Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed

Charts, Pie Charts & Histograms

In one sentence. Pie chart angles, scatter-graph correlation, and the Higher-tier histogram rule that area — not height — is frequency.

Statistics — one of 3 modules in this strand, and one of 53 in Pearson Edexcel International GCSE Mathematics. Both tiers.

This module ends with William Playfair. Learn Charts, Pie Charts & Histograms, teach it, then defend it against William Playfair.

Where this sits in the specification

Specification 4MA1, 6.1 Graphical representation of data (histograms: Higher). Incandio is aligned to this specification; it is not published by, endorsed by or affiliated with Pearson, and the sub-topic numbers are given so you can check every module against your own copy.

  • 6.1 — Graphical representation of data (histograms: Higher)

1 · Understand it

What it is

A pie chart shares 360° in proportion to the data: each category's angle is (its count/total) × 360. Scatter graphs reveal correlation — positive, negative or none. A histogram (Higher) plots frequency DENSITY (frequency ÷ class width) so that AREA represents frequency, which is what makes unequal class widths honest.

Why it works

The circle's 360° plays the role of the total: angles are just the proportions rescaled. Histograms need the density trick because with unequal classes, a wide bar would LOOK huge even with few data points — dividing by width makes area carry the count, and areas compare fairly whatever the widths.

When a question is asking for it

Pie charts: 'draw' (counts → angles) and 'read' (angles → counts) both run through the fraction-of-total. Histograms: any table with unequal classes; the two conversions are frequency = density × width and density = frequency ÷ width. 'Estimate how many lie between…' when the range cuts through a class: take the area of just that part of the bar.

How to hold it in your head

For pies: one item is worth 360/total degrees — a currency conversion. For histograms: think of each bar as a tray of data spread evenly over its width; the HEIGHT tells you how crowded the tray is, and crowding × width = how many are in it.

2 · The mistakes that cost marks

  • Pie angles read as counts or percentages directly. An angle is a fraction OF THE TOTAL: convert via 360.
  • Comparing two pie charts' slice sizes to compare quantities. Different totals make same-looking slices different amounts.
  • Histogram bar HEIGHT read as frequency. Height is density; frequency is height × width.
  • Correlation claimed as causation: ice-cream sales don't cause drownings — summer causes both.

3 · Worked examples

Laid out the way an examiner wants working shown — every step is a mark.

A pie chart shows the favourite fruit of 90 people. The 'apple' sector has angle 132°. How many people chose apple?

  1. Fraction of the circle: 132/360.
  2. 132/360 × 90 = 33. (Or: 360° shares 90 people, so 1 person = 4°, and 132 ÷ 4 = 33.)

Answer: 33 people

In a histogram, the class 10 ≤ x < 30 has frequency density 1.5. Find its frequency.

  1. Class width: 30 − 10 = 20.
  2. Frequency = density × width = 1.5 × 20.

Answer: 30

A histogram class 20 ≤ t < 40 has frequency 32. Estimate how many values lie between 25 and 40.

  1. Frequency density: 32 ÷ 20 = 1.6.
  2. The part of the bar from 25 to 40 is 15 wide: its area is 15 × 1.6 = 24.
  3. It is an ESTIMATE because it assumes the values are spread evenly across the class.

Answer: 24 (estimate)

4 · Prove it — the five questions

The five questions climb Grade 6 → 9+ and are marked inside Incandio on your own device, against authored accepted forms, with a diagnosis of the wrong answer you actually gave. The answers stay in the app so that the practice is worth doing; the questions themselves are here.

  1. Grade 6 — A pie chart shows how 120 students travel to school. The 'bus' sector has an angle of 90°. How many students travel by bus?
  2. Grade 7 — 45 of the same 120 students walk to school. Work out the angle of the 'walk' sector on the pie chart. (answer in °)
  3. Grade 8 — A scatter graph of price against demand shows a strong NEGATIVE correlation. As price rises, what happens to demand? (Answer with one word.)
  4. Grade 9 — In a histogram, the class 20 ≤ x < 25 is drawn with a frequency density of 3.2, and the class 25 ≤ x < 40 with a frequency density of 1.4. How many data values lie in the range 20 ≤ x < 40 altogether?
  5. 9+ — A histogram class 20 ≤ x < 35 contains 24 data points. Work out the frequency density it should be drawn with.

Think you understand it?

Reading is the start. On Incandio a topic counts as mastered only once you have taught it and defended it — the two things a revision guide cannot ask of you.

Incandio this topic → Prove it. Teach it. Defend it. What does “Incandio it” mean?

  1. Prove it — five questions on Charts, Pie Charts & Histograms, marked on the spot, that tell you what was missing rather than just what was wrong.
  2. Teach it — Explain how Charts, Pie Charts & Histograms works — and why — to Ember, an AI pupil who does not have it yet. The method matters more than the vocabulary.
  3. Defend it — Argue Charts, Pie Charts & Histograms against William Playfair — three rounds, marked against descriptors you can read before you begin.
  4. Then the exam — read all 9 authored exam-style questions on this unit, each with its command word and its tariff, then have them marked on Incandio with the mistake you actually made named.

Completely free. No subscriptions, no paywalls, no account needed to start.

Carry on through the course