad), Advanced Statistics

Median absolute deviation (MAD): It is the very robust estimator of the scale given by the following equation

1368_MAD.png 
or, in other words we can say that, the median of the absolute deviations from the median of data. In order to use MAD as the consistent estimator of the standard deviation it is multiplied by a scale factor which depends on the distribution of the data. For normally distributed data the constant is 1.4826 and expected value of 1.4826 MAD is approximately equal to population standard deviation.

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