Averages and range
Mean, median, mode and range, including from tables
Averages give one number to represent a whole set of data. The range shows how spread out the data is.
The three averages and the range
- Mean = total of all values ÷ number of values.
- Median = the middle value when the data is in order. (If there are two middle values, find halfway between them.)
- Mode = the most common value (“mode = most”).
- Range = largest − smallest.
Worked examples
Example 1. Find the mean, median, mode and range of 4, 8, 3, 8, 7.
Example 2. Find the median of 12, 5, 9, 15.
Example 3. The mean of 4 numbers is 9. Three of them are 7, 10 and 12. Find the fourth.
Top tips and common mistakes
- Always put the data in order before finding the median.
- The mean is affected by extreme values; the median is not.
- A set of data can have more than one mode, or no mode.
I used the mean to work out my average score in my spelling tests. It went up every week!
Practise
Answer as many as you like. Every question is new, and you get a “correct” tick for each one you get right first time. Use “Show answer” to see a worked solution.
Quiz: earn your stamp
Printable worksheet
Averages and range worksheet. The questions come first and the answers for grown-ups are on the last page, so you can print just the question pages.
Printing is optional. A4 size.