Mean, Median, Mode & Range
Calculating and comparing averages and understanding what each one tells us about a data set.
What is Mean, Median, Mode & Range?
Averages are ways of summarising a set of data with a single value. There are three types of average – mean, median and mode – and the range tells us how spread out the data is.
In the 11+ exam, you need to know how to calculate all three averages and the range, and understand when each is most useful.
Step-by-Step Method
Mean: add up all values, divide by how many
Mean = total of all values / number of values.
Median: put in order, find the middle value
Order the data from smallest to largest. The middle value is the median. If there are two middle values, find their average.
Mode: find the most common value
The mode is the value that appears most often. There can be more than one mode, or no mode at all.
Range: largest minus smallest
Range = highest value – lowest value. It measures how spread out the data is.
Check which average the question asks for
Read carefully – the question might ask for mean, median, mode or range. They give different answers!
Worked Examples
Find the mean of 4, 7, 2, 9, 3.
Working
- Total: 4 + 7 + 2 + 9 + 3 = 25.
- Number of values: 5.
- Mean: 25 / 5 = 5.
Find the median of 12, 5, 8, 15, 3, 9, 7.
Working
- Order the data: 3, 5, 7, 8, 9, 12, 15.
- There are 7 values, so the middle one is the 4th.
- The 4th value is 8.
Find the mode and range of: 3, 5, 7, 3, 8, 5, 3, 9.
Working
- Mode: 3 appears 3 times (more than any other). Mode = 3.
- Range: 9 – 3 = 6.
Common Mistakes
Forgetting to put data in order before finding the median.
ALWAYS order the data first. The median is the middle of the ORDERED list.
Dividing by the wrong number when finding the mean.
Count the number of values carefully. Divide the total by this count.
Confusing the range with the largest value.
Range = largest – smallest. It is the DIFFERENCE, not just the largest number.
Top Tips
- For the mean: if the question says “the average is 6”, this usually means the mean is 6.
- For an even number of data values, the median is the average of the two middle values.
- A data set can have no mode (if all values appear once) or more than one mode.
- If you know the mean and the number of values, you can find the total: total = mean x number of values.
Ready to practise?
Put these techniques into action with our free practice papers.
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