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The mean absolute deviation (MAD) is a measure of the dispersion or spread of a sample or a population. So one of its purposes is as a measure.

As such it's an alternative to the standard deviation that is said to be more robust in the sense that the sample MAD can be used to provide more accurate estimates of the population dispersion because it is less sensitive to outliers.

Beyond this, some distributions that have no standard deviations do have MADs; for example, the Cauchy. This means that the dispersions of virtually all distributions can be compared in terms of their MADs.

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Q: What is the purpose of mean absolute deviation?
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