MedianΒΆ
Global Algorithm - One-Dimensional Algorithm
For a set of ordered data values, the following formulas are used to compute the Median value:
\[m = Y_{\frac{N+1}{2}}, \quad \text{for odd values of } N\]
\[m = \frac{Y_{\frac{N}{2}} + Y_{\frac{N}{2} + 1}}{2}, \quad \text{for even values of } N\]
where \(Y\) is the input data vector and must be ordered. In case \(Y\) is not ordered, a sorting algorithm is required. \(N\) is the length of the data vector and \(m\) represents the computed median value.
Input Parameters
| Parameter | Type | Constraint | Description | Remarks |
|---|---|---|---|---|
| \(Y\) | \(Y \in \mathbb R^N\) | \(N \in \mathbb{N}\) | Input data vector of length \(N\) |
Output Parameters
| Parameter | Type | Constraint | Description | Remarks |
|---|---|---|---|---|
| \(m\) | \(m \in \mathbb R\) | Median value of \(Y\) | The result is sensitive to improper values such as ‘nan’, ‘inf’, ‘null’, etc. |
Tool Support
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For details refer to the online documentation of the function ‘MEDIAN’.
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For details refer to the function ‘median’.
For details refer to the online documentation of the function ‘median’.
Single Steps using the Algorithm