Mode and Range –

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 cover

§Key definitions

Question:

Find the mode and range of: 3, 7, 5, 3, 8, 5, 3, 9, 5, 3.

Answer:

The mode is 3 and the range is 6.

(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.

Q1 (Foundation):

Find the mode and range of: 2, 5, 7, 5, 3, 8, 5, 1.

§Formulas to memorise

Range = Highest value − Lowest value

Modal class = The class interval with the highest frequency (for grouped data)

Mode = 3 (highest frequency).

Range = 9 − 3 = 6.

Worked example

Find the mode and range of: 3, 7, 5, 3, 8, 5, 3, 9, 5, 3.

Working:

⚠ 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.

MMXXVI specification · AQA · Edexcel · OCRgcsemathsai.co.uk/formulas/mode-and-range

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