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

*Mean* algorithm takes the average of the available values. The basic formula is stated as follows:

.. math::

   \mu = \frac{\sum_{i=1}^{N} Y_i}{N}

where :math:`Y_i` denotes the :math:`i`\ th value in the data set, :math:`N` is the length of the data vector and :math:`\mu` is the computed mean value.

.. 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`          |         |
+--------------------+--------------------------------------------+----------------------------------------+------------------------------------------------+---------+

.. rubric:: Output Parameters

+------------------------+--------------------------------------------+------------+-----------------------------------------------------------+-------------------------------------------------------------------------------+
| Parameter              | Type                                       | Constraint | Description                                               | Remarks                                                                       |
+========================+============================================+============+===========================================================+===============================================================================+
| :math:`\mu`            | :math:`\mu \in \mathbb R`                  |            | Mean value of data values available in :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 `'AVERAGE' <https://support.office.com/en-us/article/AVERAGE-function-047bac88-d466-426c-a32b-8f33eb960cf6>`__.

* :doc:`/Tools/MapleTool/index`

  For details refer to the online documentation of the function `'MEAN' <http://www.maplesoft.com/support/help/Maple/view.aspx?path=Statistics/Mean>`__.

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

  For details refer to the online documentation of the function `'mean' <http://www.mathworks.de/help/techdoc/ref/mean.html>`__.

.. rubric:: Single Steps using the Algorithm

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

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

* :doc:`/DataPreprocessing/DataIntegration/ResolvingDataValueConflict/ResolvingDataValueConflictWithMean/index`