GCSE & IGCSE maths practice

Histograms questions and answers

In a histogram the area of each bar shows the frequency, so the height is the frequency density: $\text{frequency density} = \dfrac{\text{frequency}}{\text{class width}}$ . Turn it round to read a frequency from a bar: frequency $=$ frequency density $\times$ class width. This lets classes have different widths.

8 questions · Higher tier · Every answer is checked as you type it, with a full worked solution. Updated 27 Oct 2026.

Start the questions Histograms guide

Where histograms comes up

GCSE (AQA, Edexcel, OCR)	Higher only: construct and interpret histograms with equal and unequal class intervals.
Cambridge IGCSE (0580)	Extended only: draw and interpret histograms, and calculate frequency density.

The method

Class width = upper bound − lower bound.
Frequency density = frequency ÷ class width.
Frequency = frequency density × class width.
Part of a class: take the matching fraction of that bar's area.

Histograms questions

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Warm-up

Question 1Warm-upHigher

A class has width 10 and frequency 30. Find its frequency density.

Question 2Warm-upHigher

A class has width 5 and frequency 12. Find its frequency density.

Exam-style

Question 3Exam-styleHigher

A bar has frequency density 1.6 and class width 20. Find the frequency.

Question 4Exam-styleHigher

The bar for $20 < t \le 50$ has frequency density 0.8. How many values are in this class?

Question 5Exam-styleHigher

Find the frequency density for the class $15 < t \le 30$ .

Time, t (s)	Frequency
0 < t ≤ 10	10
10 < t ≤ 15	15
15 < t ≤ 30	12

Question 6Exam-styleHigher

What goes on the vertical axis of a histogram with unequal class widths?

Challenge

Question 7ChallengeHigher

A histogram has bars for $0 < x \le 10$ (frequency density 2), $10 < x \le 20$ (3.5) and $20 < x \le 40$ (1.5). Find the total frequency.

Question 8ChallengeHigher

Using the same histogram, estimate how many values are between 15 and 30.

Common mistakes

Plotting frequency instead of frequency density.
Reading the class width wrongly from the table.
Using bar heights, not areas, to compare frequencies.

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Sources

The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:

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