Dispersion

Standard Deviation

Summing the squared deviations from the mean

Extremely sensitive to outliers as we are squaring the deviations

The mean absolute deviation (MAD)

A more robust alternative

Because deviations are not squared, large deviations do not get a large impact

MAD <= STD for a given sample size

There is still a mean which can still be sensitive to outliers although less than STD

We can use median absolute deviation

medAbsDev = median(|xi - median(x)|)

(Arithmetic) Mean (L2 Central tendency) Median (L1 Central tendency) SD (L2 Dispersion) MAD (L1 Dispersion)

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