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Statistics

 TrimmedMean
 compute the trimmed mean
 WinsorizedMean
 compute the Winsorized mean

 Calling Sequence TrimmedMean(A, l, u, options) WinsorizedMean(A, l, u, options)

Parameters

 A - 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

 > $\mathrm{with}\left(\mathrm{Statistics}\right):$

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

 > $A≔\mathrm{Sample}\left('\mathrm{Β}'\left(3,5\right),{10}^{5}\right):$
 > $\mathrm{TrimmedMean}\left(A,5,95\right)$
 ${0.370866512196985}$ (1)
 > $\mathrm{WinsorizedMean}\left(A,5,95\right)$
 ${0.373119772244118}$ (2)

Compute the trimmed mean of a weighted data set.

 > $V≔⟨\mathrm{seq}\left(i,i=57..77\right),\mathrm{undefined}⟩:$
 > $W≔⟨2,4,14,41,83,169,394,669,990,1223,1329,1230,1063,646,392,202,79,32,16,5,2,5⟩:$
 > $\mathrm{TrimmedMean}\left(V,5,95,\mathrm{weights}=W\right)$
 ${67.0243176820592}$ (3)
 > $\mathrm{TrimmedMean}\left(V,5,95,\mathrm{weights}=W,\mathrm{ignore}=\mathrm{true}\right)$
 ${67.0217433508057}$ (4)

Consider the following Matrix data set.

 > $M≔\mathrm{Matrix}\left(\left[\left[3,1130,114694\right],\left[4,1527,127368\right],\left[3,907,88464\right],\left[2,878,96484\right],\left[4,995,128007\right]\right]\right)$
 ${M}{≔}\left[\begin{array}{ccc}{3}& {1130}& {114694}\\ {4}& {1527}& {127368}\\ {3}& {907}& {88464}\\ {2}& {878}& {96484}\\ {4}& {995}& {128007}\end{array}\right]$ (5)

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

 > $\mathrm{TrimmedMean}\left(M,25,75\right)$
 $\left[\begin{array}{ccc}{3.33333333333333}& {1010.66666666667}& {112848.666666667}\end{array}\right]$ (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.