Understand the idea.
Ask a question that needs data
A statistical question anticipates variation between observations. Travel times can differ between students; the scheduled bell time is usually one fixed fact. Specify the population, variable and observation period so that each response answers the same question.
Words such as “enough” need a stated comparison. Record the measured sleep hours first, then compare their distribution with the chosen benchmark. A benchmark does not make all students alike.
Follow the investigation cycle
Plan how to select people and measure the variable before collecting data. Check the records, display the distribution, calculate useful centre and spread summaries, and interpret them in the context of the original question.
A small pilot can expose an unclear question or inconsistent units. Revise the collection rule before the main investigation and document the change. Report limitations alongside the evidence, rather than changing inconvenient responses.
See the method in action.
Make the question measurable
Improve “Are students getting enough sleep?”
Worked solution
- 1
Identify the group.
Use Year 11 students at this school so the intended population is clear.
- 2
Define the measurement and period.
Ask for hours actually slept last school night, excluding time awake in bed, to make responses comparable.
- 3
Include the comparison in the question.
Ask how the sleep-hour distribution compares with this benchmark; do not presume one common sleep time.
“How many hours did Year 11 students at this school sleep last school night, and how does the distribution compare with 8 hours?”
Plan a comparison
Compare weekly leisure-reading time in two classes.
Worked solution
- 1
Use a common measurement rule.
Ask both classes for leisure-reading minutes during the same seven-day period.
- 2
Choose comparable participants.
Use each full class or comparable random samples, recording who does not respond.
- 3
Compare the distributions.
Use a common graph scale and suitable centre and spread summaries so typical time and variation are both considered.
- 4
Limit the conclusion to comparable periods.
A holiday week and a school week offer different reading opportunities, so such a comparison would mix class and calendar effects.
Use comparable collection, then compare typical minutes and variation. Do not compare a school week with a holiday week.
Try it yourself.
Check your understanding
Is “What proportion of our Year 11 cohort cycles to school?” statistical?
Show answer & reasoning
Yes.
Yes. Whether a student cycles varies across the cohort. The proportion requires several students' travel methods, with the number cycling compared with the number observed.
Keep practising
6 worksheet questions · 12 marks
Read the questions online
- Rewrite “Is the canteen popular?” as a clear statistical question.2 marks
- Explain why “How tall is the school flagpole?” is not normally statistical.2 marks
- List four decisions to make before collecting travel times.2 marks
- A study asks about exercise but records only running. Identify the problem.2 marks
- In a pilot, some students include homework in screen time and others do not. What next?2 marks
- What should accompany a reported median travel time of 16 minutes?2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Rewrite “Is the canteen popular?” as a clear statistical question.2 marks
The population, variable and period are stated.
For example: “On how many of the last five school days did Year 11 students buy food from the canteen?” - Explain why “How tall is the school flagpole?” is not normally statistical.2 marks
Repeated measurements could support a different question about measurement error.
It asks for one fixed height, not a distribution. - List four decisions to make before collecting travel times.2 marks
These determine whether values answer the question.
Population; measurement rule and units; sampling method; collection period. - A study asks about exercise but records only running. Identify the problem.2 marks
Broaden collection or narrow the question to running.
The measured variable does not cover all exercise. - In a pilot, some students include homework in screen time and others do not. What next?2 marks
Consistent rules make responses comparable.
Clarify the definition and pilot it again before main collection. - What should accompany a reported median travel time of 16 minutes?2 marks
For example, report the actual calculated IQR; do not invent it.
A suitable spread statement, sample/context and 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 ↗