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Statistics[MedianDeviation] - compute the median absolute deviation from the median
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Calling Sequence
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MedianDeviation(A, ds_options)
MedianDeviation(X, rv_options)
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Parameters
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A
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Vector or Matrix data set; data sample
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X
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algebraic; random variable or distribution
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ds_options
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(optional) equation(s) of the form option=value where option is one of ignore, or weights; specify options for computing the median absolute deviation of a data set
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rv_options
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(optional) equation of the form numeric=value; specifies options for computing the median absolute deviation of a random variable
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Description
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The MedianDeviation function computes the median absolute deviation from the median of the specified random variable or data set.
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Computation
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By default, all computations involving random variables are performed symbolically (see option numeric below).
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All computations involving data are performed in floating-point; therefore, all data provided must have type realcons and all returned solutions are floating-point, even if the problem is specified with exact values.
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Data Set Options
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The ds_options argument can contain one or more of the options shown below. More information for some options is available in the Statistics[DescriptiveStatistics] help page.
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ignore=truefalse -- This option controls how missing data is handled by the MedianDeviation command. Missing items are represented by undefined or Float(undefined). So, if ignore=false and A contains missing data, the MedianDeviation command will return undefined. If ignore=true all missing items in A will be ignored. The default value is false.
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weights=Vector -- Data weights. The number of elements in the weights array must be equal to the number of elements in the original data sample. By default all elements in A are assigned weight  .
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Random Variable Options
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The rv_options argument can contain one or more of the options shown below. More information for some options is available in the Statistics[RandomVariables] help page.
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numeric=truefalse -- By default, the median absolute deviation is computed symbolically. To compute the median absolute deviation numerically, specify the numeric or numeric = true option.
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Compatibility
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The A parameter was introduced in Maple 16.
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Examples
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Compute the median absolute deviation from the median of the Normal distribution with mean 3 and standard deviation 1.
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Generate a random sample of size 1000000 drawn from the above distribution and compute the sample median absolute deviation.
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Compute the standard error of the median absolute deviation for the normal distribution with parameters 5 and 2.
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Compute the median absolute deviation of a weighted data set.
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Consider the following Matrix data set.
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![M := Matrix([[3, 1130, 114694], [4, 1527, 127368], [3, 907, 88464], [2, 878, 96484], [4, 995, 128007]])](/support/helpjp/helpview.aspx?si=4681/file02897/math304.png)
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![M := Matrix([[3, 1130, 114694], [4, 1527, 127368], [3, 907, 88464], [2, 878, 96484], [4, 995, 128007]])](/support/helpjp/helpview.aspx?si=4681/file02897/math307.png)
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We compute the median absolute deviation of each of the columns.
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](/support/helpjp/helpview.aspx?si=4681/file02897/math316.png)
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References
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Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.
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Download Help Document
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