Home > Maths > Handling data > Measures of average

Maths

Measures of average

Print

# The median

If you place a set of numbers in order, the median number is the middle one.

If there are two middle numbers, the median is the mean of those two numbers.

## Finding the median

Question

Find the median of each of the following sets of numbers:

a) 2, 4, 7, 1, 9, 3, 11
b) 4, 1, 3, 10, 6, 9,

Answer

a) Place the numbers in order:
1, 2, 3, 4, 7, 9, 11
The middle number is 4. Therefore the median is 4.

b) Place the numbers in order:
1, 3, 4, 6, 9, 10
there are two middle numbers (4 and 6), so we find the mean of these two numbers. The median is therefore:

(4 + 6) ÷ 2 = 5

In general:

If there are n numbers, the median will be the (n + 1) ÷ 2 = th number

If there are 3 numbers, the median will be the (3 + 1) ÷ 2 = 2nd number.

If there are 4 numbers, the median will be the (4 + 1) ÷ 2 = 21/2th number

### Example

Question

Rachel records the number of goals scored by her five-a-side team in their first 20 matches.

The results are shown in the frequency table below:

Numbers of goals Frequency
0 7
1 5
2 6
3 0
4 2
4 0

What is the median number of goals scored?

Answer

20 matches were played, so the median will be the 21 ÷ 2 th value.
7 matches scored 0 goals, and 5 matches scored 1 goal.

The 21 ÷ 2 th value lies in the '1 goal' category.
21 ÷ 2 = 10 1/2
Therefore, the median number of goals is 1.

BBC iD

## BBC navigation

This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.