Year 9 Mathematics · AC9M9ST02

Sampling Methods, Sample Variation and Misleading Displays

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

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Learning goalsSay it simply

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
Key conceptTeach from the board

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.

Worked examplesWe do

Worked examples

AC9M9ST02 - Sampling Methods, Sample Variation and Misleading Displays
Example 1

Convenience bias Surveying only students in the library may distort a whole-school study-time estimate.

Example 2

Stratified sampling Sample each year level in proportion to its size when year groups differ substantially.

Example 3

Truncated axis Starting a bar chart at 90 rather than 0 can make a small difference look dramatic.

Example 4

Compare convenience, simple-random and stratified methods for a school survey.

Curriculum examplesCopied content

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.

Lesson componentAustralian CurriculumVictoriaNSW
Concept teaching + worked examplesAC9M9ST02VC2M9ST02 — 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
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.
Practice and reviewReady for practice
  • 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. [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.

Curriculum alignmentStart here

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
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