Choosing and Interpreting Data Displays — AC9M9ST04

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

Recall categorical and numerical variables, bar charts, histograms, dot plots, stem-and-leaf plots, tables and basic summary statistics.

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.

• 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. Choose a display for favourite-sport categories.
2. Choose a display for 80 reaction-time measurements.
3. Compare a dot plot and histogram for a sample of 12 values.
4. Explain one scale choice needed for fair comparison.

Guided method: Name the mathematical structure first, show the calculation or representation, then verify with an estimate, inverse operation, second representation or digital check.

1. Choose and justify a display for rainfall across 12 months.
2. Choose a display for survey categories with frequencies.
3. Explain why a histogram is poor for eye-colour categories.
4. Suggest a better display for comparing two small numerical groups.
5. Identify a misleading scale feature in a supplied chart.
6. Rewrite a display justification so it mentions both variable type and investigative purpose.

A dataset can be shown as a dot plot or a histogram. Explain when each representation is more informative and what information is lost when individual values are grouped into bins.

Reasoning standard: Make a claim, show the relevant mathematical evidence, explain why it supports the conclusion and state any condition or limitation.

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.

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.

• I can classify the data type before choosing a display.
• I can distinguish bar charts from histograms.
• I can justify scale and bin choices.
• I can compare what displays reveal or hide.
• I can prioritise truthful communication over decoration.

Exit ticket: Solve one unfamiliar example and explain the key decision in words, not just symbols.

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.

Use these links to move through the Year 9 learning sequence rather than studying the code in isolation.

• AC9M9ST03 — Comparing Numerical Data Distributions
• AC9M9ST05 — Planning and Conducting Statistical Investigations

• Australian Curriculum v9.0 — Mathematics
• Victorian Curriculum F–10 Version 2.0 — Mathematics
• NSW Mathematics K–10 Syllabus (2022)

Curriculum equivalents for Choose appropriate forms of display or visualisation for a given...

Mapped skill: choose appropriate forms of display or visualisation for a given type of data; justify selections and interpret displays for a given context

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.

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.