How to Find the Median
Finding the Median
We can find the median of a set of numbers.
Imagine a teacher wanted to find the class's average test score in mathematics.
How to Find the Median
The median is found by ordering the numbers and finding the middle number.
The middle number is slightly different depending on whether there are an odd or even number of numbers in the set.

If there are an odd number of numbers, the median is simply the middle number in the set.

If there are an even number of numbers, the median is halfway between the middle two numbers. (It is the mean of the middle two numbers).
Let's look at an example of an odd numbered set and an even numbered set separately.
Odd Numbered Set
Question
What is the median of the test scores below?
StepbyStep:
1
List the numbers in numerical order (going from the smallest to the largest number).
7 10 8 6 4 → 4 6 7 8 10
2
Find the middle number. In our example, the middle number is the 3^{rd} number of 5.
4 6 7 8 10
Median = 7
Answer:
The median of the test scores is 7.
Even Numbered Set
This time, 6 students take a mathematics test.
Question
What is the median of the test scores below?
StepbyStep:
1
List the numbers in numerical order (going from the smallest to the largest number).
8 9 5 6 5 10 → 5 5 6 8 9 10
2
Find the middle two numbers. In our example, the middle two numbers are the 3^{rd} 4^{th} numbers of 6.
5 5 6 8 9 10
Middle two numbers = 6 8
3
Answer:
The median of the test scores is 7.
A Formula to Find the Middle Number
In the two examples above, we have quoted that the 3^{rd} number is the middle of 5 and that the 3^{rd} and 4^{th} are the middle two of 6.
It is relatively easy to see by eye where the middle number is when there are relatively few of them and they are written out in front of us. It may not always be this easy.
Luckily, there is a formula for finding which is the middle number.
In this formula, n is how many numbers there are in the set.
Let's apply this formula to the two examples above.

In the first example, we are asked to find the median of 5 numbers (7, 10, 8, 6 and 4). This means that n = 5.
Using the formula to find the middle number gives:
Middle number = (n + 1) ÷ 2 = (5 + 1) ÷ 2 = 6 ÷ 2 = 3
The median of 7 10 8 6 4 is the 3^{rd} number when they are ordered:
7 10 8 6 4 → 4 6 7 8 10
Median = 7

In the second example, we are asked to find the median of 6 numbers (8, 9, 5, 6, 5 and 10). This means that n = 6.
Using the formula to find the middle number gives:
Middle number = (n + 1) ÷ 2 = (6 + 1) ÷ 2 = 7 ÷ 2 = 3.5
The median of 8 9 5 6 5 10 is the 3.5^{th} number when they are ordered, which means halfway between the 3^{rd} and 4^{th} numbers:
8 9 5 6 5 10 → 5 5 6 8 9 10
Halfway between 3^{rd} and 4^{th} numbers = (6 + 8) ÷ 2 = 7
Median = 7