GCSE Maths Histograms & Frequency Density Notes
Histograms show grouped data with unequal class widths. The bar height is frequency density, so area — not height — represents frequency.
Key concepts
- Frequency density
- The vertical axis of a histogram: frequency divided by class width.
- Unequal class widths
- Histograms handle groups of different sizes, unlike ordinary bar charts.
- Area = frequency
- The area of each bar equals the frequency for that class, so counts come from area not height.
Key formulas
Frequency density
frequency density = frequency ÷ class width
Frequency from a bar
frequency = frequency density × class width
Worked example
A class 20 ≤ x < 30 has frequency 15. Find its frequency density.
- 1Find the class width: 30 − 20 = 10.
- 2Divide frequency by width: 15 ÷ 10.
- 3Frequency density = 1.5.
Answer: Frequency density = 1.5
Common mistakes
✗ Plotting frequency instead of frequency density on the y-axis.
✓ Always divide frequency by class width first for a histogram.
✗ Reading frequency straight off the height.
✓ Frequency = area = frequency density × class width.
✗ Leaving gaps between bars.
✓ Histograms use continuous data, so bars touch with no gaps.
Quick check
Try these, then reveal the answers.
Class width 5, frequency 20. Frequency density?Reveal answer
4
Frequency density 3, class width 4. Frequency?Reveal answer
12
What does area represent on a histogram?Reveal answer
Frequency
Exam tips
- Add a frequency density column to the table before drawing anything.
- To estimate a value part-way through a class, take the matching fraction of that bar's area.
- Label the y-axis 'Frequency density' — the wrong label loses marks.
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Frequently asked questions
How is a histogram different from a bar chart?+
Histograms use continuous data with no gaps and plot frequency density, so bars can have different widths.
Why do we use frequency density?+
It fairly compares classes of different widths, since a wider class would otherwise look artificially taller.
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