Year 9 Mathematics · AC9M9ST04

Choosing and Interpreting Data Displays

A good data display matches the variable type and the question. Choice of graph, scale, grouping and labels should make the intended comparison clear without distorting…

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Learning goalsSay it simply

A good data display matches the variable type and the question. Choice of graph, scale, grouping and labels should make the intended comparison clear without distorting the data.

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

  • match data types to appropriate displays
  • justify a display choice for a context
  • interpret key features accurately
  • identify when an alternative display would communicate better
Key conceptTeach from the board

Variable type constrains display choice

Bar charts suit categorical frequencies; histograms suit numerical intervals; dot or stem plots retain individual values for smaller numerical datasets.

Purpose matters

A display for exact individual values may differ from one designed to show distribution shape or compare groups.

Design should support truthful reading

Use clear labels, units, consistent scales and sensible bins. Avoid effects that exaggerate differences.

Justification is part of the mathematics

Explain why the representation reveals the feature needed for the investigative question better than plausible alternatives.

Worked examplesWe do

Worked examples

AC9M9ST04 - Choosing and Interpreting Data Displays
Example 1

Categorical data Transport mode by student → bar chart, not histogram.

Example 2

Continuous measurement Heights of 200 students → histogram can show distribution shape.

Example 3

Small numerical sample A dot plot preserves repeated individual values, clusters and gaps.

Example 4

Comparing groups Aligned histograms or back-to-back stem-and-leaf plots can support distribution comparison.

Curriculum examplesCopied content

Australian Curriculum v9.0 — AC9M9ST04: choose appropriate forms of display or visualisation for a given type of data; justify selections and interpret displays for a given context

Victoria: VC2M9ST04 — 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 Core — Data classification, visualisation and analysis; Path — Data analysis and statistical enquiry. 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 examplesAC9M9ST04VC2M9ST04 — Level 9 StatisticsStage 5 Core — Data classification, visualisation and analysis; Path — Data analysis and statistical enquiry
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 is the first display-choice question?
What type of variable or data do I have?
Why might I use a histogram?
To show the distribution of numerical data across intervals.
What makes a justification strong?
It links the representation to the data type and the feature or question being investigated.
Practice and reviewReady for practice
  • Any graph displays any data equally well: Some representations obscure or distort important structure.
  • Histogram and bar chart are interchangeable: Histogram bars represent numerical intervals; bar charts represent categories.
  • More decorative means more informative: Visual clarity and truthful scale matter more than effects.
  • A graph choice needs no explanation: Justification should connect display features to data type and question.
  1. [5 marks] Choose and justify displays for three different datasets.
  2. [6 marks] Compare two representations of the same data and evaluate what each reveals or hides.
  3. [7 marks] Redesign a poor visualisation, justifying graph type, scale, labels and grouping choices.

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 good data display matches the variable type and the question. Choice of graph, scale, grouping and labels should make the intended comparison clear without distorting the data.

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

  • match data types to appropriate displays
  • justify a display choice for a context
  • interpret key features accurately
  • identify when an alternative display would communicate better
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