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

Written for Cambridge O Level Statistics (4040), version 1, examined in 2025, 2026 and 2027, this guide covers section 2.1 (classification and representation in tabular form, including two-way tables) and the part of section 2.2 that deals with pictograms, pie charts, comparative pie charts, bar charts, sectional and percentage bar charts and dual bar charts. The syllabus applies to all candidates; it is not tiered.

Other pages deal with Venn, box-and-whisker and stem-and-leaf diagrams, and with choosing and interpreting representations. To see where each sits, use the subject hub and the printable checklist. This guide has a revision-notes page and a practice set. For wider context, read the Topic 2 overview and frequency distributions. A quick diagnostic will show what to revise first.

What you must be able to do

Syllabus	Skill
2.1	Classify data into categories and show it in a table, including a two-way table
2.2	Construct a pictogram
2.2	Construct a pie chart and a comparative pie chart
2.2	Construct a bar chart and a dual bar chart
2.2	Construct a sectional bar chart and a percentage bar chart

The assessment overview in the syllabus states: “Essential working must be shown for full marks to be awarded.” So write down each calculation behind a chart: the scale, the angle or the height.

2.1 Classification and tables

Classifying data means sorting each observation into a category. The categories must not overlap, and every observation must fit one of them. Count with a tally (groups of five, four strokes and a diagonal), then write the totals as frequencies. Check that the frequencies add up to the number of observations.

Worked example 1: a frequency table

A kiosk records the drink bought by each of 40 customers (T = tea, C = coffee, J = juice, W = water):

C C T C W C W J C T C W W J T J T T T T
T J C J C T T J W T J T T C J T J C C W

Tally each letter and count.

Drink	Tally	Frequency
Tea	two groups of five and four more	14
Coffee	two groups of five and one more	11
Juice	one group of five and four more	9
Water	one group of five and one more	6
Total		40

The total is 14 + 11 + 9 + 6 = 40, which matches the number of customers, so no observation was missed or counted twice.

Two-way tables

A two-way table classifies each observation by two features at once. Row totals, column totals and the grand total must all agree. The grand total is found by adding the row totals or the column totals, and both must give the same number.

Worked example 2: completing a two-way table

A club has 150 members. Each member is a boy or a girl and plays one of swimming, tennis or athletics. Some entries are missing.

	Swimming	Tennis	Athletics	Total
Boys	28	20		80
Girls	24		16
Total		50		150

Step 1. Boys in athletics: 80 − 28 − 20 = 32. Step 2. Girls in total: 150 − 80 = 70. Step 3. Girls in tennis: 70 − 24 − 16 = 30. Check against the tennis column: 20 + 30 = 50, which matches. Step 4. Swimming column: 28 + 24 = 52. Athletics column: 32 + 16 = 48. Check: 52 + 50 + 48 = 150.

Question: what percentage of the girls play tennis? The base is the girls, not the whole club, so 30/70 × 100 = 42.9% (1 d.p.). Choosing the correct row or column as the base is where this kind of question is usually decided.

2.2 Pictograms

In a pictogram, one picture stands for a set number of items. A key is essential. Every symbol must be the same size and equally spaced. A part of a symbol stands for the matching part of the key value, and you should only use fractions you can draw clearly, such as a half.

Worked example 3: building a pictogram

A bicycle shop repairs bicycles on five days: Monday 24, Tuesday 36, Wednesday 12, Thursday 20, Friday 28. Use a key of one symbol = 8 bicycles.

Divide each value by 8.

Day	Calculation	Symbols
Mon	24 ÷ 8	3
Tue	36 ÷ 8	4½
Wed	12 ÷ 8	1½
Thu	20 ÷ 8	2½
Fri	28 ÷ 8	3½

Draw the rows with a label, the symbols and the key. To read a pictogram, multiply the number of symbols by the key value: 3½ symbols represent 3.5 × 8 = 28. Choose a key that gives whole or half symbols for your data. A key of 10 would make 36 and 12 hard to draw accurately.

2.2 Pie charts

A pie chart shows how a total divides into parts. Each sector’s angle grows in step with its frequency.

Angle of a sector = (frequency ÷ total) × 360°

It is quicker and more accurate to find the angle for one item first: 360° ÷ total.

Worked example 4: drawing a pie chart

45 pupils choose their favourite after-school club: chess 15, drama 12, football 9, art 6, coding 3.

One pupil is 360° ÷ 45 = 8°.

Club	Frequency	Angle
Chess	15	15 × 8 = 120°
Drama	12	12 × 8 = 96°
Football	9	9 × 8 = 72°
Art	6	6 × 8 = 48°
Coding	3	3 × 8 = 24°
Total	45	360°

The angles add to 360°, which is your check. Draw a circle, mark a radius, and measure each angle from the previous one with a protractor. Label each sector with its name, and add its value or percentage if the question asks for it.

To read a pie chart, reverse the process: frequency = (angle ÷ 360) × total. A 72° sector in a chart of 45 pupils is 72/360 × 45 = 9 pupils.

Comparative pie charts

When you compare two totals, two circles of equal size hide the difference in totals. A comparative pie chart draws the circles with different sizes. A common convention is that the area of each circle is in proportion to its total. Since area depends on the radius squared, the radii are in proportion to the square roots of the totals:

radius₂ = radius₁ × √(total₂ ÷ total₁)

Read the question for the rule it expects, and state the one you use.

Worked example 5: a comparative pie chart

A town sorts household waste. In 2024 it handled 400 tonnes: recycling 160, food 120, garden 80, other 40. In 2025 it handled 900 tonnes: recycling 450, food 225, garden 135, other 90. Draw the 2024 circle with radius 2 cm.

Radius for 2025: 2 × √(900 ÷ 400) = 2 × 1.5 = 3 cm.

Angles for 2024 (360° ÷ 400 = 0.9° per tonne): 144°, 108°, 72°, 36°. Total 360°. Angles for 2025 (360° ÷ 900 = 0.4° per tonne): 180°, 90°, 54°, 36°. Total 360°.

Each pie uses its own total. The recycling sector is 144° in 2024 and 180° in 2025, so its share rose from 40% to 50%. The larger 2025 circle shows that the total is bigger as well.

2.2 Bar charts

A bar chart compares frequencies for separate categories. Bars have equal width, equal gaps and a common baseline at zero. The vertical axis needs an even scale, labelled with units, and each bar needs a label. The height of a bar is the frequency divided by the number of units per centimetre.

Dual bar charts

A dual bar chart puts two bars side by side for each category, one for each group, so the groups can be compared directly. Keep the pair touching, leave a gap between categories, and give a key that identifies the two groups.

Worked example 6: a dual bar chart

Absences in a school on each weekday are recorded for two terms.

Day	Mon	Tue	Wed	Thu	Fri
Term 1	18	12	10	14	22
Term 2	15	9	11	10	19

Scale: 1 cm for 4 absences. Heights in cm:

Day	Term 1	Term 2
Mon	18 ÷ 4 = 4.5	15 ÷ 4 = 3.75
Tue	12 ÷ 4 = 3	9 ÷ 4 = 2.25
Wed	10 ÷ 4 = 2.5	11 ÷ 4 = 2.75
Thu	14 ÷ 4 = 3.5	10 ÷ 4 = 2.5
Fri	22 ÷ 4 = 5.5	19 ÷ 4 = 4.75

Totals are 76 and 64 absences. Draw each pair side by side with a key.

2.2 Sectional and percentage bar charts

A sectional bar chart (also called a component or stacked bar chart) splits each bar into parts, one for each component. The total height of the bar is the total frequency. Each part sits on top of the one before, so you work with cumulative heights.

A percentage bar chart is similar, but every bar has the same total height and each part shows a percentage of its own total. It compares proportions when the totals differ.

Worked example 7: both charts from one table

A community theatre sells tickets on three nights.

Night	Adult	Child	Senior	Total
Friday	60	25	15	100
Saturday	90	45	15	150
Sunday	50	30	20	100

Sectional bar chart, scale 1 cm for 10 tickets. Heights of the boundaries (adult, then adult + child, then the total):

Night	Adult top	Child top	Senior top (total)
Friday	6.0	8.5	10.0
Saturday	9.0	13.5	15.0
Sunday	5.0	8.0	10.0

Percentage bar chart. Percentage of each night’s total:

Night	Adult	Child	Senior
Friday	60%	25%	15%
Saturday	60%	30%	10%
Sunday	50%	30%	20%

Draw each bar 10 cm tall, so 1% is 0.1 cm. Friday boundaries are at 6.0 cm, 8.5 cm and 10 cm. Saturday boundaries are at 6.0 cm, 9.0 cm and 10 cm. Sunday boundaries are at 5.0 cm, 8.0 cm and 10 cm.

Notice what each chart shows. The sectional chart shows that Saturday was the busiest night. The percentage chart shows that the adult share was the same on Friday and Saturday (60%), which the sectional chart hides.

Common errors

• Drawing a pie chart angle as the frequency instead of the share of 360°.
• Giving the angles but not checking that they add to 360°.
• Using the same circle size for both pies in a comparative pie chart.
• Using radii in proportion to the totals rather than to their square roots, when areas should be in proportion to totals.
• Choosing a bar chart scale that does not start at zero.
• Using bars of different widths, or leaving no key on a dual bar chart.
• In a sectional bar chart, drawing each part from the baseline instead of stacking it on the part below.
• In a percentage bar chart, using the overall total as the base instead of each bar’s own total.
• Taking a percentage of the wrong row or column in a two-way table.
• Leaving off a title, axis labels or a key.

Next steps

Test yourself on the practice set, then use the revision notes as a final check. Use the diagnostics to decide what to revise first.

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.