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DfE statement S3 · Statistics

Histograms and cumulative frequency graphs

Higher onlyCalculator

Histograms and cumulative frequency graphs is content statement S3 of the DfE GCSE mathematics subject content, in the statistics area. It is Higher tier only, and it is normally a calculator-paper question. Below is what the specification actually requires, the 3 mistakes that cost marks on this topic most often, and practice questions written to the statement — original questions, not past papers.

What the specification says

The DfE subject content for GCSE mathematics states, verbatim: "Construct and interpret diagrams for grouped discrete data and continuous data, i.e. histograms with equal and unequal class intervals and cumulative frequency graphs, and know their appropriate use." (statement S3). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.

— Department for Education, Mathematics: GCSE subject content and assessment objectives, statement S3

Tier

Higher tier only. A Foundation entry is never asked for this, so if you are sitting Foundation you can leave it out of your revision entirely.

Calculator

This is calculator work, which places it on Papers 2 and 3. Know your own calculator before the exam, keep full accuracy through the working and round only at the end.

Common mistakes

  • Plotting frequency on a histogram instead of frequency density. With unequal class widths this is simply a bar chart, and it is wrong.
  • Plotting a cumulative frequency point at the midpoint of the class rather than at its upper boundary.
  • Reading the median from a cumulative frequency graph at half the highest frequency rather than at half the total frequency — they are the same only by coincidence.

Sample questions (10 of 30)

S3 · Histograms and cumulative frequency graphsQuestion 1 of 10 · 0 correct
Practice mode· no pressure · hints available

Statistics

S3

Expert

In a histogram of the lengths, x cm, of some rods, the bar for 10 ≤ x < 30 has a frequency density of 3 per cm. The bar for 30 ≤ x < 45 is twice as tall as the bar for 10 ≤ x < 30. Work out the number of rods with a length in the class 30 ≤ x < 45.

💡 Hints:
Higher worksheetHigher statistics practice

Nearby statements

S1Sampling and inference about populationsS2Tables, charts and diagrams for dataS4Averages, spread and comparing distributionspart HigherS5Describing a population with statistics

Questions people ask

Is histograms and cumulative frequency graphs on Foundation or Higher?

Higher only. Foundation papers do not ask for it.

Can I use a calculator for histograms and cumulative frequency graphs?

Yes, on Papers 2 and 3, which are the calculator papers and where questions on this usually sit. Paper 1 is non-calculator.

What is the single most common mistake here?

Plotting frequency on a histogram instead of frequency density. With unequal class widths this is simply a bar chart, and it is wrong.

Are these past paper questions?

No. Every question is original, written to this DfE content statement and checked before publication. We do not host past papers or mark schemes.

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