Planning and Conducting Statistical Investigations — AC9M9ST05

A statistical investigation connects a clear question to appropriate data collection, analysis, representation and a conclusion whose strength matches the evidence.

By the end of this lesson, you should be able to:

• formulate a statistical investigative question
• plan suitable data collection
• analyse data using appropriate summaries and displays
• report findings and evaluate the strength and limitations of evidence

Recall sampling, variable types, centre, spread, shape, display choice and basic ethical treatment of survey data.

The question determines the design

Define population, variables and the comparison or estimate required before collecting data.

Collection quality limits every later conclusion

Choose a defensible sample and method, consistent measurement and enough data for the intended analysis.

Analysis must fit the variables

Use suitable displays and summaries for categorical or numerical variables; compare groups using relevant measures.

Conclusions need calibrated strength

Distinguish what data show from what they merely suggest. State limitations, possible bias and whether the design supports generalisation.

• Collecting data before defining the question: A vague question produces unfocused data.
• Any sample supports population claims: Generalisation depends on sampling design.
• A pattern proves causation: Observational associations can have confounders.
• A conclusion just repeats the graph: It should answer the question and discuss evidence strength and limitations.

1. Turn a broad topic into a measurable statistical question.
2. Define population, sample and variables.
3. Choose a collection method and display.
4. Write a cautious conclusion including one limitation.

Guided method: Name the mathematical structure first, show the calculation or representation, then verify with an estimate, inverse operation, second representation or digital check.

1. Design a question comparing two groups on a numerical variable.
2. Choose a sampling method and justify it.
3. Define how one variable will be measured consistently.
4. Choose appropriate summaries and displays.
5. State one ethical or privacy consideration.
6. Write the strongest conclusion the proposed design could legitimately support.

A class finds that students who sleep more tend to have higher test scores. Explain why the investigation can describe an association but cannot by itself prove that extra sleep caused the higher scores, and name two plausible confounders.

Reasoning standard: Make a claim, show the relevant mathematical evidence, explain why it supports the conclusion and state any condition or limitation.

What comes before data collection?

A clear investigative question and design.

What limits population generalisation?

Sampling quality and representativeness.

How strong should a conclusion be?

Only as strong as the design and evidence justify.

1. [6 marks] Critique a proposed statistical investigation and repair weaknesses in its question, sampling and measurement.
2. [8 marks] Design a complete Year 9 statistical investigation from question through planned analysis and reporting.
3. [7 marks] Given investigation results, write a conclusion that distinguishes findings, limitations and what cannot be inferred.

Review hint: A full-mark response shows the method, keeps units and restrictions visible, interprets the result in context and checks whether the answer is reasonable.

• I can formulate a measurable statistical question.
• I can align sampling and measurement to the question.
• I can choose analysis appropriate to variable types.
• I can state bias and limitations.
• I can keep conclusions within the evidence.

Exit ticket: Solve one unfamiliar example and explain the key decision in words, not just symbols.

Australian Curriculum v9.0 — AC9M9ST05: plan and conduct statistical investigations involving the collection and analysis of different kinds of data; report findings and discuss the strength of evidence to support any conclusions

Victoria: VC2M9ST05 — Level 9 Statistics. The mapping names direct Level 9 content where available and explicitly identifies supporting content where the Victorian structure separates an idea differently.

NSW: Stage 5 Path — Data analysis and statistical enquiry, supported by Core data analysis. NSW organises Years 7–10 Mathematics through Stage 5 Core content groups and Paths rather than a one-code-per-Year-9 structure, so this lesson does not force a false one-to-one outcome.

Use these links to move through the Year 9 learning sequence rather than studying the code in isolation.

• AC9M9ST01 — Analysing Survey Reports and Population Estimates
• AC9M9ST04 — Choosing and Interpreting Data Displays

• Australian Curriculum v9.0 — Mathematics
• Victorian Curriculum F–10 Version 2.0 — Mathematics
• NSW Mathematics K–10 Syllabus (2022)

Curriculum equivalents for Plan and conduct statistical investigations involving the collection and analysis...

Mapped skill: plan and conduct statistical investigations involving the collection and analysis of different kinds of data; report findings and discuss the strength of evidence to support any conclusions

These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.

Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.