The idea, step by step
Make selection explicit
Simple random sampling gives every possible sample of a chosen size an equal chance. Number a complete list and select distinct random IDs. Systematic sampling selects every kth entry after a random start. Stratified sampling selects randomly within relevant groups, often proportionally.
Cluster sampling selects groups such as classes, then measures their members. It is useful where individual lists are difficult, but members of a cluster may be similar.
A large biased sample is still biased
Convenience sampling uses accessible people; voluntary-response sampling relies on people choosing to reply. Either can systematically miss viewpoints. Non-response can distort a random initial selection if respondents differ from non-respondents.
Random selection reduces systematic selection bias, but does not guarantee a statistic equals the parameter. Describe chance variation separately from systematic bias and record collection limitations.
A common trap
Random means choosing whoever is nearby.
Instead: Nearby selection is convenience sampling; random sampling needs a chance-based rule.
See the thinking
Allocate proportional strata
A cohort has 120 Year 11 and 180 Year 12 students. Allocate a sample of 50.
- Total is 300.
- Year 11: ; Year 12: .
- Select randomly within each list.
Check a systematic pattern
A list repeats junior, junior, senior, senior. A sample takes every fourth entry.
- The interval matches the list’s four-person pattern.
- A particular starting position can repeatedly select only one age group.
- Consider randomising the list or using a suitable stratified random sample to ensure both groups are covered.
Check your understanding
A website invites people to vote. Name the selection risk.
Show answer
Voluntary-response bias.
Strong views or regular access may affect response.
Your turn
6 questions · 12 marks · Work at your own pace.
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 ↗