How this calculator works
Absolute deviation removes the sign of each distance before averaging, so positive and negative departures do not cancel. The mean-centred version describes average distance from the mean; changing the centre changes the question. A median centre minimises the total absolute distance. The divisor stays n, because this is an average of distances rather than the usual unbiased sample-variance calculation.
Formula
Mean absolute deviation about c = Σ|x_i - c|/n. By default c = Σx_i/n.
Worked example
For 1, 2, 3, 4, 5, the mean is 3 and absolute distances are 2, 1, 0, 1, 2. Their average is 6/5 = 1.2.
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Frequently asked questions
Does MAD always mean this statistic?
No. MAD also abbreviates median absolute deviation. This page takes the mean of distances; the median version has its own tool.
What unit does it use?
The same unit as the observations and centre. It does not square that unit.
Can I compare different centres?
Yes. For 0, 0, 6, the median centre 0 gives an average distance of 2; the mean centre 2 gives 8/3.