Understand the idea.
Answer the question
Begin a report with the investigation question, intended population and collection method. Present labelled displays and summaries that directly answer the question. State the variable, units and type of average whenever reporting a typical value.
Distinguish the respondents from the larger target group. Report sample size and missing responses so readers can assess coverage. Numbers should support the conclusion, rather than merely accompany a description of the graph.
Make limitations useful
A useful limitation identifies a specific problem, explains its possible effect and suggests a practical improvement. For example, surveying only present students may miss different travel patterns among absentees; arrange a follow-up rather than writing only “human error”.
An observational association does not isolate a cause. Prior achievement, access to support or motivation could differ between groups. State what the evidence shows and which competing explanations the design leaves unresolved.
See the method in action.
Ground the conclusion
Forty respondents have median travel 18 min/IQR 12 min; six selected students did not respond. Summarise.
Worked solution
- 1
Name the observed group.
The reported summaries describe the forty respondents, not automatically every selected student or the whole cohort.
- 2
Report centre and spread with units.
These give typical travel time and the span of the respondents' middle half.
- 3
Disclose the missing responses.
Six selected students did not respond and their travel times may differ from those recorded.
- 4
Limit the generalisation.
Among respondents the median was eighteen minutes and IQR twelve minutes; non-response may affect any estimate for the whole cohort.
Among respondents, median travel was 18 min and IQR 12 min. Non-response may affect a cohort-level estimate.
Improve a causal claim
A survey says more revision caused higher marks. Improve it.
Worked solution
- 1
Describe the observed relationship.
Students reporting more revision tended to have higher marks; this states an association.
- 2
Identify a competing explanation.
Prior attainment or access to support might affect both revision habits and marks.
- 3
Qualify the causal conclusion.
The survey does not establish that revision alone caused the difference, because it does not isolate revision from those other influences.
Students reporting more revision tended to have higher marks; the survey does not establish revision alone caused the difference.
Try it yourself.
Check your understanding
What is missing from “the average was 14”?
Show answer & reasoning
Variable, units, group and type of average.
“Average” does not identify whether fourteen is a mean or median, what was measured, its unit or whose values were recorded. “The sample mean waiting time was fourteen minutes” supplies these essentials.
Keep practising
6 worksheet questions · 12 marks
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 ↗