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Statistics

  

TrimmedMean

  

compute the trimmed mean

  

WinsorizedMean

  

compute the Winsorized mean

 

Calling Sequence

Parameters

Description

Computation

Options

Examples

References

Compatibility

Calling Sequence

TrimmedMean(A, l, u, options)

WinsorizedMean(A, l, u, options)

Parameters

A

-

data set or Matrix data set

l

-

numeric; lower percentile

u

-

numeric; upper percentile

options

-

(optional) equation(s) of the form option=value where option is one of ignore, or weights; specify options for computing the trimmed mean of a data set

Description

• 

The TrimmedMean function computes the mean of points in the dataset data between the lth and uth percentiles.

• 

The WinsorizedMean function computes the winsorized mean of the specified data set.

• 

The first parameter can be a data set (given as e.g. a Vector) or a Matrix data set.

• 

The second parameter l is the lower percentile, the third parameter u is the upper percentile. Note, that both l and u must be numeric constants between 0 and 100. A common choice is to trim 5% of the points in both the lower and upper tails.

Computation

• 

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.

Options

  

The 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 TrimmedMean command. Missing items are represented by undefined or Float(undefined). So, if ignore=false and A contains missing data, the TrimmedMean command may 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.

Examples

withStatistics:

Generate a random sample of size 100000 drawn from the Beta distribution and compute the sample trimmed mean.

ASample'Β'3,5,105:

TrimmedMeanA,5,95

0.370866512196985

(1)

WinsorizedMeanA,5,95

0.373119772244118

(2)

Compute the trimmed mean of a weighted data set.

Vseqi,i=57..77,undefined:

W2,4,14,41,83,169,394,669,990,1223,1329,1230,1063,646,392,202,79,32,16,5,2,5:

TrimmedMeanV,5,95,weights=W

67.0243176820592

(3)

TrimmedMeanV,5,95,weights=W,ignore=true

67.0217433508057

(4)

Consider the following Matrix data set.

MMatrix3,1130,114694,4,1527,127368,3,907,88464,2,878,96484,4,995,128007

M31130114694415271273683907884642878964844995128007

(5)

We compute the 25 percent trimmed mean of each of the columns.

TrimmedMeanM,25,75

3.333333333333331010.666666666671.12848666666667105

(6)

References

  

Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.

Compatibility

• 

The A parameter was updated in Maple 16.

See Also

Statistics

Statistics[Computation]

Statistics[DescriptiveStatistics]

Statistics[Distributions]

Statistics[ExpectedValue]

Statistics[RandomVariables]

Statistics[StandardError]

 


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