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.

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.

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 $1$.

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

$A≔\mathrm{Sample}\left('\mathrm{{\rm B}}'\left(3\,5\right)\,{10}^5\right)\:$

$\mathrm{TrimmedMean}\left(A\,5\,95\right)$

$0.370778654310778$

$\mathrm{WinsorizedMean}\left(A\,5\,95\right)$

$0.373017971242823$

$V≔⟨\mathrm{seq}\left(i\,i=57..77\right)\,\mathrm{undefined}⟩\:$

$W≔⟨2\,4\,14\,41\,83\,169\,394\,669\,990\,1223\,1329\,1230\,1063\,646\,392\,202\,79\,32\,16\,5\,2\,5⟩\:$

$\mathrm{TrimmedMean}\left(V\,5\,95\,\mathrm{weights}=W\right)$

$67.0243176820592$

$\mathrm{TrimmedMean}\left(V\,5\,95\,\mathrm{weights}=W\,\mathrm{ignore}=\mathrm{true}\right)$

$67.0217433508057$

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

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

$\mathrm{TrimmedMean}\left(M\,25\,75\right)$

$\left[\begin{array}{ccc}3.33333333333333& 1010.66666666667& 112848.666666667\end{array}\right]$

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

The A parameter was updated in Maple 16.