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Mathematica > Data Manipulation > Statistics > Descriptive Statistics >

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Built-in Mathematica Symbol

MedianDeviation

MedianDeviation[list]
gives the median absolute deviation from the median of the elements in list.

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

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

MedianDeviation of columns of a matrix:

MedianDeviation of columns of a matrix:

Compute results for any real numeric values:

Compute results at machine precision:

Obtain results at any precision:

Compute results for a large vector or matrix:

Compute results for a SparseArray:

Obtain a robust estimate of dispersion when extreme values are present:

Measures based on the Mean are heavily influenced by extreme values:

MedianDeviation is the Median of absolute deviations from the Median:

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

MedianDeviation requires real numeric values:

Ratio of MedianDeviation to MeanDeviation for increasing sample size: