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Built-in Mathematica Symbol

MeanDeviation

MeanDeviation[list]
gives the mean absolute deviation from the mean of the elements in list.

For the list {x₁, x₂, ..., x_n}, the mean deviation is given by , where is the mean of the list.

MeanDeviation[{{x₁, y₁, ...}, {x₂, y₂, ...}, ...}] gives {MeanDeviation[{x₁, x₂, ...}], MeanDeviation[{y₁, y₂, ...}, ...]}.

MeanDeviation of columns of a matrix:

MeanDeviation of columns of a matrix:

Compute results at machine precision:

Obtain results at any precision:

Compute results for a large vector or matrix:

Compute results for a SparseArray:

MeanDeviation is the Mean of absolute deviations from the Mean:

MeanDeviation is equivalent to the 1-norm of the deviations divided by the Length:

For large uniform datasets, MeanDeviation and MedianDeviation are nearly the same:

Ratio of MeanDeviation to MedianDeviation for increasing sample size: