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Statistics[MedianDeviation] - compute the median absolute deviation from the median
Calling Sequence
MedianDeviation(A, ds_options)
MedianDeviation(X, rv_options)
Parameters
A
-
Vector or Matrix data set; data sample
X
algebraic; random variable or distribution
ds_options
(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
rv_options
(optional) equation of the form numeric=value; specifies options for computing the median absolute deviation of a random variable
Description
The MedianDeviation function computes the median absolute deviation from the median of the specified random variable or data set.
The first parameter can be a data set, a distribution (see Statistics[Distribution]), a random variable, or an algebraic expression involving random variables (see Statistics[RandomVariable]).
Computation
By default, all computations involving random variables are performed symbolically (see option numeric below).
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.
For more information about computation in the Statistics package, see the Statistics[Computation] help page.
Data Set Options
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.
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.
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 .
Random Variable Options
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.
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.
Compatibility
The A parameter was introduced in Maple 16.
For more information on Maple 16 changes, see Updates in Maple 16.
Examples
Compute the median absolute deviation from the median of the Normal distribution with mean 3 and standard deviation 1.
Generate a random sample of size 1000000 drawn from the above distribution and compute the sample median absolute deviation.
Compute the standard error of the median absolute deviation for the normal distribution with parameters 5 and 2.
Compute the median absolute deviation of a weighted data set.
Consider the following Matrix data set.
We compute the median absolute deviation of each of the columns.
See Also
Statistics, Statistics[Computation], Statistics[DescriptiveStatistics], Statistics[Distributions], Statistics[ExpectedValue], Statistics[Median], Statistics[RandomVariables]
References
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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