GCSE Maths Statistics Notes
Statistics is about collecting, representing and interpreting data. Averages and spread summarise data, while charts reveal patterns and comparisons.
Key concepts
- Mean
- Add all values and divide by how many there are — uses every value.
- Median
- The middle value when the data is in order — resistant to extreme values.
- Mode
- The most common value — the only average usable for non-numerical data.
- Range
- Largest minus smallest — a simple measure of spread, not an average.
- For an even number of values, the median is the mean of the middle two.
- The mean is affected by outliers; the median is not.
- Use the midpoints of class intervals to estimate the mean of grouped data.
Key formulas
Mean
mean = sum of values ÷ number of values
Estimated mean (grouped)
mean ≈ Σ(midpoint × frequency) ÷ Σfrequency
Worked example
Find the mean, median, mode and range of 4, 7, 7, 2, 10.
- 1Mean: (4 + 7 + 7 + 2 + 10) ÷ 5 = 30 ÷ 5 = 6.
- 2Order the data: 2, 4, 7, 7, 10. Median is the middle value: 7.
- 3Mode is the most common value: 7.
- 4Range: 10 − 2 = 8.
Answer: Mean 6, median 7, mode 7, range 8
Common mistakes
✗ Forgetting to order the data before finding the median.
✓ Always sort from smallest to largest first.
✗ Confusing range with an average.
✓ Range measures spread, not a typical value.
✗ Dividing by the wrong count for the mean.
✓ Divide by how many values there are, including repeats.
Quick check
Try these, then reveal the answers.
Mean of 3, 5, 10?Reveal answer
6
Median of 2, 4, 6, 8?Reveal answer
5
Range of 12, 4, 9?Reveal answer
8
Exam tips
- Read carefully which average is asked for — mean, median or mode.
- For grouped data you can only estimate the mean using midpoints.
- When comparing two data sets, comment on both an average and the spread.
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Frequently asked questions
Which average should I use?+
Use the mean for balanced data, the median when there are outliers, and the mode for the most common category.
How do I estimate the mean from a grouped frequency table?+
Multiply each class midpoint by its frequency, add these up, then divide by the total frequency.
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