Five named ways to pick a sample: The IB syllabus names five ways to choose a sample.
A common exam question gives you a scenario and asks you to name the technique used.
The five techniques: • Simple random — every member equally likely (draw lots / random numbers). • Systematic — order the list, take every k-th member. • Stratified — split into groups, sample each in proportion. • Quota — fill fixed numbers per group, chosen non-randomly. • Convenience — whoever is easiest or first available.
IB-style question — name the technique
A manager puts all 200 staff names in a hat and draws out 20 for a survey.
Which sampling technique is this?
Step by step
- Every staff member is equally likely to be drawn, purely by chance.
- That is the definition of one technique.
Final answer
Simple random sampling.
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Equal chance, or every k-th: Simple random: every member has an equal chance (random numbers / drawing lots).
Systematic: order the list and take every k-th member after a random start, where k = population size ÷ sample size.
IB-style question — systematic interval
A club has 800 members.
A sample of 50 is taken systematically.
Find the sampling interval and describe how to choose the sample.
Step by step
- Interval = population ÷ sample size.
- Pick a random start, then step by k.
Final answer
k = 16: choose a random starting member from the first 16, then take every 16th member after that.
Random start matters: Systematic sampling needs a random first member — otherwise you always pick the same positions and could introduce bias.
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Sample each group in proportion to its size: Stratified sampling splits the population into groups (strata) and takes from each group a number proportional to its size — so big groups contribute more.
IB-style question — how many from a group
A school has 600 junior and 400 senior students (1000 in total).
A stratified sample of 50 is taken.
Find how many juniors should be in the sample.
Step by step
- Write the group's proportion times the sample size.
- Evaluate.
Final answer
30 juniors (and so 20 seniors).
Check it adds up: The numbers from all strata should sum to the total sample size (here 30 + 20 = 50).
Non-random methods risk bias: Quota fills fixed numbers from each group but picks members non-randomly; convenience takes whoever is easiest/first.
Because selection isn't random, these are the most likely to be biased.
Random-based (fairer)
- simple random — equal chance
- systematic — every k-th
- stratified — proportional groups
Non-random (bias risk)
- quota — fixed numbers, chosen non-randomly
- convenience — easiest / first available
- often unrepresentative
IB-style question — name it and judge it
A reporter interviews the first 30 people leaving a train station at 9 am.
Name the sampling technique and give one reason the sample may be biased.
Step by step
- First / easiest available → name the technique.
- Who is missing?
Final answer
Convenience sampling; biased because only people travelling at 9 am are included, so it doesn't represent everyone.