The Sample Median

For a sample $\mathbf{x} = ( x_1, x_2, \ldots, x_n )$, the sample median is defined as follows:

$$ \operatorname{Median}(\mathbf{x}) = \begin{cases} x_{(n+1)/2} & \text{if $n$ is odd}, \\ \big( x_{(n/2)} + x_{(n/2+1)}\big) / 2 & \text{if $n$ is even}, \end{cases} $$

where $x_{(i)}$ is the $i^\textrm{th}$ order statistic.

In the sorted list of values, the sample Median is the middle value. If the number of values is even, the sample Median is the arithmetic average of two middle values.