Cambridge O Level Statistics: Tables and bar-type, pie and pictorial charts (4040) – Revision Notes

Use these notes after the full study guide. They fit Cambridge O Level Statistics (4040), version 1, examined in 2025, 2026 and 2027. They cover sections 2.1 and the construction of pictograms, pie charts, comparative pie charts, bar charts, sectional and percentage bar charts and dual bar charts from section 2.2. Test yourself afterwards with the practice set. When you plan revision, open the Statistics hub, tick off the checklist and take a diagnostic. For the whole of Topic 2, there is also an overview page.

Formulas and rules at a glance

Chart	Key rule
Pictogram	Symbols per row = value ÷ key value
Pie chart	Angle = (frequency ÷ total) × 360°
Reading a pie chart	Frequency = (angle ÷ 360) × total
Comparative pie chart	radius₂ = radius₁ × √(total₂ ÷ total₁), if areas are in proportion to totals
Bar chart	Height = value ÷ units per cm
Sectional bar	Stack the parts; mark cumulative heights
Percentage bar	Every bar has the same height; part = percentage of that bar’s own total

2.1 Tables: method in steps

1. Decide the categories. They must not overlap and must cover every observation.
2. Tally in groups of five and write the frequencies.
3. Add the frequencies and compare with the number of observations.
4. For a two-way table, fill the row totals, the column totals and the grand total. Each must agree with the others.

A missing entry in a two-way table is found by subtraction from a total. Check it a second way, using the other direction.

Worked reminder: a two-way table

60 pupils: 24 are in Year 10 and the rest in Year 11. Year 10 has 9 cyclists and 15 walkers. Year 11 has 11 cyclists and 25 walkers.

	Cycle	Walk	Total
Year 10	9	15	24
Year 11	11	25	36
Total	20	40	60

The share of Year 11 who walk is 25 ÷ 36 × 100 = 69.4% (1 d.p.). The base is the Year 11 row, not the 60 pupils.

2.2 Pictograms

• Give a key. Draw all symbols at the same size and spacing.
• Use whole and half symbols only.
• Choose a key that fits the data.

Example: books borrowed 14, 18, 6, 10 with a key of 1 symbol = 4 books give 3½, 4½, 1½ and 2½ symbols. To read the chart, multiply: 4½ symbols represent 18 books.

2.2 Pie charts

1. Total the frequencies.
2. Find the angle for one item: 360° ÷ total.
3. Multiply each frequency by it.
4. Check the angles sum to 360°.
5. Draw, label each sector and give the title.

Worked reminder: 60 pupils choose a trip: museum 22, zoo 18, park 12, beach 8. One pupil is 360° ÷ 60 = 6°, so the angles are 132°, 108°, 72° and 48°. The sum is 360°.

2.2 Comparative pie charts

Draw two circles. Compute each set of angles from its own total. Size the circles by the rule your question gives. A common convention is that area is in proportion to the total, so the radii are in proportion to the square roots of the totals.

Worked reminder: a cinema sells 50 snacks on a quiet night and 200 on a busy night. If the quiet-night circle has radius 2 cm, the busy-night radius is 2 × √(200 ÷ 50) = 2 × 2 = 4 cm. Doubling the radius gives four times the area, matching four times the total.

Quiet night (50 snacks: popcorn 25, sweets 15, drinks 10): angles 180°, 108°, 72°. Busy night (200 snacks: popcorn 80, sweets 70, drinks 50): angles 144°, 126°, 90°.

2.2 Bar charts and dual bar charts

• Equal bar widths, equal gaps, baseline at zero.
• An even, labelled vertical scale.
• Height = value ÷ units per cm.
• Dual bar: two touching bars per category, with a key for the two groups.

Worked reminder: weekly sales of two drinks, scale 1 cm = 5 units.

Day	Mon	Tue	Wed
Hot drinks	35	20	15
Cold drinks	10	25	40

Heights in cm: hot drinks 7, 4, 3; cold drinks 2, 5, 8. Each day gets one pair of bars with the same width, and a key says which shade is which.

2.2 Sectional and percentage bar charts

• Sectional: the bar’s total height is the total frequency. Draw each part on top of the previous one.
• Percentage: choose a standard bar height, for example 10 cm for 100%, so 1% is 0.1 cm.

Worked reminder: two canteens record meal choice.

	Hot	Packed	Other	Total
Canteen X	18	14	8	40
Canteen Y	30	54	36	120

Percentages: X is 45%, 35%, 20%; Y is 25%, 45%, 30%. With 10 cm bars, the boundaries for X are at 4.5 cm, 8.0 cm and 10.0 cm. For Y they are at 2.5 cm, 7.0 cm and 10.0 cm. A sectional chart would make Y three times as tall as X, but the percentage chart compares the shares.

A checklist for every construction

Before you hand in a drawn chart, run through these points.

1. Is there a title that says what the chart shows?
2. Are the scale or key stated, and do they match the heights, angles or symbols you drew?
3. Are the categories labelled in the same order as the table?
4. Do the angles sum to 360°, or the heights end at the total, or the percentages reach 100%?
5. Is the working for each angle, height or symbol count on the page?

If a chart is already drawn and you must read it, work backwards. Divide the angle by 360 and multiply by the total. Multiply symbols by the key. Read the bar height against the scale. For a stacked bar, subtract the lower boundary from the upper one to find a part.

Worked reminder: reading a stacked bar. In a sectional bar chart with 1 cm = 10 units, the bottom part ends at 4 cm and the next part ends at 6.5 cm. The bottom part is 4 × 10 = 40 units. The second part is (6.5 − 4) × 10 = 25 units. The whole bar so far is 65 units. A common slip is to read 6.5 cm as the second part on its own.

Must-know distinctions

• A sectional bar shows amounts. A percentage bar shows shares.
• A dual bar chart puts groups side by side. A sectional bar chart stacks components.
• A pie chart shows one total. A comparative pie chart compares two or more totals.
• A frequency table has one classification. A two-way table has two.
• In a pictogram, the key value sets the scale. In a bar chart, the axis does.

Quick self-test

1. Find the angle for one item in a pie chart with a total of 48.
2. In a chart with a total of 56, what is the angle for a frequency of 14?
3. A sector of 135° is in a pie chart of 80 people. How many people is that?
4. A pictogram uses 1 symbol = 4 items. How many symbols show 22 items?
5. A pie with total 40 has radius 3 cm. Find the radius of a pie with total 90 if areas are in proportion to totals.
6. A bar of 36 units is drawn with 1 cm = 6 units. How tall is it?
7. In a percentage bar chart 10 cm tall, how tall is the part for 12 out of 48?
8. In a sectional bar chart (1 cm = 10 units), parts of 18 and 7 are stacked. At what height does the second part end?
9. In the two-way table above, how many pupils cycle?
10. Which of a sectional bar chart and a percentage bar chart compares shares when the totals differ?

Answers

1. 360 ÷ 48 = 7.5°.
2. 14 ÷ 56 × 360 = 90°.
3. 135 ÷ 360 × 80 = 30 people.
4. 22 ÷ 4 = 5½ symbols.
5. 3 × √(90 ÷ 40) = 3 × 1.5 = 4.5 cm.
6. 36 ÷ 6 = 6 cm.
7. 12 ÷ 48 = 25%, so 2.5 cm.
8. 18 + 7 = 25 units, so 2.5 cm.
9. 9 + 11 = 20 pupils.
10. A percentage bar chart.

Where marks are usually lost

• Pie angles that do not sum to 360°, with no check.
• Using the same circle size in a comparative pie chart.
• Giving the radius ratio as the total ratio instead of its square root, when areas should match totals.
• Forgetting the key on a pictogram or dual bar chart.
• Drawing sectional parts from the baseline rather than stacking them.
• Taking percentages of the wrong total in a percentage bar chart.
• Using a percentage base from the wrong row or column of a two-way table.
• An uneven or non-zero starting scale on a bar chart.
• Leaving out titles, axis labels or sector labels.
• Showing only the final figures when the question asks for working.

Official syllabus

This page is written against the Cambridge International Education syllabus Cambridge O Level Statistics (4040), version 1, valid for the 2025, 2026 and 2027 examinations. Publisher: Cambridge University Press & Assessment. Sections used: 2.1 and 2.2.