============
Trimmed Mean
============
:doc:`/WorkProcessClassifiers/GlobalAlgorithm/index` - :doc:`/WorkProcessClassifiers/OneDimensionalAlgorithm/index`

*Trimmed Mean* algorithm chops off values at the high and low extremes and applies the *Mean* algorithm to the remaining observations. In this way, the effect caused by a small number of extreme values can be offsetted.

.. rubric:: Input Parameters

+--------------------+--------------------------------------------+--------------------------------------------+----------------------------------------------------+---------+
| Parameter          | Type                                       | Constraint                                 | Description                                        | Remarks |
+====================+============================================+============================================+====================================================+=========+
| :math:`Y`          | :math:`Y \in \mathbb R^N`                  | :math:`N \in \mathbb{N}`                   | Input data vector of length :math:`N`              |         |
+--------------------+--------------------------------------------+--------------------------------------------+----------------------------------------------------+---------+
| :math:`p`          | :math:`p \in \mathbb R`                    | :math:`0\% \lt p \lt 50\%`                 | Percentage of high and low extremes to be trimmed  |         |
+--------------------+--------------------------------------------+--------------------------------------------+----------------------------------------------------+---------+

.. rubric:: Output Parameters

+------------------------+--------------------------------------------+------------+-----------------------------------------------+-------------------------------------------------------------------------------+
| Parameter              | Type                                       | Constraint | Description                                   | Remarks                                                                       |
+========================+============================================+============+===============================================+===============================================================================+
| :math:`\mu`            | :math:`\mu \in \mathbb R`                  |            | Trimmed mean value of data :math:`Y`          | The result is sensitive to improper values such as 'nan', 'inf', 'null', etc. |
+------------------------+--------------------------------------------+------------+-----------------------------------------------+-------------------------------------------------------------------------------+

.. rubric:: Tool Support

* :doc:`/Tools/ExcelTool/index`

  For details refer to the online documentation of the function `'TRIMMEAN' <http://office.microsoft.com/en-gb/excel-help/trimmean-HP005209322.aspx>`__.

* :doc:`/Tools/MatlabTool/index`

  For details refer to the online documentation of the function `'trimmean' <http://www.mathworks.de/help/toolbox/stats/trimmean.html>`__.

.. rubric:: Single Steps using the Algorithm

* :doc:`/DataPreprocessing/MathematicalComputation/ComputingTrimmedMeanValueWithTrimmedMean/index`

* :doc:`/DataPreprocessing/DataCleaning/OutlierDetection/OutlierDetectionWithTrimmedMean/index`

* :doc:`/DataPreprocessing/DataCleaning/HandlingImproperValues/ReconstructingImproperValues/ReconstructingImproperValuesWithLocalCenteredMovingTrimmedMean/index`