Sampling Methods, Sample Variation and Misleading Displays — AC9M9ST02

Different sampling methods—and even different random samples using the same method—can produce different results. Representation choices can also amplify or hide differences.

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

• compare common sampling methods
• explain sample-to-sample variation
• identify bias in sampling procedures
• analyse how display choices can support a particular point of view

Recall population and sample, random sampling, percentages, measures of centre/spread and common statistical graphs.

Sampling method changes who can be selected

Convenience and voluntary-response samples can overrepresent some groups. Random or stratified methods can reduce selection bias when implemented well.

Random samples still vary

Two legitimate random samples from the same population will not usually give identical results. Larger samples tend to produce more stable estimates, although they do not remove systematic bias.

Display choices influence perception

Truncated axes, unequal intervals, 3D effects and selective time ranges can exaggerate or minimise apparent differences.

Critique needs evidence

Name the design or display choice, explain how it affects interpretation and state what change would make the evidence fairer.

• Random samples always give the same result: Randomness produces sample-to-sample variation.
• A bigger sample always fixes bias: More observations from a biased selection process remain biased.
• Graphs cannot mislead if the numbers are correct: Scale and design can distort visual impression.
• Any non-random sample is useless: It may describe a limited group, but generalisation must be restricted.

1. Compare convenience, simple-random and stratified methods for a school survey.
2. Explain why two random samples can differ.
3. Identify how a truncated axis changes a visual message.
4. Redesign one misleading display.

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. Give a likely bias from surveying at one location only.
2. Explain how stratification can improve representation.
3. Why can a sample of 1000 still be biased?
4. Compare two random-sample percentages and explain why they need not match.
5. Identify two misleading graph techniques.
6. Rewrite a conclusion so it matches the sampling method’s limitations.

A company advertises 90% satisfaction from a survey sent only to loyalty-program members who chose to reply. Explain at least three reasons the figure may not estimate satisfaction among all customers.

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

Does random sampling remove variation?

No. It can reduce selection bias, but random samples still vary.

Can a huge sample be biased?

Yes, if the selection process systematically excludes or overrepresents groups.

How can a graph support a point of view?

Scale, range, grouping and visual design can make differences appear larger or smaller.

1. [5 marks] Compare three proposed sampling methods and rank them for representativeness with justification.
2. [6 marks] Explain why two random samples from the same population differ and how sample size affects stability.
3. [7 marks] Critique a misleading media graph and sampling statement, then redesign the graph and rewrite the claim.

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 identify selection bias.
• I can explain sample variation.
• I can choose a defensible sampling method.
• I can spot misleading display choices.
• I can limit conclusions to what the sample supports.

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

Australian Curriculum v9.0 — AC9M9ST02: analyse how different sampling methods can affect the results of surveys and how choice of representation can be used to support a particular point of view

Victoria: VC2M9ST02 — 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.

• AC9M9ST01 — Analysing Survey Reports and Population Estimates
• AC9M9ST03 — Comparing Numerical Data Distributions

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

Curriculum equivalents for Analyse how different sampling methods can affect the results of...

Mapped skill: analyse how different sampling methods can affect the results of surveys and how choice of representation can be used to support a particular point of view

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.