Cambridge O Level Statistics: Surveys and questionnaire design (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.

These questions follow section 1.4 of the Cambridge O Level Statistics syllabus (4040), for examination in 2025, 2026 and 2027: general ideas of surveys, including closed and open questions in questionnaires. Learn the content first from the study guide and the revision notes. Course links: hub and printable checklist.

Questions

1. A school survey asks pupils how they travel to school.

(a) Write a closed question on this topic, with four response options. [2] (b) Write an open question on the same topic. [1]

2. (a) State two advantages of closed questions compared with open questions. [2] (b) State one advantage of an open question compared with a closed question. [1]

3. A questionnaire records the age, in whole years, of cinema customers using these options: “Under 18”, “18–30”, “30–45”, “50 or over”.

(a) State two faults in these response options. [2] (b) Write a corrected set of options. [2]

4. Each question below is badly worded. Name the fault and rewrite the question.

(i) “How often do you take exercise? Often, Sometimes, Rarely.” [2] (ii) “Do you think the library should open for longer and have more computers?” [2] (iii) “Do you agree that the terrible food in the canteen needs to be improved?” [2]

5. Thirty residents answer the open question “What annoys you most about living on your street?” The answers are coded as: parking 11, noise 8, litter 6, other 5.

(a) Find the percentage of residents who mentioned litter. [1] (b) Calculate the angle for each category in a pie chart. [2] (c) Explain why the answers had to be coded before the pie chart was drawn. [1] (d) State one piece of information lost when answers are coded. [1]

6. A researcher tries a questionnaire on 12 pupils before the main survey. She finds that 5 pupils left question 4 blank because no option matched their answer, 3 asked what “extracurricular” means, and the form took 25 minutes on average.

(a) Give one reason for carrying out a pilot survey. [1] (b) For each of the three findings, suggest a change to the questionnaire. [3]

7. A club hands out 250 questionnaires. 135 are returned, and 5 of these are incomplete and cannot be used.

(a) Calculate the response rate, using usable forms only. [2] (b) Explain why non-response can make the results biased. [2] (c) Suggest two ways to increase the response rate. [2]

8. Fifty shoppers answer “How would you rate the new car park?” The results are: very good 12, good 21, neither 9, poor 5, very poor not shown.

(a) Find the number who chose “very poor”. [1] (b) Find the percentage who chose “good” or “very good”. [2] (c) The researcher adds an open question after this one. Give a reason for doing so. [1]

9. A gym manager wants to know why members do or do not use the swimming pool.

(a) Write three questions for the questionnaire: one closed question with options, one rating-scale question, and one open question. [3] (b) Explain why the manager might use both open and closed questions. [2] (c) Describe how the manager should pilot the questionnaire. [3]

10. A council asks residents: “Do you think the council should waste money on cycle lanes? Yes / No”.

(a) State two faults in this question. [2] (b) Rewrite it as a closed question with a five-point rating scale. [2] (c) The council adds the open question “Why?”. Give one benefit and one drawback of this for the analysis. [2] (d) The form is available online only. State one way this could bias the results. [1]

11. A school asks 80 pupils the open question “What one change would improve lunch breaks?” The coded answers are: longer break 26, more clubs 18, better seating 14, shorter queues 12, other 10.

(a) Show that “longer break” was the most common answer and find its percentage of the 80 pupils. [2] (b) Calculate the pie chart angle for each category. [2] (c) Comment on the size of the “other” category. [2] (d) One pupil writes “the queues are long and the seating is dirty”. Explain how a coding rule should deal with an answer like this. [2]

Answers

1. (a) A clear question about the journey, for example “How do you usually travel to school?” [1] with four distinct options such as walk, cycle, bus, car (adding “other” gives an exhaustive list) [1] (b) For example “Why do you travel to school in this way?” [1] [3] Examiner insight: A closed question gains credit only when the options are shown. Check that no two options could both be true for one pupil.

2. (a) Any two from: quicker to answer; quicker and cheaper to tally and analyse; answers are in the same categories, so easy to compare; more likely to be completed [2] (b) Respondents can give reasons or answers the researcher did not think of [1] [3] Examiner insight: Two separate points are needed in part (a). Restating “quick” and “fast” is one point written twice.

3. (a) 30 appears in two options (18–30 and 30–45), so options are not mutually exclusive [1]; ages 46 to 49 appear in no option, so the options are not exhaustive [1] (b) For example: Under 18, 18–30, 31–45, 46 or over. No overlaps [1], no gaps [1] [4] Examiner insight: A corrected list that still has a gap or an overlap is unlikely to earn full credit. Test every whole number between the bands.

4. (i) Vague: “often” and “sometimes” mean different things to different people [1]. Rewrite: “On how many days in the last week did you take exercise? 0, 1–2, 3–4, 5–7” [1] (ii) Double-barrelled: asks about opening hours and computers at once [1]. Rewrite as two separate questions, one on opening hours and one on computers [1] (iii) Leading and loaded: “terrible” and “needs to be improved” suggest the answer [1]. Rewrite: “How would you rate the food in the canteen? Very good, good, neither, poor, very poor” [1] [6] Examiner insight: Naming the fault is not enough for the rewrite mark. The new question must remove the fault, so a rewrite that keeps “terrible” is not a fix.

5. (a) 6/30 × 100 = 20% [1] (b) Angle = frequency/30 × 360°, so each person is worth 12° [1]. Parking 132°, noise 96°, litter 72°, other 60° (total 360°) [1] (c) The answers were written in many different words, so they had to be sorted into categories before they could be counted [1] (d) For example: a resident’s second complaint, the strength of feeling, or the reasons given [1] [5] Examiner insight: Show the total of the angles. Adding to 360° is a quick check on arithmetic.

6. (a) To find and fix problems in the questionnaire before the main survey [1] (b) Question 4: add an option such as “Other (please state)” or check that the options cover every answer [1]. “Extracurricular”: replace it with plain words such as “school clubs” [1]. Time: shorten the form by removing questions that are not needed for the aim [1] [4] Examiner insight: Match each change to its finding. A general reply such as “make it better” is unlikely to be credited.

7. (a) Usable forms = 135 − 5 = 130 [1]. Response rate = 130/250 × 100 = 52% [1] (b) The people who did not reply may differ from those who did [1], so the replies may not represent the whole group, and results are pushed in one direction [1] (c) Any two from: send a reminder; shorten the form; give a prepaid reply envelope; explain the purpose clearly [1] [1] [6] Examiner insight: Read “usable forms only” carefully. Using 135 gives 54%, which does not answer the question asked.

8. (a) 50 − (12 + 21 + 9 + 5) = 50 − 47 = 3 [1] (b) 12 + 21 = 33 [1]. 33/50 × 100 = 66% [1] (c) It lets respondents explain their rating, which the scale alone cannot show [1] [4] Examiner insight: Give a reason specific to the rating. “To get more information” is too general.

9. (a) A closed question with options, for example “Do you use the pool? Yes / No” [1]; a rating question such as “How satisfied are you with pool opening times? Very satisfied, satisfied, neither, dissatisfied, very dissatisfied” [1]; an open question such as “What would make you use the pool more?” [1] (b) Closed questions give counts that are easy to tally and compare [1]. Open questions give reasons and ideas that the manager had not listed [1] (c) Try the questionnaire on a small group of members, like the real respondents [1]. Look for unclear questions, blank answers, options that do not fit, and the time taken [1]. Change the questionnaire to fix these before the main survey [1] [8] Examiner insight: In a design question, wording quality is judged. A leading or double-barrelled question can lose the mark even if it is the right type.

10. (a) “Waste” is a loaded word that suggests the answer [1]. Only Yes/No is offered, so there is no neutral or “don’t know” option [1] (b) “How far do you agree that the council should spend money on cycle lanes?” [1] with a balanced scale: strongly agree, agree, neither, disagree, strongly disagree [1] (c) Benefit: it gives reasons behind the answer [1]. Drawback: the answers must be read and coded before they can be counted, which takes longer [1] (d) Residents without internet access cannot reply, so they are under-represented [1] [7] Examiner insight: For part (c) give one benefit and one drawback that both refer to analysis. An answer about the respondent’s time does not address the question.

11. (a) 26 is greater than 18, 14, 12 and 10, so it is the largest [1]. 26/80 × 100 = 32.5% [1] (b) Each pupil is worth 360°/80 = 4.5° [1]. Longer break 117°, clubs 81°, seating 63°, queues 54°, other 45° (total 360°) [1] (c) “Other” is 10 of 80, which is 12.5% [1]. This is smaller than the main categories so it is acceptable, but the 10 answers should be read in case several share a theme that deserves its own category [1] (d) The rule must be decided before counting [1]. For example, code only the first point made (shorter queues), or count the answer in both categories and then say that percentages are of answers, not of pupils [1] [8] Examiner insight: In part (c) give a judgement and a reason, not just the percentage. In part (d) state the rule you chose and apply it to every answer.

Where marks are usually lost

• Writing response options that overlap (such as 20–30 and 30–40) or leave gaps between bands.
• Naming a fault in a question but not rewriting it, or keeping the loaded word in the rewrite.
• Giving the same advantage twice in different words when two separate points are asked for.
• Describing open and closed questions in general terms without linking the point to the survey in the question.
• Treating the pilot survey as a small copy of the main survey instead of a test of the questionnaire.
• Using the number returned instead of the number usable when finding a response rate.
• Leaving out working or units for percentages and pie chart angles.

Next steps

• Revision notes for this unit
• Study guide for this unit
• Cambridge O Level Statistics hub
• Printable checklist
• All free 10-minute diagnostics
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Official syllabus

Cambridge O Level Statistics 4040, syllabus for examination in 2025, 2026 and 2027, published by Cambridge University Press & Assessment. Section 1.4: general ideas of surveys, including the use of closed and open questions in questionnaires.