The idea, step by step
Answer the question
State the question and population, then explain how data were collected. Include a suitable labelled graph and relevant summaries. The conclusion must answer the question with numbers and units, rather than merely say a graph was produced.
Distinguish the observed sample from the larger population. State size and missing responses so readers can judge the evidence.
Make limitations useful
“Human error” says little. Name an actual limitation: a convenience sample excluded absent students, recall affected self-reported time, or only one unusual week was observed. Explain how it could affect the result and propose a practical improvement.
Association alone does not establish causation. Program volunteers may differ in prior attainment or motivation. State what the design supports and what further information could help.
A common trap
A limitation makes an investigation worthless.
Instead: An honest report still explains what the evidence supports.
See the thinking
Ground the conclusion
Forty respondents have median travel 18 min/IQR 12 min; six selected students did not respond. Summarise.
- Describe the 40 respondents.
- Include median/IQR with minutes.
- Mention possible non-response effects.
Improve a causal claim
A survey says more revision caused higher marks. Improve it.
- The survey shows an association.
- Prior achievement or support may also differ.
- Do not isolate a cause from this design.
Check your understanding
What is missing from “the average was 14”?
Show answer
Variable, units, group and type of average.
For example: sample mean waiting time 14 minutes.
Your turn
6 questions · 12 marks · Work at your own pace.
Read the questions online
- Rewrite “B was faster” using medians A 16 min, B 12 min.2 marks
- Surveying one sports team estimates all students’ exercise. Give a limitation.2 marks
- Give an improvement to that sample.2 marks
- Why report missing responses?2 marks
- Tutoring attendance and marks are associated. State justified and unjustified claims.2 marks
- Name four useful report elements accompanying a graph.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Rewrite “B was faster” using medians A 16 min, B 12 min.2 marks
Name statistic, values and units.
B had a lower median time by 4 minutes: 12 versus 16. - Surveying one sports team estimates all students’ exercise. Give a limitation.2 marks
Selection can overestimate cohort exercise.
Team members may exercise more than non-members. - Give an improvement to that sample.2 marks
Chance-based wider coverage better matches the population.
Randomly sample the whole cohort, or relevant strata. - Why report missing responses?2 marks
Readers need to know how much of the planned sample was measured.
Non-response can affect representativeness. - Tutoring attendance and marks are associated. State justified and unjustified claims.2 marks
Prior achievement/motivation may differ.
Justified: sample association. Unjustified: tutoring alone caused the difference. - Name four useful report elements accompanying a graph.2 marks
These explain how to interpret the display.
Question/context; source/sampling; numerical summaries/units; conclusion/limitations.
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 ↗