- explain the central idea: Plan, conduct and report bivariate statistical investigations while recognising limitations on the inferences that can be made.
- choose and apply an appropriate method without relying on keyword matching
- check results using units, substitution, estimation, a second representation or contextual reasonableness
- justify a conclusion and communicate limitations where the context requires them
Year 10 Mathematics · AC9M10ST05
Planning Bivariate Statistical Investigations
A good bivariate investigation asks a focused question, measures two variables consistently, uses an appropriate display and limits conclusions to what the design and…
Ready to project and teach
Learning goalsSay it simply
Key conceptTeach from the board
Plan: question → variables/population → collection method → data → scatterplot/analysis → conclusion → limitations. Bivariate evidence can support association and prediction, but causal claims need stronger design.
Question
Specify two variables and target population/context.
Collect
Consistent units, method, sample and ethical handling.
Analyse
Plot paired data; describe direction, strength, form and unusual values.
Report
Answer question, quantify evidence, state interpolation/extrapolation and design limitations.
Worked examplesWe do
Worked examples
AC9M10ST05 - Planning Bivariate Statistical Investigations
Example 1
Question Specify two variables and target population/context.
Example 2
Collect Consistent units, method, sample and ethical handling.
Example 3
Analyse Plot paired data; describe direction, strength, form and unusual values.
Example 4
Report Answer question, quantify evidence, state interpolation/extrapolation and design limitations.
Curriculum examplesCopied content
Australian Curriculum: AC9M10ST05 — Year 10 Statistics. Plan, conduct and report bivariate statistical investigations while recognising limitations on the inferences that can be made.
Victoria: VC2M10ST05 — Level 10 Statistics
NSW: Stage 5 Path — Data analysis and statistical enquiry, supported by Core data analysis
Alignment explanation: The explicit teaching and worked examples address the Australian Curriculum concept directly. The Victorian mapping follows the current Version 2.0 descriptor structure; where Victoria combines or extends content, that difference is stated rather than hidden. NSW uses a Stage 5 Core–Paths structure, so this page maps to the relevant content group(s) and Working mathematically processes instead of inventing a Year 10 one-to-one code.
| Lesson component | Australian Curriculum | Victoria | NSW |
|---|---|---|---|
| Explicit concept teaching and worked examples | AC9M10ST05 | VC2M10ST05 — Level 10 Statistics | Stage 5 Path — Data analysis and statistical enquiry, supported by Core data analysis |
| Guided and independent practice | Builds fluency and application for AC9M10ST05 | Practises the mapped Level 10/10A knowledge as applicable | Practises the mapped Stage 5 Core/Path content |
| Reasoning and assessment tasks | Applies reasoning/problem solving in the descriptor context | Supports Victorian reasoning and modelling expectations | Embeds Working mathematically: reasoning, problem solving and communication |
Australian Curriculum elaborations
AC9M10ST05: plan and conduct statistical investigations involving bivariate data; evaluate and report findings considering limitations of inferences.
- E1: design investigations collecting bivariate data over time through observation/experiment/measurement, graph/analyse/report. Examples 1–4,10.
- E2: investigate anecdotal claims in climate, housing affordability/natural resources considering validity and interpolation/extrapolation. Examples 5–7.
- E3: use statistical investigation on relationship between vaccines and immunity. Example 8.
- E4: investigate biodiversity changes in Australia before/after colonisation using related bivariate numerical data and report associations. Example 9.
Questions and answersWith answers
- Rewrite “Does study help?” as a bivariate question.
- Example: Is weekly study time associated with test score among Year 10 students?
- Why standardise measurement method?
- So differences reflect variables rather than inconsistent measurement.
- What is wrong with sampling only sports academy students for all-school fitness?
- Sample may not represent all students.
Practice and reviewReady for practice
- Asking a vague question with undefined variables.
- Mixing measurement methods/units.
- Using convenience sample as if representative.
- Claiming causation from observational bivariate data.
- Hiding interpolation/extrapolation limitations.
Curriculum alignmentStart here
- explain the central idea: Plan, conduct and report bivariate statistical investigations while recognising limitations on the inferences that can be made.
- choose and apply an appropriate method without relying on keyword matching
- check results using units, substitution, estimation, a second representation or contextual reasonableness
- justify a conclusion and communicate limitations where the context requires them
- Australian Curriculum Version 9 — ACARA
- Victorian Curriculum Mathematics Version 2.0 — VCAA
- NSW Mathematics K–10 Syllabus (2022) — NSW Curriculum/NESA
Official wording is paraphrased on SkillrHub; use the linked curriculum sites as the source of record.
Other curriculum comparisons retained
US CCSS HSS-ID.B.6 and HSS-IC; UK GCSE statistical enquiry; NSW Stage 5 and Victorian Level 10 investigation/inference; comparable Canadian/NZ statistical investigation standards.
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