Q.Find the median of the data $6, 7, 10, 12, 13, 4, 8, 12$.

Median of Ungrouped Data

The median is the middle value of a data set — the observation that splits the ordered data into two equal halves. Being a positional average, it is unaffected by extreme values, which makes it more representative than the mean when the data contain outliers. The essential first step is always to arrange the raw observations in ascending (or descending) order.

For $n$ ungrouped observations arranged in order, the rule depends on whether $n$ is odd or even. If $n$ is odd, the median is the single middle value, the $\left(\dfrac{n+1}{2}\right)$th observation. If $n$ is even, there are two middle values and the median is their average:

$\text{Median} = \frac{1}{2}\left[\left(\frac{n}{2}\right)\text{th} + \left(\frac{n}{2}+1\right)\text{th}\right].$ …