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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

-

data set or Matrix data set

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 (given as e.g. a Vector), a Matrix 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 1.

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.

Examples

withStatistics:

Compute the median absolute deviation from the median of the Normal distribution with mean 3 and standard deviation 1.

MedianDeviationNormal3,1

RootOf2erf_Z12

(1)

MedianDeviationNormal3,1,numeric

0.674489750196106

(2)

Generate a random sample of size 1000000 drawn from the above distribution and compute the sample median absolute deviation.

A:=SampleNormal3,1,106:

MedianDeviationA

0.674786032284129

(3)

Compute the standard error of the median absolute deviation for the normal distribution with parameters 5 and 2.

X:=RandomVariableNormal5,2:

B:=SampleX,106:

MedianDeviationX

2RootOf2erf_Z12

(4)

M:=MedianX

M:=5

(5)

MedianXM

2RootOf2erf_Z12

(6)

MedianDeviationX,numeric

1.34897950039221

(7)

MedianDeviationB

1.34782956254174

(8)

Compute the median absolute deviation of a weighted data set.

V:=seqi,i=57..77,undefined:

W:=2,4,14,41,83,169,394,669,990,1223,1329,1230,1063,646,392,202,79,32,16,5,2,5:

MedianDeviationV,weights=W

2.

(9)

MedianDeviationV,weights=W,ignore=true

2.

(10)

Consider the following Matrix data set.

M:=Matrix3,1130,114694,4,1527,127368,3,907,88464,2,878,96484,4,995,128007

M:=31130114694415271273683907884642878964844995128007

(11)

We compute the median absolute deviation of each of the columns.

MedianDeviationM

1.117.13313.

(12)

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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