Understand the idea.
Make selection explicit
In simple random sampling, every possible sample of the chosen size has equal chance. Use a complete numbered list and distinct randomly selected IDs. Systematic sampling instead takes every th entry after a random start.
Stratified sampling selects randomly within relevant groups; proportional allocation preserves their population shares. Cluster sampling selects whole groups, such as classes. Similarity within clusters can reduce how much independent information a sample provides.
A large biased sample is still biased
Convenience sampling favours accessible people; voluntary response favours those who choose to participate. Either can systematically exclude experiences. A large response count does not repair a selection rule that misses part of the population.
Bias is a systematic tendency, whereas sampling variation is chance-to-chance fluctuation. Random selection does not guarantee balanced coverage in every realised sample. Non-response can also undo the advantages of a sound initial selection.
See the method in action.
Allocate proportional strata
A cohort has 120 Year 11 and 180 Year 12 students. Allocate a sample of 50.
Worked solution
- 1
Find the population total.
Both year groups contribute to the same cohort.
- 2
Allocate Year 11 places.
The sample receives the same Year 11 proportion as the population.
- 3
Allocate Year 12 places.
The remaining population share gives thirty places, and the allocations total fifty.
- 4
Select within each group.
Use random selection from each year list; proportional counts alone do not make selection random.
20 Year 11 and 30 Year 12 students.
Check a systematic pattern
A list repeats junior, junior, senior, senior. A sample takes every fourth entry.
Worked solution
- 1
Identify the repeating cycle.
The list repeats after four positions, exactly matching the sampling interval.
- 2
Track the starting position.
Starting in a junior position selects juniors on every fourth step; starting in a senior position selects seniors.
- 3
Interpret the random start carefully.
A random start gives a chance of either group, but an individual sample can still miss one group entirely.
- 4
Improve coverage.
Randomise the list first or take a suitable random sample within each age stratum to avoid locking selection to the repeating pattern.
With a random start, this design can still produce poor coverage and high sampling variation in an individual sample; random selection does not guarantee a representative realised sample.
Try it yourself.
Check your understanding
A website invites people to vote. Name the selection risk.
Show answer & reasoning
Voluntary-response bias.
This risks voluntary-response bias. People with strong opinions or regular website access may be more likely to vote, so voters need not represent the intended population.
Keep practising
6 worksheet questions · 12 marks
Read the questions online
- A generator selects 60 distinct IDs from 600 students. Name the method.2 marks
- Every 12th customer is selected after a random start from 1–12. Name it.2 marks
- Allocate a sample of 30 from 80 full-time and 120 part-time staff.2 marks
- Only tutoring attendees answer about homework difficulty. Identify a risk.2 marks
- A random survey has 50% non-response. Why might bias remain?2 marks
- Describe a cluster sample of geographically spread households.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- A generator selects 60 distinct IDs from 600 students. Name the method.2 marks
It uses chance selection from a defined list.
Simple random sampling. - Every 12th customer is selected after a random start from 1–12. Name it.2 marks
A fixed interval follows the start.
Systematic sampling. - Allocate a sample of 30 from 80 full-time and 120 part-time staff.2 marks
Multiply population fractions by 30.
12 full-time and 18 part-time. - Only tutoring attendees answer about homework difficulty. Identify a risk.2 marks
The selection excludes non-attendees.
Tutoring attendees may have different experiences from other students. - A random survey has 50% non-response. Why might bias remain?2 marks
Random initial selection does not guarantee unbiased final responses.
Respondents may differ systematically from non-respondents. - Describe a cluster sample of geographically spread households.2 marks
Blocks are clusters; consider differences between selected and unselected blocks.
Randomly choose neighbourhood blocks and survey households within them.
Curriculum reference & lesson scope
SACE Board of South Australia
Stage 1 General Mathematics: statistical investigation, univariate data, sampling, displays, summaries and interpretation.
Official curriculum source ↗