Build and annotate the model
Represent comparing categorical and numerical data sets and label the important parts, quantities or choices.
Learning goals
Learning goal
Students identify variable type, read displays accurately and compare centre, mode, range, clusters, gaps, skew and possible extremes without claiming causes unsupported by the data.
Success criteria
- I can represent or identify the concept.
- I can explain the underlying relationship.
- I can select an appropriate strategy or feature.
- I can apply it in a new context.
- I can justify and verify the response.
Teaching routine
- Represent
- Reason
- Calculate
- Interpret
- Verify
Curriculum focus: interpret and compare data sets for ordinal and nominal categorical, discrete and continuous numerical variables using appropriate displays; compare distributions in terms of mode, range and shape
Key concept
Compare two numerical distributions
Use the visual model first. Ask students to identify the quantities, structure or conditions before calculating or explaining.
featureClass AClass Bmode1212 and 15range95shapeclustered 11–14, one high valuemore even 11–16variationgreatersmaller
One statistic does not describe a full distribution. Use several features and connect them to the measured context.
Worked examples
Match display to variable type
Connect the central relationship to a new context, then verify the conclusion with a second representation, estimate, inverse operation or reasonableness check.
nominal categoriescolumn graph or table
ordinal ratingsordered columns
discrete numericaldot plot or column graph
continuous numericalgrouped display or line-related context
two distributionssame scale and aligned categories
Comparisons require consistent scales and definitions. Avoid interpreting an association as a causal explanation.
Curriculum elaborations explicitly taught
AC9M6ST01: interpret and compare data sets for ordinal and nominal categorical, discrete and continuous numerical variables using comparative displays or visualisations and digital tools; compare distributions in terms of mode, range and shape
- E1: determining the range for a numerical data set by finding the difference between the highest and the lowest value in the set and comparing the range for different data sets
- E2: representing acquired numerical data sets using side-by-side column graphs, comparing the spread of each data set using the range, the highest frequency for each data set using the mode, and discussing the shape
- E3: representing ordinal data collected through surveys, using visualisation tools including dot plots and bar charts, and discussing the distribution of data in terms of shape
- E4: using technology to access data sets and graphing software to construct side-by-side column graphs or stacked line graphs; comparing data sets that are grouped by gender, year level, age group or other variables and discussing findings
Use the central and application models above to connect each elaboration to the same underlying concept.
Common misconceptions
Ordinal categories treated as equal numerical intervalsOrder is meaningful, spacing may not be.
Range used as complete descriptionAlso discuss concentration and shape.
Different graph scales compared visuallyRead actual values.
Cause inferred from group differenceData comparison alone does not establish cause.
Classroom activities
Compare and reason
Use the application model to compare two cases, explain the relationship and identify a likely error.
Transfer and verify
Apply the idea in an unfamiliar context and use a second method, evidence source or text feature to check it.
Revision Notes and quick mastery check
Check understanding
- Classify a variable.
- Find mode/range.
- Describe shape.
- Compare two groups.
- Check graph scale.
Evidence of mastery
- Represent or identify the concept
- Explain the underlying relationship
- Select an appropriate strategy or feature
- Apply it in a new context
- Justify and verify the response
Decision: continue when students can explain the model, apply it to a new example and justify their check. Otherwise return to the central model and reduce the numerical or representational load.
Curriculum wording and references
Australian Curriculum v9.0
AC9M6ST01: interpret and compare data sets for ordinal and nominal categorical, discrete and continuous numerical variables using appropriate displays; compare distributions in terms of mode, range and shape
The Australian Curriculum code and wording are exact. International teachers can use the underlying mathematical concept while matching the lesson to their local grade or year outcomes.
Resources and next steps
Teacher Slides
Project the fixed, branded four-page teaching sequence.
Open Classroom ViewHomework
Use the printable activity for written practice.
Open HomeworkPractice and Test
Use supported Practice first, then the separate Test when ready.
Open PracticeOpen Test
🎥 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: Data and Graphs
Math Antics — Use labelled data displays to make comparisons; extend the ideas to comparing two distributions in the lesson.
As you watch: How do labels and scale help you compare groups fairly?
Load video player Loads YouTube in this lesson. See the video notice below.
Try it: Make dot plots for A: 2,2,3,4,7 and B: 1,3,3,5,6. Compare their modes, ranges and shapes.
Video unavailable, inaccurate or unsuitable for this year? Report a video problem to SkillrHub by email. You can continue with the written lesson and practice resources.
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Curriculum equivalents: Victoria, NSW and international
Curriculum equivalents for Interpret and compare data sets for ordinal and nominal categorical...
Mapped skill: interpret and compare data sets for ordinal and nominal categorical, discrete and continuous numerical variables using comparative displays or visualisations and digital tools; compare distributions in terms of mode, range and shape
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 | AC9M6ST01 · Year 6 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M6ST01 · Level 6 |
| New South Wales | NSW Mathematics K–10 Syllabus (2022) | MA3-DATA-02 · Stage 3 |
| United States (USA) | Common Core State Standards for Mathematics | Grade 6 |
| Canada (Ontario) | Ontario Curriculum — Mathematics | Grade 6 |
| United Kingdom (England) | National Curriculum in England — Mathematics | Year 7, Key Stage 3 |
| India | NCERT / CBSE — Mathematics | Class 6 |
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: AC9M6ST01 — Comparing Categorical and Numerical Data Sets
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