The mode and range are two of the simplest statistical measures in GCSE Maths, but they still carry marks on every AQA, Edexcel and OCR paper. The mode identifies the most common value, while the range measures how spread out the data is. Together with the mean and median, they allow you to describe and compare data sets. This guide covers everything you need, including modal class for grouped data. For a full list of topics, see our complete GCSE Maths topics list.
What Is the Mode?
The mode is the value that appears most often in a data set. A data set can have one mode, more than one mode (bimodal or multimodal), or no mode if all values appear the same number of times.
What Is the Range?
The range measures the spread of data:
A large range means the data is widely spread; a small range means the values are close together.
Key Formulas
For grouped data you cannot identify a single mode — instead you state the modal class, which is the group with the greatest frequency.
Step-by-Step Method
- To find the mode, look for the value with the highest frequency. If two values share the highest frequency, the data is bimodal.
- To find the range, identify the highest and lowest values, then subtract.
- For grouped data, find the class interval with the greatest frequency — this is the modal class.
Worked Example 1 — Foundation Level
Question: Find the mode and range of: 3, 7, 5, 3, 8, 5, 3, 9, 5, 3.
Working:
Tally each value: 3 appears 4 times, 5 appears 3 times, 7 once, 8 once, 9 once.
Mode = 3 (highest frequency).
Range = 9 − 3 = 6.
Answer: The mode is 3 and the range is 6.
Worked Example 2 — Higher Level
Question: The grouped frequency table shows the times (in seconds) for 25 pupils to complete a puzzle.
| Time (s) | 0 < t ≤ 10 | 10 < t ≤ 20 | 20 < t ≤ 30 | 30 < t ≤ 40 |
|---|---|---|---|---|
| Frequency | 4 | 9 | 8 | 4 |
(a) State the modal class. (b) Explain why you cannot find the exact range.
Working:
(a) The class with the highest frequency is 10 < t ≤ 20 (frequency 9). Modal class = 10 < t ≤ 20.
(b) The data is grouped, so we do not know the exact highest and lowest values — only the class intervals they fall in. The maximum possible range is 40 − 0 = 40 seconds, but the actual range could be smaller.
Answer: Modal class is 10 < t ≤ 20. The exact range cannot be found because the individual data values are unknown.
Worked Example 3 — Exam Style
Question: Two classes sit the same test. Class A scores: 45, 52, 52, 60, 71. Class B scores: 48, 55, 55, 55, 67. Compare the two distributions using the mode and range.
Working:
Class A: Mode = 52, Range = 71 − 45 = 26.
Class B: Mode = 55, Range = 67 − 48 = 19.
Answer: Class B has a higher mode (55 vs 52), suggesting a more typical higher score. Class B also has a smaller range (19 vs 26), meaning its scores are more consistent.
Common Mistakes
- Giving the frequency as the mode. The mode is the value with the highest frequency, not the frequency itself.
- Forgetting there can be no mode. If every value appears the same number of times, there is no mode — say so explicitly.
- Using the first and last values for the range. The range uses the highest and lowest values, which may not be the first and last if data is unordered.
Exam Tips
- When comparing two distributions, mention both an average (mode, median or mean) and the range. This earns full comparison marks.
- For grouped data, always state the modal class using the class interval notation (e.g. 10 < t ≤ 20), not just "10–20".
- The range is affected by outliers — if asked to evaluate, mention this limitation.
- For related averages, see finding the mean and finding the median. For key formulas, visit our GCSE Maths formulas page.
Practice Questions
Q1 (Foundation): Find the mode and range of: 2, 5, 7, 5, 3, 8, 5, 1.
Q2 (Foundation): A data set is: 4, 4, 6, 6, 9. How many modes does it have?
Q3 (Higher): A grouped frequency table has classes 0–10 (freq 5), 10–20 (freq 12), 20–30 (freq 12), 30–40 (freq 3). State the modal class and explain any issue.
Practise mode, range and other averages free on GCSEMathsAI.
Related Topics
Summary
- The mode is the most frequently occurring value in a data set.
- The range is the difference between the highest and lowest values.
- For grouped data, identify the modal class — the class interval with the greatest frequency.
- When comparing distributions, comment on both an average and the range to earn full marks.
- The range is sensitive to outliers, which is an important limitation to mention in evaluation questions.
Test your understanding
5 quick MCQs to identify any misconceptions on this topic.
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