Median

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

• Excel

  For details refer to the online documentation of the function ‘MEDIAN’.

• Matlab

  For details refer to the function ‘median’.

  For details refer to the online documentation of the function ‘median’.

Single Steps using the Algorithm

• Computing Median Value with Median Algorithm
• Reconstructing Improper Values with Local Centered Moving Median