How this calculator works
First find the ordinary median, then take each absolute distance from it, and find the median of those distances. Raw MAD has the original data unit. The optional factor 1.4826 makes it an asymptotically consistent estimate of standard deviation for normal data, following the conventional rounded factor used by R. It is not an exact conversion for arbitrary distributions or very small samples.
Formula
Raw MAD = median(|x_i - median(x)|); normal-consistent MAD ≈ 1.4826 × raw MAD.
Worked example
For 1, 2, 3, 4, 100, the median is 3 and absolute distances are 2, 1, 0, 1, 97. Their median is 1, so raw MAD is 1.
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Frequently asked questions
Can MAD be zero with an outlier?
Yes. If enough observations equal the median, the middle absolute distance is zero even when other values differ.
Is this mean absolute deviation?
No. This tool takes a median twice. The mean absolute deviation tool averages distances from a chosen centre.
Should I always use the scaled result?
Use scaling when you want a normal-model estimate of standard deviation. Report raw MAD when describing the median absolute distance itself.