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MAD versus STD Dev

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This is more a purpose of use question than understanding of the concept. Has anyone every ran into or can give me an example when you would rather use MAD (mean abs deviation) rather than the standard deviation? As stated, in general the MAD will be less than the Std deviation of a population or sample. Just thinking about it conceptually the context of what you are looking at might be a worthwhile mention. If the context of measuring is around the mean than STD dev makes sense. But if the context is about the median, then maybe you use MAD?  

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