Appears in: Functional Skills Level 1 · Functional Skills Level 2 · GCSE foundation
Mean, median, mode and range
Averages appear on every paper we cover, from Level 1 upwards. Four measures, each with a one-line definition — the trick is remembering which is which under pressure, and spotting the twist when the data comes in a table.
The four measures
- Mean: add all the values, divide by how many there are.
- Median: put the values in order and take the middle one. With an even number of values, take the mean of the middle two.
- Mode: the value that appears most often. There can be more than one, or none.
- Range: biggest value minus smallest value. It measures spread, not average.
- From a frequency table: multiply each value by its frequency, add those up, and divide by the total frequency.
Worked examples
Example 1
Find the mean, median, mode and range of 12, 15, 9, 15, 20, 7.
- Mean: 12 + 15 + 9 + 15 + 20 + 7 = 78; 78 ÷ 6 = 13.
- Median: in order, 7, 9, 12, 15, 15, 20; the middle two are 12 and 15, so (12 + 15) ÷ 2 = 13.5.
- Mode: 15 (it appears twice).
- Range: 20 − 7 = 13.
Example 2
20 people were asked how many pets they have: 5 said 0, 8 said 1, 4 said 2 and 3 said 3. What is the mean number of pets?
- Total pets: (0 × 5) + (1 × 8) + (2 × 4) + (3 × 3) = 0 + 8 + 8 + 9 = 25.
- Mean = 25 ÷ 20 = 1.25 pets.
Example 3
The mean of four numbers is 9. Three of them are 7, 12 and 8. What is the fourth?
- If the mean of 4 numbers is 9, they add up to 4 × 9 = 36.
- 7 + 12 + 8 = 27, so the fourth number is 36 − 27 = 9.
Where the marks go missing
- Finding the median without ordering the numbers first.
- In a frequency table, adding up the frequencies and dividing by the number of rows, instead of value × frequency divided by total frequency.
- Giving the range as 'from 7 to 20' rather than a single number, 13.
Frequently asked questions
How do you work out the mean?
Add all the values together and divide by how many values there are. The mean of 4, 8 and 9 is 21 ÷ 3 = 7.
What is the difference between median and mode?
The median is the middle value once the numbers are in order. The mode is the value that occurs most often.