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

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs – examination boards hold copyright in their own papers. Use these alongside the official past papers from your board or school.

This set is for Cambridge O Level Statistics (4040), version 1, examined in 2025, 2026 and 2027. It covers section 2.1 (tabular representation, including two-way tables) and the construction of pictograms, pie charts, comparative pie charts, bar charts, dual bar charts, sectional bar charts and percentage bar charts from section 2.2. Drawing tasks ask for the numbers you would use, such as angles, radii and heights. Draw the charts as well for practice.

If a method is unfamiliar, see the study guide or the revision notes.

Questions

1. Twenty-four pupils state how they travel to school: B = bus, W = walk, C = car.

B W B C B W C B W W B C
B W B W C B W B B W C B

(a) Make a frequency table for the three methods. [2] (b) Show that your frequencies are consistent with the number of pupils. [1]

2. A school has 90 students taking one language each. The table is incomplete.

	French	Spanish	German	Total
Year 10	18		9	45
Year 11
Total	40	36		90

Copy and complete the table. [4]

3. A pictogram uses one symbol to represent 6 books. Books borrowed on four days were 15, 33, 9 and 24.

(a) State how many symbols are needed for each day. [2] (b) A fifth day shows 3½ symbols. How many books is that? [1]

4. Forty people state their favourite exercise: running 14, swimming 10, cycling 8, yoga 5, dance 3. Work out the sector angles needed for a pie chart of these results. [4]

5. A pie chart shows how 240 visitors chose a museum gallery. The sector angles are art 150°, history 105°, science 60° and other 45°. Calculate the number of visitors for each gallery. [4]

6. Shop A sold 250 items and Shop B sold 360 items. The sales of Shop B were: toys 150, books 110, games 60, other 40. A comparative pie chart is drawn with areas in proportion to the totals. The circle for Shop A has radius 5 cm.

(a) Calculate the radius of the circle for Shop B. [3] (b) Calculate the sector angles for Shop B. [3]

7. The numbers of plants sold are 35, 50, 20 and 45. A bar chart uses a scale of 1 cm for 5 plants.

(a) Calculate the height of each bar. [2] (b) Give a reason why the vertical axis should start at zero. [1]

8. Two Year groups choose a subject. Year 9: art 12, music 21, drama 9, dance 15. Year 10: art 18, music 6, drama 24, dance 12. A dual bar chart uses a scale of 1 cm for 3 students.

(a) Calculate the bar heights for Year 9. [2] (b) Calculate the bar heights for Year 10. [2] (c) State what the key must show. [1]

9. A road survey counts vehicles on three days.

	Cars	Vans	Cycles
Monday	40	15	25
Tuesday	50	20	30
Wednesday	36	24	10

A sectional bar chart is drawn with 1 cm for 10 vehicles, with cars at the bottom, then vans, then cycles. Calculate the height at which each section ends, for each day, and describe how the chart is labelled. [6]

10. Two schools record how pupils travel. School P (250 pupils): bus 100, walk 75, car 50, cycle 25. School Q (200 pupils): bus 50, walk 90, car 40, cycle 20.

(a) Calculate the percentage in each category for each school. [2] (b) A percentage bar chart uses bars 10 cm tall. Calculate the heights at which the sections end for each bar. [3] (c) Give one reason for using a percentage bar chart rather than a sectional bar chart here. [1]

11. A company has 240 employees. The two-way table is incomplete.

	Sales	Admin	Production	Support	Total
Full-time	42	30		12	164
Part-time	18		16
Total	60	48	96	36	240

(a) Complete the table. [4] (b) Calculate the angles for the four departments in a pie chart. [3] (c) Calculate the percentage of part-time employees who work in Support. Give your answer to 1 decimal place. [1]

12. A park counts visitors in two years.

	Adults	Children	Seniors	Total
2024	100	60	40	200
2025	180	180	90	450

(a) Calculate the pie chart sector angles for 2024 and for 2025. [4] (b) The 2024 circle has radius 2 cm. Calculate the radius for 2025 if areas are in proportion to the totals. [2] (c) For percentage bars 10 cm tall, calculate the height at which each section ends, for each year. [3] (d) State one change in the visitor shares between the two years. [1]

Answers

1. (a) Count bus: 11 [1]. Walk 8 and car 5 [1]. Table: bus 11, walk 8, car 5. (b) 11 + 8 + 5 = 24, which equals the number of pupils [1]. [3] Examiner insight: Crossing off each letter as you tally helps, and a total that disagrees with the number of observations is the first sign of a slip.

2. Year 10 Spanish: 45 − 18 − 9 = 18 [1]. Year 11 total: 90 − 45 = 45 [1]. Year 11 Spanish: 36 − 18 = 18, and Year 11 French: 40 − 18 = 22 [1]. Year 11 German: 45 − 22 − 18 = 5, so the German total is 9 + 5 = 14 [1]. Year 11: 22, 18, 5, 45; German total 14. Check: 40 + 36 + 14 = 90. [4] Examiner insight: Find missing entries by subtraction, then check along the other direction.

3. (a) 15 ÷ 6 = 2.5 and 33 ÷ 6 = 5.5 [1]. 9 ÷ 6 = 1.5 and 24 ÷ 6 = 4 [1]. 2½, 5½, 1½ and 4 symbols. (b) 3.5 × 6 = 21 books [1]. [3] Examiner insight: A pictogram answer is clearest when the key is repeated and fractions of a symbol are written as halves.

4. One person is 360° ÷ 40 = 9° [1]. Running 14 × 9 = 126°, swimming 10 × 9 = 90° [1]. Cycling 8 × 9 = 72°, yoga 5 × 9 = 45° [1]. Dance 3 × 9 = 27°, and 126 + 90 + 72 + 45 + 27 = 360° [1]. 126°, 90°, 72°, 45°, 27°. [4] Examiner insight: Show the angle for one item and the check that the angles add to 360°.

5. Frequency = angle ÷ 360 × 240, so art is 150 ÷ 360 × 240 = 100 [1]. History 105 ÷ 360 × 240 = 70 [1]. Science 40 [1]. Other 30 [1]. Art 100, history 70, science 40, other 30. Check: 240. [4] Examiner insight: Write the multiplier 240 ÷ 360 once, then apply it to each angle.

6. (a) Radius ratio = √(360 ÷ 250) [1] = √1.44 = 1.2 [1]. Radius = 5 × 1.2 = 6 cm [1]. (b) One sale is 360° ÷ 360 = 1° [1]. Angles are toys 150°, books 110°, games 60°, other 40° [1]. Their sum is 360° [1]. [6] Examiner insight: Show the square root and state the rule used for the circle sizes.

7. (a) 35 ÷ 5 = 7 and 50 ÷ 5 = 10 [1]. 20 ÷ 5 = 4 and 45 ÷ 5 = 9 [1]. 7 cm, 10 cm, 4 cm, 9 cm. (b) The bar length is then in proportion to the frequency, so comparisons of height are fair [1]. [3] Examiner insight: Link the zero baseline to the comparison of bar heights.

8. (a) Year 9: 12 ÷ 3 = 4 and 21 ÷ 3 = 7 [1]. 9 ÷ 3 = 3 and 15 ÷ 3 = 5 [1]. 4, 7, 3, 5 cm. (b) Year 10: 18 ÷ 3 = 6 and 6 ÷ 3 = 2 [1]. 24 ÷ 3 = 8 and 12 ÷ 3 = 4 [1]. 6, 2, 8, 4 cm. (c) The key identifies which shade or pattern is Year 9 and which is Year 10 [1]. [5] Examiner insight: List heights in the table’s category order so each pair matches its subject.

9. Totals: Monday 80, Tuesday 100, Wednesday 70 [1]. Monday ends at 40 ÷ 10 = 4.0 cm, then 55 ÷ 10 = 5.5 cm, then 8.0 cm [1]. Tuesday ends at 5.0 cm, 7.0 cm and 10.0 cm [1]. Wednesday ends at 3.6 cm, 6.0 cm and 7.0 cm [1]. The sections are stacked in the same order each day, with a key for cars, vans and cycles [1]. The chart has a title, labelled axes, an even scale and a label under each day [1]. [6] Examiner insight: Cumulative heights are the usual slip: each section starts where the one beneath ends.

10. (a) School P: 100/250 = 40%, 30%, 20%, 10% [1]. School Q: 25%, 45%, 20%, 10% [1]. (b) 1% = 0.1 cm for a 10 cm bar [1]. P ends at 4.0, 7.0, 9.0 and 10.0 cm [1]. Q ends at 2.5, 7.0, 9.0 and 10.0 cm [1]. (c) The totals differ (250 and 200), and the percentage bars compare the shares [1]. [6] Examiner insight: Each percentage uses its own school’s total. Using 450 as a shared base would distort both.

11. (a) Production full-time: 164 − 42 − 30 − 12 = 80 [1]. Admin part-time: 48 − 30 = 18 [1]. Support part-time: 36 − 12 = 24 [1]. Part-time total: 240 − 164 = 76, and 18 + 18 + 16 + 24 = 76 [1]. (b) One employee is 360° ÷ 240 = 1.5° [1]. Sales 60 × 1.5 = 90°, admin 48 × 1.5 = 72° [1]. Production 96 × 1.5 = 144°, support 36 × 1.5 = 54° [1]. (c) 24 ÷ 76 × 100 = 31.6% [1]. [8] Examiner insight: Part (c) turns on the base: the part-time total of 76, not the department total of 36 or the company total of 240.

12. (a) 2024: 360° ÷ 200 = 1.8° per visitor [1]. Angles 180°, 108°, 72° [1]. 2025: 360° ÷ 450 = 0.8° per visitor [1]. Angles 144°, 144°, 72° [1]. (b) Radius = 2 × √(450 ÷ 200) [1] = 2 × 1.5 = 3 cm [1]. (c) 2024 shares 50%, 30%, 20%, giving ends at 5.0, 8.0 and 10.0 cm [1]. 2025 shares 40%, 40%, 20% [1], giving ends at 4.0, 8.0 and 10.0 cm [1]. (d) For example, the adult share fell from 50% to 40% [1]. [10] Examiner insight: A comparison of shares is stronger when it quotes both percentages.

Where marks are usually lost

• Pie chart angles that are not checked against 360°.
• Using the same circle size for two pies with different totals.
• Using the total ratio instead of its square root for the radius.
• Stacking a sectional bar from the baseline instead of from the previous section.
• Taking a percentage of the wrong row or column in a two-way table.
• No key on a dual bar chart or pictogram.
• Scales that do not start at zero or are uneven.
• Leaving out the calculation for each angle or height.

Next steps

• Reread the study guide for any question you missed.
• Use the revision notes as a final check.
• Visit the course hub and the checklist.
• Find all free 10-minute diagnostics here.
• Book a free trial class.

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.