Statistical charts and diagrams

Revise Statistical charts and diagrams for Mathematics D 4024 (O Level) — revision notes, 24 practice questions and instant AI marking.

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Cambridge O Level Mathematics (Syllabus D) 4024

Statistical charts and diagrams

The big idea: Each chart shows frequency with something you can see: the height of a bar, the angle of a sector, a number of symbols. Know what the chart uses, and drawing and reading it are the same calculation in opposite directions.

Summary — What This Chapter Covers

Bar charts: equal-width bars with gaps, labelled axes and a title; the height shows the frequency.
Composite (stacked) and dual (side-by-side) bar charts compare groups.
Pie charts: angle = frequency ÷ total × 360°.
Pictograms: every symbol stands for a stated number of items, shown in a key.
Simple frequency distributions: a frequency table and the chart drawn from it.

1. Bar Charts

Syllabus 9.4 · Paper 1 & 2

Height shows frequency

A bar chart has one bar per category. The bars are the same width with equal gaps between them, and the height of each bar is its frequency. Label both axes, start the frequency axis at 0, use an even scale, and give the chart a title. Bars can be vertical or horizontal.

A dual (side-by-side) bar chart puts two bars next to each other for each category, one for each group, with a key. A composite (stacked) bar chart stacks the parts of one total on top of each other, so the full height is the total and each section is a part.

Worked Example

A composite bar chart shows how Year 9 and Year 10 students travel to school. The Year 9 bar has sections Walk 0 to 40, Bus 40 to 65 and Car 65 to 80. The Year 10 bar has sections Walk 0 to 35, Bus 35 to 75 and Car 75 to 90.
(a) How many Year 9 students travel by bus? (b) Which year has more students who travel by car? (c) What fraction of Year 10 students walk?

Reading a stacked section

The number for a section is the difference between its top and bottom readings, not the top reading. Only the bottom section starts at 0.

2. Pie Charts

Syllabus 9.4 · Paper 1 & 2

The angle of the sector

A pie chart shows how a whole is split up. The whole circle is 360°, so each item gets 360° ÷ total. Draw sectors with a protractor, accurate to within 2°, and label each one. To read a pie chart, turn the angle back into a fraction of the total.

Pie chart angles angle = frequency ÷ total × 360° frequency = angle ÷ 360° × total

Worked Example

72 students chose their favourite fruit: apple 26, banana 18, mango 20, other 8. Work out the angle for each sector of a pie chart.

Practice Question 1

A pie chart shows how 540 people travel to work. The sector for cycling has an angle of 48°. How many people cycle to work?

3. Pictograms

Syllabus 9.4 · Paper 1 & 2

Symbols and a key

A pictogram uses a repeated symbol. The key says how many items one symbol stands for, and parts of a symbol stand for fractions of that number. Every symbol must be the same size, and the rows must line up.

Worked Example

In a pictogram about cars using a car park, the key shows that one circle represents 8 cars.
(a) Monday’s row shows 3½ circles. How many cars is that?
(b) 20 cars used the car park on Tuesday. How should Tuesday’s row be drawn?

4. Simple Frequency Distributions

Syllabus 9.4 · Paper 1 & 2

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Statistical charts and diagrams