The idea, step by step
Ask a question that needs data
A statistical question expects answers that vary. Asking how long Year 11 students spend travelling to school needs data from several students. Asking when the school bell rings usually asks for one fixed fact. Define who, what, where and when so the investigation has a clear boundary.
A conclusion such as “the average is 18” is incomplete without a variable, units and population. Answer the original question and describe how much the observations varied.
Follow the investigation cycle
Start with a question and plan: define the population, choose a sampling method and decide how each value will be measured. Collect and check data before choosing displays and summary statistics. Interpret patterns, consider limitations, and report a conclusion supported by evidence.
The cycle allows revision. A pilot survey may reveal an unclear definition or impossible units. Fix the plan before the main collection and record the change rather than silently altering inconvenient responses.
A common trap
An investigation is just calculating a mean.
Instead: The question, collection, data quality, variation and interpretation are also essential.
See the thinking
Make the question measurable
Improve “Are students getting enough sleep?”
- Choose a population: Year 11 students at one school.
- Define hours slept last school night, excluding time awake in bed.
- Ask for a distribution rather than assuming one common value.
Plan a comparison
Compare weekly leisure-reading time in two classes.
- Ask the same question for the same seven-day period.
- Use all students or comparable random samples; record non-response.
- Compare displays on a common scale and suitable centre/spread summaries.
Check your understanding
Is “What proportion of our Year 11 cohort cycles to school?” statistical?
Show answer
Yes.
Travel method varies, so several observations are needed.
Your turn
6 questions · 12 marks · Work at your own pace.
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 ↗