====== Median ====== :doc:`/WorkProcessClassifiers/GlobalAlgorithm/index` - :doc:`/WorkProcessClassifiers/OneDimensionalAlgorithm/index` For a set of ordered data values, the following formulas are used to compute the *Median* value: .. math:: m = Y_{\frac{N+1}{2}}, \quad \text{for odd values of } N .. math:: m = \frac{Y_{\frac{N}{2}} + Y_{\frac{N}{2} + 1}}{2}, \quad \text{for even values of } N where :math:`Y` is the input data vector and must be ordered. In case :math:`Y` is not ordered, a sorting algorithm is required. :math:`N` is the length of the data vector and :math:`m` represents the computed median 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:`m` | :math:`m \in \mathbb R` | | Median value of :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 `'MEDIAN' `__. * :doc:`/Tools/MatlabTool/index` For details refer to the function `'median' `__. For details refer to the online documentation of the function `'median' `__. .. rubric:: Single Steps using the Algorithm * :doc:`/DataPreprocessing/MathematicalComputation/ComputingMedianValueWithMedian/index` * :doc:`/DataPreprocessing/DataCleaning/HandlingImproperValues/ReconstructingImproperValues/ReconstructingImproperValuesWithLocalCenteredMovingMedian/index`