Median

curriculum-key-fact
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

a) Place these numbers in order:

1,~2,~3,~4,~7,~9,~11

The middle number is 4. Therefore the median is 4.

b) Place these 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) \div 2 = 5

Generally, when there are n numbers, the median will be the \frac{(n + 1)} {2} th number.

For example, if there are 3 numbers, the median will be the (3+1)\div{2}={2}^{nd} number.

If there are 4 numbers, the median will be the (4 + 1) \div 2 = 2 {\frac{1}{2}}^{th} number.

This refers to the value halfway between the {2}^{nd} and {3}^{rd} numbers.

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:

Table showing the amount of goals scored by Rachel's 5-a-side team

What is the median number of goals scored?

20 matches were played, so the median will be the (21 \div {2})^{th} = {10}\frac{1}{2}^{th} value.

0 goals were scored in 7 of the matches, and 1 goal was scored in 5 of the matches.

The {10}\frac{1}{2}^{th} value lies in the ' {1} goal' category.

This is because both the {10}^{th} and {11}^{th} values are ‘ {1} goal’.

Therefore, the median number of goals is 1.