# Median¶

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 $$N$$ None

Output Parameters

Parameter Type Constraint Description Remarks
$$m$$ $$m \in \mathbb R$$ None Median value of $$Y$$ The result is sensitive to improper values such as ‘nan’, ‘inf’, ‘null’, etc.

Single Steps using the Algorithm