Maiths

Edexcel International GCSE Mathematics A · 4MA1

Histograms

A histogram represents grouped continuous data with bar area proportional to frequency. Unequal class widths make height alone misleading. The vertical axis normally shows frequency density, so a wider bar can contain more observations despite being shorter.

Practise histograms

Key method

Frequency density = frequency/class width. Recover frequency by multiplying a bar’s width by its frequency density.

Worked example

Classes 0 ≤ t < 10 and 10 ≤ t < 30 have frequencies 15 and 20. Find the bar heights.

  • The first class width is 10 and the second is 20.
  • First density: 15/10 = 1.5.
  • Second density: 20/20 = 1; its lower height still represents the greater frequency.

Answer and interpretation

Frequency densities 1.5 and 1.

Common mistake

Plotting frequencies directly as heights overstates the contribution of wider intervals.

Practise independently

A bar from 30 to 45 has density 2.4. Find its frequency.

Check your answer

(45 − 30) × 2.4 = 36.

Syllabus connection

This lesson develops histograms within the statistics area. Start with the worked method, attempt the independent question without looking at its answer, then explain any correction in your own words. Check the official specification for your tier’s full requirements.

Pearson specification and assessment resources

Related resources

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