Understand the idea.
Random means a chance method
A random sample uses a stated chance method. Number every eligible member of a complete list, then draw numbers fairly without replacement so a member cannot be selected twice. Choosing people who merely 'look random' leaves the decision to personal judgement.
A convenience sample uses whoever is easy to reach, while a voluntary poll relies on people choosing to respond. Both can favour particular groups. A sample's size alone does not show whether all parts of the population had a fair chance of inclusion.
Plan groups and intervals
A systematic sample selects every th entry after a random start among the first . Check the list for repeating patterns: selecting every twelfth entry may be misleading if the relevant characteristic also repeats every twelve entries.
Stratified sampling selects within important groups, rather than leaving their inclusion entirely to chance. For proportional allocation, a group containing of the population supplies of the sample. Still use a fair selection method inside each group.
See the method in action.
Worked example 1
Compare drawing 30 numbers from a full list of 240 students with asking 30 friends.
Worked solution
- 1
Inspect the numbered-draw frame.
The full list contains all 240 students, so a fair draw of 30 distinct numbers can include students throughout the school.
- 2
Inspect the friends-only frame.
Asking 30 friends is convenient but excludes students outside the friendship group, who may have different views.
- 3
Compare the selection methods.
The random draw is the stronger general plan because of its coverage and chance method; the matching sample sizes do not remove the friends-only bias.
The random draw is the stronger general plan.
Worked example 2
A list has 600 addresses. Select every 12th after a random start. Find the sample size.
Worked solution
- 1
Identify the sampling interval.
Selecting every twelfth address takes one entry per block of twelve.
- 2
Count complete blocks in the list.
The list has exactly fifty blocks of twelve addresses.
- 3
State the sample size.
Any start from 1 to 12 produces fifty selected entries before reaching the end of this 600-entry list.
50 addresses.
Try it yourself.
Check your understanding
Only teammates are asked about all students’ exercise. What is the concern?
Show answer & reasoning
Convenience-sample selection bias.
Teammates are an easy-to-reach convenience group and may exercise differently from other students. Their selection can bias a conclusion about the whole student population.
Keep practising
6 worksheet questions · 13 marks
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
.
60. - Groups A and B contain 240 and 360 students. Allocate a proportional sample of 50.3 marks
Total 600.
; .
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 ↗