The Population MAD
The population MAD is defined analogously to the sample MAD, but is based on the complete distribution rather than on a sample. For a symmetric distribution with zero mean, the population MAD is the 75th percentile of the distribution.
Unlike the variance, which may be infinite or undefined, the population MAD is always a finite number. For example, the standard Cauchy distribution has undefined variance, but its MAD is 1.
The earliest known mention of the concept of the MAD occurred in 1816, in a paper by Carl Friedrich Gauss on the determination of the accuracy of numerical observations.
Read more about this topic: Median Absolute Deviation
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