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The Mean Deviation, also referred to as Absolute Average Deviation, is sometimes preferred to the Standard Deviation (Cf. Gorard 2004). For a sample, it can be expressed as:

$MD = \frac{1}{n} \sum\limits_{i=1}^n |x_i - \overline{x}|$

In order to compare the mean deviations of multiple samples for multiple variables defined with different units, one might want to use a relative version of the Mean Deviation, defined by dividing the Mean Deviation by the absolute value of the mean:

$RMD = \frac{\frac{1}{n} \sum\limits_{i=1}^n |x_i - \overline{x}|}{|\overline{x}|} = \frac{\sum\limits_{i=1}^n |x_i - \overline{x}|}{|X|}$

This Relative Mean Deviation is mentioned in a few articles, but has it been thoroughly studied?

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closed as too broad by whuber Feb 7 '18 at 21:39

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