What is MAD and why is it robust?

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Answer

$\mathrm{MAD}(X)\; = \;\mathrm{median}( \mid X_{i}\; - \;\mathrm{median}(X) \mid )$
$Robust measure of dispersion — breakdown point 50% (half the data can be arbitrarily corrupted before MAD explodes; SD breaks down at 0%).$
$Use MAD instead of SD when data has outliers.$
$Scaled MAD: 1.4826 * MAD estimates σ under normality (approximately unbiased).$
$Foundation of robust statistics.$

Check yourself — multiple choice

Same as SD
$\mathrm{median}( \mid X\; - \;\mathrm{median}(X) \mid )$ — 50% breakdown point (SD has 0%); scaled by 1.4826 approximates σ under normality
Not robust
Requires normality

MAD: median absolute deviation; 50% breakdown → robust dispersion measure.

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