Year 8 Mathematics · AC9M8ST02

Sampling Methods and Data Distributions

Analyse distributions from primary and secondary sources, and connect the reliability of conclusions to how the sample was selected

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Key conceptTeach from the board

Sampling method affects who can appear in the data. Simple random sampling gives every member an equal chance; systematic sampling follows a fixed interval after a start; stratified sampling represents defined subgroups. Clustered, quota, convenience and judgement methods make different practical trade-offs and may introduce bias.

A distribution should be described as a whole. Consider typical value or centre, spread, overall shape, clusters, gaps and unusual values rather than choosing one striking observation.

Primary data are collected for the current investigation. Secondary data already exist and must be checked for source, definitions, date, coverage and sampling method before conclusions are reported.

Large samples can reduce random fluctuation but cannot automatically repair a systematically biased selection method. Reliability depends on both sample size and sample design.

When working with reconciliation data concerning Aboriginal and Torres Strait Islander Peoples and non-Indigenous Australians, use reputable sources, retain context and avoid turning sensitive social data into decontextualised percentages.

Worked examplesWe do

Worked examples

AC9M8ST02 - Sampling Methods and Data Distributions
Example 1

Classify five sampling descriptions as simple random, systematic, stratified, cluster, quota or convenience.

Example 2

Describe centre, spread and one unusual feature of a dot plot.

Example 3

Explain why a convenience sample may over-represent one subgroup.

Example 4

List four checks to make before using a secondary data source.

Curriculum examplesCopied content

Australian Curriculum v9.0 — AC9M8ST02: analyse and report on the distribution of data from primary and secondary sources using random and non-random sampling techniques.

Victorian Curriculum F–10 Version 2.0 — Level 8, VC2M8ST02:Exact.

NSW Mathematics K–10 Syllabus (2022) — Stage 4, MA4-DAT-C-01; MA4-DAT-C-02; MAO-WM-01:Partial. NSW directly supports data visualisation and analysis, while the national descriptor places more explicit emphasis on comparing sampling techniques and source reliability.

LessonAC v9VictoriaNSW
Sampling methods and distributionsAC9M8ST02VC2M8ST02 — ExactMA4-DAT-C-01; MA4-DAT-C-02; MAO-WM-01 — Partial
Questions and answersWith answers
  1. What makes a sample random? Selection is controlled by a chance mechanism rather than researcher convenience or judgement.
  2. Why use stratified sampling? To ensure important subgroups are represented in planned proportions.
  3. What should a distribution report include? Centre, spread, shape and notable features, interpreted in context.
  4. Why can secondary data mislead? Definitions, timing, coverage or sampling may differ from the current question.
  5. Does a large sample remove bias? No. It reduces some random variation but not systematic selection bias.
Practice and reviewReady for practice
  • Random means haphazard. Random sampling uses a defined chance process.
  • Large means representative. A large biased sample can still mislead.
  • One summary statistic describes everything. Centre, spread and shape should be read together.
  • Published data are automatically reliable. Source, definitions, date and sampling method still need evaluation.
  • Different percentages prove change. Different samples or methods may explain the difference.
Curriculum alignmentStart here
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