Year 9 Mathematics · AC9M9ST05

Planning and Conducting Statistical Investigations

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

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Learning goalsSay it simply

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
Key conceptTeach from the board

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.

Worked examplesWe do

Worked examples

AC9M9ST05 - Planning and Conducting Statistical Investigations
Example 1

Question Do Year 9 students who report more weekly sport have different resting heart rates?

Example 2

Design Define sport hours and heart-rate measurement, sample across the year level and standardise measurement conditions.

Example 3

Analysis Use suitable displays and summaries, then describe patterns without claiming causation from an observational study.

Example 4

Turn a broad topic into a measurable statistical question.

Curriculum examplesCopied content

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.

Lesson componentAustralian CurriculumVictoriaNSW
Concept teaching + worked examplesAC9M9ST05VC2M9ST05 — Level 9 StatisticsStage 5 Path — Data analysis and statistical enquiry, supported by Core data analysis
Guided + independent practiceApplies the descriptor through progressively less-scaffolded problemsBuilds the corresponding Level 9 mathematical knowledge and fluencySupports Stage 5 Core/Path application and Working mathematically
Reasoning + assessment + masteryChecks transfer, justification, interpretation and model limitsChecks Level 9 reasoning at the mapped content depthChecks relevant Stage 5 reasoning without claiming a false Year 9 equivalent
Questions and answersWith answers
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.
Practice and reviewReady for practice
  • 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. [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.

Curriculum alignmentStart here

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
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