### Theory:

Median refers to the middle value among a set or series of values after they have been arranged in numerical order. Thus median means the middle of the set of values.
Case 1: If the number of observations (n) in the set is odd, then the median is the value at the position  $\frac{\left(n+1\right)}{2}$.

Case 2: If the number of observation (n) in the set is even:
Step 1: Find the value at position $\frac{n}{2}$

Step 2: Find the value at position $\frac{n+1}{2}$

Step 3: Find the average of both the values to get the median.
Example:
Find the median of the following set of points in a game:
$$15, 14, 10, 8, 12, 8, 16$$

Solution:

First arrange the point values in an ascending order (or descending order).
$$8, 8, 10, 12, 14, 15, 16$$

The number of point values is $$7$$, an odd number. Hence, the median is the value in the middle position.

$\begin{array}{l}\frac{\left(n+1\right)}{2}\\ \\ =\frac{7+1}{2}\\ \\ =\frac{8}{2}\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}4\end{array}$

The value at the $$4$$th position is $$12$$.

Median $$= 12$$.
Example:
Find the median of the following set of points:
$$15, 14, 10, 8, 12, 8, 16, 13$$

Solution:
First, arrange the point values in ascending order (or descending order).

8, 8, 10, 12, 13, 14, 15, 16
The number of point values is $$8$$, an even number. Hence the median is the average of the middle two values.

The first, middle value, $\frac{n}{2}=\frac{8}{2}=4$ is at $$4$$th position, which is $$12$$.

The second middle value is,

$\begin{array}{l}\frac{n+1}{2}=\frac{8+1}{2}=\frac{9}{2}\\ \\ =\phantom{\rule{0.147em}{0ex}}4.5\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}5\phantom{\rule{0.147em}{0ex}}\left(\mathit{rounded}\phantom{\rule{0.147em}{0ex}}\mathit{off}\phantom{\rule{0.147em}{0ex}}\mathit{to}\phantom{\rule{0.147em}{0ex}}\mathit{integer}\phantom{\rule{0.147em}{0ex}}\mathit{value}\right)\end{array}$

The value at the $$5$$th position is $$13$$.

The average of them is $\frac{12+13}{2}=\phantom{\rule{0.147em}{0ex}}12.5$.

Therefore $$12.5$$ is the median.