IB Maths AI SL · Unit 4: Statistics and Probability
IB Maths AI SL Sampling Techniques Questions
Updated October 2026
Exam-style IB Maths AI SL sampling techniques questions with worked solutions. Start with the 3 fully worked examples below — each is solved step by step, showing the working that earns the marks — then try the practice questions and check your working against the mark scheme.
The question bank covers these sampling techniques question types (number of questions in brackets):
Stratified sampling (6)
Convenience and Self-selection (5)
Systematic sampling (4)
Sampling Techniques worked examples
Worked example 1: Identifying a sampling technique · easy
A researcher surveys the first students entering the library at 9 AM Monday. Name the sampling method and give one reason for bias.
Solution
1. Recall: choosing people simply because they are accessible is Convenience Sampling.
2. State: Convenience Sampling.
3. Analyse: library-goers early on a Monday have distinctive habits.
4. State bias: excludes students not visiting the library at that time, so the sample is unrepresentative of the whole university.
4 steps
Examiner tip: If the researcher had a quota (e.g., 15 males + 15 females), it would be Quota Sampling rather than pure Convenience.
Worked example 2: Stratified sampling calculation · medium
School has Year 11 and Year 12 students. A stratified sample of is required. How many Year 11 students should be in the sample?
Solution
1. Rule: stratified proportions must match the population.
2. Total: .
3. Proportion: .
4. Apply to sample: .
5. Evaluate: exactly Year 11 students.
3. Proportion: .
5 steps · 1 to fill in
Examiner tip: Stratified sampling guarantees proportional representation and prevents minority groups being missed by chance.
Worked example 3: Systematic sampling — interval and start · hard
A factory produces bulbs. Use systematic sampling to select . Find the interval and explain the unbiased start.
Solution
1. Formula: .
2. Substitute: .
3. Round down: (avoids running out of population).
4. Random start: use a random number generator to pick the first bulb from positions to .
5. Then: sample every nd bulb thereafter.
2. Substitute: .
5 steps · 1 to fill in
Examiner tip: Automatically picking bulb #1 breaks randomness. The first pick must be random within the first interval block.
Try these IB Maths AI SL sampling techniques questions
Three questions from the bank, easiest first. Mark schemes and AI marking of your written working are in the practice area. One of them has its full worked solution here, open to everyone.
Question 1 · easy · 2 marks · Paper 1
A headmaster wants to survey student opinions on the new school uniform. He takes an alphabetical list of all students in the school and selects every 15th name on the list to form his sample.
Identify the sampling technique used by the headmaster.
A student wishes to investigate the average amount of sleep teenagers get. She decides to collect data by asking her 20 closest friends at school.
Identify the sampling technique used by the student.
Explain one reason why this sampling method may lead to biased or unreliable data.
Full worked solution Free, no sign-in
Convenience sampling. A1
Her friends are likely to share similar habits, schedules or backgrounds, R1 so they are not representative of the wider teenage population. A1
Every question here has a full worked solution.See them all →
Question 3 · hard · 3 marks · Paper 1
A market researcher is tasked with surveying 50 men and 50 women about a new product. She stands outside a shopping mall and asks people who walk past until she has spoken to exactly 50 men and 50 women.
Identify the sampling technique being used here.
State one key difference between this sampling method and stratified sampling.
How many IB Maths AI SL sampling techniques questions are there?
There are 15 exam-style sampling techniques questions in the AI SL question bank (Paper 1: 11 · Paper 2: 4), graded 3 easy, 7 medium, 5 hard. Every question has a full IB-style mark scheme (M, A and R marks).
Is sampling techniques on Paper 1 or Paper 2?
Both. In the bank, Paper 1: 11 · Paper 2: 4. Practise with your GDC — AI papers expect calculator methods throughout.
Where can I get the mark schemes?
Open the AI SL Unit 4 practice page: every question has a step-by-step IB-style mark scheme, and you can photograph your working for instant AI marking. The worked examples on this page are free.