Median absolute deviation

In <a href="/facts/Statistics/DNPsKGYU">statistics</a>, the median absolute deviation (MAD) is a <a href="/facts/Robust_statistics/RwIMvtD2">robust</a> measure of the <a href="/facts/Statistical_dispersion/xqevRHmz">variability</a> of a <a href="/facts/Univariate/PYwC7u5H">univariate</a> sample of <a href="/facts/Quantitative_data/C1t5h075">quantitative data</a>. It can also refer to the <a href="/facts/Statistical_population/KAILs8E3">population</a> <a href="/facts/Parameter/zFvVFMv9">parameter</a> that is <a href="/facts/Statistical_estimation/4nbgFDec">estimated</a> by the MAD calculated from a sample.
For a univariate data set X1, X2, ..., Xn, the MAD is defined as the <a href="/facts/Median/YwXGWTyr">median</a> of the <a href="/facts/Absolute_deviation/F7cqnhtF">absolute deviations</a> from the data's median 
 
 
 
 
 
 
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 {\displaystyle {\tilde {X}}=\operatorname {median} (X)}
 
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    {\displaystyle \operatorname {MAD} =\operatorname {median} (|X_{i}-{\tilde {X}}|)}

that is, starting with the <a href="/facts/Errors_and_residuals_in_statistics/Ef0LgAS4">residuals</a> (deviations) from the data's median, the MAD is the <a href="/facts/Median/YwXGWTyr">median</a> of their <a href="/facts/Absolute_value/dwJBpEs5">absolute values</a>.

Median absolute deviation open-in-new

Median absolute deviation