Year 8 Mathematics · AC9M8ST04

Statistical Investigations and Population Inference

Plan a statistical investigation from question to report: define the population, select a fair and ethical sample, analyse the data, make a cautious inference and…

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Key conceptTeach from the board

A statistical investigation is a connected cycle: question → population → sample → collect → analyse → infer → report. A weakness early in the cycle can limit every conclusion that follows.

The question should identify the population and variable clearly. Sampling may be necessary because a census is too expensive, slow or restricted by access. A fair sample should give relevant population members a reasonable chance of representation.

Ethical practice includes consent where appropriate, privacy/de-identification, respectful wording, safe data storage and avoiding unnecessary collection of sensitive information. Fairness is both a statistical and ethical issue.

Analyse the sample using graphs and summaries that suit the data. Then make a population inference in cautious language: “the sample suggests…” rather than “this proves…”. Acknowledge sampling variation, possible bias, measurement limits and context.

Preserve the authored applications: electricity-consumption data around major events such as pandemics; choosing samples because of efficiency, cost or restricted time; and investigating progress in reconciliation between First Nations Australians and non-Indigenous Australians using carefully evaluated sampling and data sources.

Worked examplesWe do

Worked examples

AC9M8ST04 - Statistical Investigations and Population Inference
Example 1

Turn a broad topic into a clear statistical question and identify the population.

Example 2

Compare a convenience sample with a fairer alternative.

Example 3

Identify two ethical considerations for a school survey.

Example 4

Rewrite an overconfident population conclusion in cautious statistical language.

Curriculum examplesCopied content

Australian Curriculum v9.0 — AC9M8ST04: plan and conduct statistical investigations involving samples of a population; use ethical and fair methods to make inferences and report findings, acknowledging uncertainty.

Victorian Curriculum F–10 Version 2.0 — Level 8, VC2M8ST04:Exact.

NSW Mathematics K–10 Syllabus (2022) — Stage 4, MA4-DAT-C-01; MA4-DAT-C-02; MAO-WM-01:Partial. NSW Stage 4 supports data display, analysis and Working mathematically; the fuller statistical-inquiry outcome appears later in Stage 5 Path, so no false Stage 4 equivalence is claimed.

LessonAC v9VictoriaNSW
Statistical investigation and inferenceAC9M8ST04VC2M8ST04 — ExactMA4-DAT-C-01; MA4-DAT-C-02; MAO-WM-01 — Partial
Questions and answersWith answers
  1. What are the stages of a statistical investigation? Question, population, sample, collect, analyse, infer and report.
  2. Why use a sample instead of a census? A sample can be sufficiently informative when a census is too costly, slow or inaccessible.
  3. What makes a population inference cautious? It links the claim to the sample design and acknowledges variation, bias and other limitations.
  4. Why include ethics? Data collection affects people; consent, privacy, inclusion and respectful use are part of sound investigation design.
  5. What is the difference between evidence of change and evidence of cause? A change can be observed without proving which factor caused it.
Practice and reviewReady for practice
  • A good graph fixes a bad sample. Presentation cannot repair biased selection.
  • One sample result is the population truth. It is evidence with sampling uncertainty.
  • Association proves the event caused the change. Other factors may explain the pattern.
  • Ethics only matters for medical research. Consent, privacy, respectful wording and data minimisation matter in school and community studies too.
  • Uncertainty makes the investigation useless. Acknowledging limits makes conclusions more trustworthy.
Curriculum alignmentStart here
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