The idea, step by step
Random means a chance method
A simple random sample can be selected by numbering every eligible unit and drawing numbers fairly without replacement. “Pick people who look random” is not a defined chance method. Convenience samples use people who are easy to reach; voluntary polls use people who choose to respond. Both may favour particular groups.
Plan groups and intervals
A systematic sample selects every kth entry after a random start. Check that a repeating pattern in the list does not match the interval. Stratified sampling selects within important groups. If a sample is allocated proportionally, a group containing two-fifths of the population supplies two-fifths of the sample; selection within groups should still be fair.
A common trap
Large convenience samples automatically remove bias.
Instead: A large sample cannot repair systematic under-coverage.
See the thinking
Worked example 1
Compare drawing 30 numbers from a full list of 240 students with asking 30 friends.
- The numbered draw gives every listed student a chance.
- Friends are a convenience group.
- Equal sample sizes do not make the methods equivalent.
Worked example 2
A list has 600 addresses. Select every 12th after a random start. Find the sample size.
- 600÷12=50.
- With start 7, entries are 7,19,31,…,595.
Check your understanding
Only teammates are asked about all students’ exercise. What is the concern?
Show answer
Convenience-sample selection bias.
Teammates may exercise differently from other students.
Your turn
6 questions · 13 marks · Work at your own pace.
Read the questions online
- Give a simple random method for choosing 15 of 150 students.2 marks
- A systematic sample starts at 3 with interval 10. Give its first five entries.2 marks
- A 600-entry list uses systematic interval 10. Find the sample size.1 mark
- Groups A and B contain 240 and 360 students. Allocate a proportional sample of 50.3 marks
- An optional sports-website poll asks all students’ views on sports facilities. Explain a concern.2 marks
- A list repeats bus, walk, cycle. Why could selecting every third entry be unsuitable?3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Give a simple random method for choosing 15 of 150 students.2 marks
Use a complete list and a chance method without replacement.
Number 1–150 and fairly draw 15 distinct numbers. - A systematic sample starts at 3 with interval 10. Give its first five entries.2 marks
Add 10 each time.
3,13,23,33,43. - A 600-entry list uses systematic interval 10. Find the sample size.1 mark
600÷10=60.
60. - Groups A and B contain 240 and 360 students. Allocate a proportional sample of 50.3 marks
Total 600.
50×240/600=20; 50×360/600=30.
20 from A; 30 from B. - An optional sports-website poll asks all students’ views on sports facilities. Explain a concern.2 marks
The voluntary group may not represent everyone.
Sports-interested students may be more likely to visit and respond. - A list repeats bus, walk, cycle. Why could selecting every third entry be unsuitable?3 marks
A random start does not eliminate list periodicity.
The interval matches the pattern and may select just one travel method.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum
Population, census and sample; observational versus experimental data; random and non-random sampling; primary/secondary data; reviewing numerical displays and summary statistics; comparing samples and sample sizes; bias, variation and uncertainty; planning, conducting and reporting a fair investigation.
Official curriculum source ↗