Collect data and choose a defensible sample
Plan a survey, distinguish population and sample, select and assess sampling methods, and classify the data collected.
Section Paper 2 · Written · calculator required
Exam scope and assessment notes
This lesson maps the Collect data and choose a defensible sample section of Cambridge IGCSE Statistics 0479 (2027 and 2028–2030 syllabus versions). This is original StudyForA teaching and self-check practice, not Cambridge material, an official mark scheme, a timed mock or an official grade. Charts and written working are not automatically assessed; human subject-teacher review remains pending. Use the syllabus version for your exam year. Cambridge offers 0479 in the June series only and does not make it available in every administrative zone. Check the current Cambridge 0479 page and confirm your centre's entry eligibility with your exams officer.
Before you begin
- Use ordinary fractions, percentages and multiplication. No prior statistics course is assumed.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which group is the population if a survey asks every student in one school about travel?
What you will learn
- Define population, sample, census and representative sample
- Compare simple random, systematic, stratified and quota sampling
- Recognise bias and use a random-number table for random, systematic and stratified selection
- Choose open or closed questions and classify qualitative, quantitative, discrete and continuous data
Define who and what is being studied
The population is the complete group of interest; a sample is the part actually observed. A census attempts to collect information from every member. A representative sample reflects important features of the population, such as its proportions in relevant groups.
A sampling frame is the list or source from which members can be selected. It is needed for simple random, systematic and stratified sampling, but not for quota sampling, where an interviewer fills stated group totals.
Select a method and check for bias
A simple random sample gives each listed member an equal chance. A systematic sample selects every kth member after a random start. A stratified sample selects from each group, often in proportion to its population size. A quota sample fills target numbers in groups but lets the interviewer choose individuals, so selection within a group may be biased.
A sample is biased when the method systematically favours some outcomes or people. A large sample does not repair a biased method. Random-number tables can choose identifiers; reject numbers outside the defined range and follow the stated selection rule.
Write questions that produce usable data
Closed questions provide fixed response options, making answers easier to count, but the options may not fit every response. Open questions allow detail, but answers take longer to classify. Qualitative data describe categories; quantitative data are numerical. Discrete values are countable, while continuous values can take any value in an interval.
Pause and explain
Why can a quota sample still be biased after all quotas are filled?
Worked example
A school has 480 students: 300 in lower years and 180 in upper years. A stratified sample of 40 is required. How many should be selected from each group?
Show the worked solution
- Find the lower-year share: 300/480 = 5/8.
- Select 5/8 × 40 = 25 lower-year students.
- The remaining 15 are from upper years; check 25/40 = 300/480 and 15/40 = 180/480.
Answer Select 25 lower-year and 15 upper-year students. The sample matches each group's proportion in the population.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A library wants a representative sample of 60 readers. There are 240 readers aged under 16 and 360 aged 16 or over. Allocate a proportional stratified sample.
Give me a hint
Find each group's fraction of the 600 readers, then multiply by 60.
Compare my reasoning
- Under 16: 240/600 × 60 = 24.
- Age 16 or over: 360/600 × 60 = 36.
- Check 24 + 36 = 60.
Select 24 readers under 16 and 36 readers aged 16 or over.
Look for these in your work
- Uses population proportions
- Calculations shown
- Total checked
A town survey asks, ‘Do you agree that the excellent new bus service is convenient?’ Improve the question and explain why.
Give me a hint
Remove the leading description and ask about one clear feature.
Compare my reasoning
- ‘Excellent’ encourages a positive response and ‘convenient’ may mean different things.
- Ask neutrally, for example: ‘How convenient is the bus service for your usual journey?’
- Offer balanced fixed options or invite a reason in a follow-up open question.
A neutral question such as ‘How convenient is the bus service for your usual journey?’ avoids praising the service in advance. Balanced response options make answers easier to compare; a follow-up open question can explain the rating.
Look for these in your work
- Leading wording identified
- Neutral wording proposed
- Question format explained
A clinic wants to compare waiting times across three departments. It takes every 12th name from a complete appointment list after a random start. Classify the method, data and one limitation.
Give me a hint
Name the sampling rule, describe waiting time as a measured variable, and consider who is absent from the frame.
Compare my reasoning
- Every 12th name after a random start is systematic sampling.
- Waiting time is quantitative and continuous.
- The frame may omit walk-in patients or people whose appointments were cancelled.
This is systematic sampling. Waiting time is quantitative continuous data. The result may not represent all clinic users if the appointment list omits walk-ins or other groups relevant to the question.
Look for these in your work
- Method classified
- Data classified on both dimensions
- Frame limitation connected to context
Common mistakes
- Calling a sample representative only because it is large
- Using a sampling frame requirement for quota sampling
- Treating discrete and continuous data as synonyms for qualitative and quantitative
- Assuming a random number table makes an incomplete frame representative
What can you explain now?
A researcher interviews the first ten people leaving a sports match. What is the main sampling concern?
Compare with the explanation
The method may favour people who leave early and is not a random sample of all attendees
The selection rule can systematically exclude later leavers, so the sample may not represent the whole audience.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
What does a sampling frame provide, and which one of the four named methods does not require one?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.