Positive
As x increases, y tends to increase.
Learning goals: what you will learn
- explain the central idea: Construct and interpret scatterplots, describing association by direction, strength and linearity without confusing correlation with causation.
- 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
Prerequisite knowledge
Revise Cartesian coordinates, numerical variables, graph axes, data collection and interpreting trends.
Concept teaching
A scatterplot displays paired numerical data. Describe direction (positive/negative/none), strength (weak/moderate/strong) and form (linear/nonlinear). Then mention outliers/clusters and context.
Negative
As x increases, y tends to decrease.
Strength
Tighter clustering around a simple trend = stronger association.
Prediction
Interpolation is generally safer than extrapolation; association ≠ causation.
Worked examples
1. Strong positive
Points closely follow an upward-sloping line: strong positive linear association.
2. Weak negative
Points are widely scattered but trend downward: weak negative association.
3. Nonlinear
Points form a curved U-shape; saying “no linear association” does not mean “no relationship”.
4. Outlier
One point far from the main pattern may affect a fitted line; investigate before deciding whether it is error or genuine.
5. Association not causation
Ice-cream sales and sunburn may rise together because hot sunny weather affects both. The association does not prove ice cream causes sunburn.
6. Line of good fit
A by-eye line should pass through the centre of the cloud with roughly balanced points above/below; use it for approximate interpolation.
7. Extrapolation limit
A trend measured for ages 12–17 should not automatically be extended to age 70; the relationship may change outside observed range.
8. Data science feature check
Scatterplots can reveal whether a candidate numerical feature appears related to an outcome before modelling, but they do not replace validation.
9. AI forecasting limitation
A model may use correlation to predict accurately while still failing to explain causality or ethical/contextual implications.
10. Spear-thrower variables
An authentic dataset might pair spear-thrower length with measured range/speed and examine association. Cultural technology context must be accurate and respectfully sourced; statistical association should not be overinterpreted.
Common misconceptions and corrections
- Saying correlation proves causation.
- Describing only direction and omitting strength/form.
- Calling a nonlinear relationship “no association” because it is not straight.
- Extrapolating far beyond observed data.
- Deleting outliers automatically.
Guided practice
Sketch three scatterplots: strong positive linear, weak negative and strong curved association. For each, write a complete contextual sentence using direction, strength and form, without claiming causation.
Teacher check: require a written method choice and one verification step before revealing the worked solution.
Independent practice
- Define positive association.
- What does strong association mean visually?
- Can a curved pattern be associated?
- Why investigate an outlier?
- Give a confounder for ice-cream sales and sunburn.
- What is a line of good fit used for?
- Which is safer: interpolation or distant extrapolation?
- Does high predictive accuracy prove causation?
- Write a full association description: upward, tightly clustered, roughly straight.
- State one requirement when using culturally specific data.
Check answers and explanations
- y tends to increase as x increases.
- Points cluster closely around the trend.
- Yes; it may be strong but nonlinear.
- It may be error, rare genuine case or influential observation.
- Hot/sunny weather.
- Summarise trend and make approximate predictions within range.
- Interpolation.
- No.
- Strong positive linear association.
- Use an authentic, respectful and appropriate source/context.
Reasoning and problem-solving task
A scatterplot of screen time and sleep duration shows a moderate negative association. Write three different plausible explanations for the pattern, including one involving a third variable, and explain why the scatterplot alone cannot choose among them.
Important questions and answers
- Define positive association.
- y tends to increase as x increases.
- What does strong association mean visually?
- Points cluster closely around the trend.
- Can a curved pattern be associated?
- Yes; it may be strong but nonlinear.
Assessment-style questions
A scatterplot shows a strong positive association between exercise minutes and fitness score. Describe the association precisely, explain why causation is not established and name a plausible lurking variable. [5 marks]
Marking focus: method selection, mathematically correct working, interpretation and justification.
Review hints
- direction + strength + form + context
- do not join points
- check unusual points
- association is not causation
Exit ticket: mastery check
- I can explain the concept without copying a formula sheet.
- I can solve a routine example and check the result.
- I can choose a method in an unfamiliar problem.
- I can explain a common error and correct it.
- I can connect the answer back to the context, including units or limitations.
Teacher and parent guidance
For teachers
Give students several scatterplots with the same direction but different strength and form. Require full-sentence contextual descriptions rather than labels only.
For parents and carers
Ask your child to describe a scatterplot without using the word 'causes'. Then ask what other explanation could produce the pattern.
Curriculum alignment
Australian Curriculum: AC9M10ST03 — Year 10 Statistics. Construct and interpret scatterplots, describing association by direction, strength and linearity without confusing correlation with causation.
Victoria: VC2M10ST02 — Level 10 Statistics
NSW: Stage 5 Core — Data classification, visualisation and analysis; Path — Data analysis and statistical enquiry
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 | AC9M10ST03 | VC2M10ST02 — Level 10 Statistics | Stage 5 Core — Data classification, visualisation and analysis; Path — Data analysis and statistical enquiry |
| Guided and independent practice | Builds fluency and application for AC9M10ST03 | 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
AC9M10ST03: construct scatterplots and comment on association between 2 numerical variables in terms of strength, direction and linearity.
- E1: distinguish association from cause/effect in health, species diversity, climate contexts. Example 5.
- E2: make/justify/critique association claims in climate, migration, shopping/social media. Examples 1–7.
- E3: use line of good fit informally and discuss prediction reliability. Examples 6–7.
- E4: explore scatterplots/association in data science and machine learning. Example 8.
- E5: investigate AI forecasting based on correlation and limitations around causality/context/ethics. Example 9.
- E6: investigate paired variables relating to spear throwers used by First Peoples of Australia using scatterplots/comparison. Example 10.
Practice and teaching resources
Official curriculum references
- 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; UK GCSE scatter graphs/correlation; NSW Stage 5 and Victorian Level 10 bivariate statistics; comparable Canadian/NZ association analysis.
🎥 Optional Video Lesson
The SkillrHub lesson remains the primary learning resource. This optional video reinforces the explanation; you can complete the lesson and practice without watching.
Before you watch:
- Pause after each worked example.
- Try the examples yourself.
- Return to the SkillrHub lesson before continuing.
Recommended: Bivariate relationship linearity, strength and direction
Khan Academy — Describing the direction, strength and form of a scatterplot relationship.
As you watch: How can a relationship be strong without being linear?
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Try it: Sketch strong positive linear, weak negative linear and strong curved relationships; describe each without claiming causation.
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Curriculum equivalents: Victoria, NSW and international
Curriculum equivalents for Construct scatterplots and comment on the association between the 2...
Mapped skill: construct scatterplots and comment on the association between the 2 numerical variables in terms of strength, direction and linearity
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.
| Region | Curriculum framework | Closest level or code |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M10ST03 · Year 10 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M10ST02 · Level 10 |
| New South Wales | NSW Mathematics K–10 Syllabus (2022) | MA5-DAT-C-02 · Stage 5 |
| United States (USA) | Common Core State Standards for Mathematics | Grades 9–10 band |
| Canada (Ontario) | Ontario Curriculum — Mathematics | Grade 10 |
| United Kingdom (England) | National Curriculum in England — Mathematics | Year 11, Key Stage 4 |
| India | NCERT / CBSE — Mathematics | Class 10 |
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.
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Topic reference: AC9M10ST03 — Scatterplots and Bivariate Association — AC9M10ST03
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