=======
Boxplot
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:doc:`/WorkProcessClassifiers/LocalAlgorithm/index` - :doc:`/WorkProcessClassifiers/OneDimensionalAlgorithm/index`

*Boxplot* algorithm marks the lower quartile (:math:`Q1`\ ), the median (:math:`Q2`\ ), the upper quartile (:math:`Q3`\ ) of the given data set. The lower and upper inner fences are defined by :math:`L = Q1 - 1.5(Q3-Q1)` and :math:`U = Q3 + 1.5(Q3-Q1)`\ . Any data value beyond the fences are treated as a value outside the region of interest. 

.. rubric:: Input Parameters

+--------------------+--------------------------------------------+----------------------------------------+--------------------------------------------------+---------+
| Parameter          | Type                                       | Constraint                             | Description                                      | Remarks |
+====================+============================================+========================================+==================================================+=========+
| :math:`Y`          | :math:`Y \in \mathbb R^N`                  | :math:`N \in \mathbb{N}`               | Input data sequence of length :math:`N`          |         |
+--------------------+--------------------------------------------+----------------------------------------+--------------------------------------------------+---------+

.. rubric:: Output Parameters

+----------------------------+----------------------------------------------------+------------+-------------------------------------------------------------------------------------------+---------+
| Parameter                  | Type                                               | Constraint | Description                                                                               | Remarks |
+============================+====================================================+============+===========================================================================================+=========+
| :math:`\hat{Y}`            | :math:`\hat{Y} \in \mathbb R^N`                    |            | Values in the :math:`Y`          list which are outside the region of interest are marked |         |
+----------------------------+----------------------------------------------------+------------+-------------------------------------------------------------------------------------------+---------+

.. rubric:: Tool Support

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

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

.. rubric:: Single Steps using the Algorithm

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

.. rubric:: References

- R.\  McGill, J.W. Tukey, and W.A. Larsen, Variations of Boxplots, The American Statistician., vol. 32(1), pp. 12-16, 1978.