TrimmedMean - Maple Help

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.

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.

 > $A≔\mathrm{Sample}\left('\mathrm{Β}'\left(3,5\right),{10}^{5}\right):$
 > $\mathrm{TrimmedMean}\left(A,5,95\right)$
 ${0.370778654310778}$ (1)
 > $\mathrm{WinsorizedMean}\left(A,5,95\right)$
 ${0.373017971242823}$ (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.