Year 8 Mathematics · AC9M8ST03

Sampling Variation and Sample Size

Random samples from the same population do not give identical results. Compare repeated samples and recognise that larger random samples usually give more stable…

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Key conceptTeach from the board

Two random samples from the same population can contain different members, so their proportions, means, medians and ranges can differ. This is sampling variation, not automatically an error.

Repeated samples show the pattern of possible results. A single sample estimate should therefore be reported as evidence about the population, not as the exact population value.

When selection remains random and fair, larger samples usually fluctuate less from sample to sample because each estimate uses information from more population members. This does not guarantee that every larger sample is closer to the population value, and it does not fix selection bias.

Digital simulation is useful because many repeated samples can be generated quickly. At Year 8, the goal is to compare variation visually and numerically, not to introduce formal confidence intervals or hypothesis tests.

Sampling ideas have real uses: school-uniform opinion polling, heights and arm spans, weather forecasting, visitor proportions, biodiversity monitoring by First Nations Ranger Groups and other groups, and data-driven/AI decision-making.

Worked examplesWe do

Worked examples

AC9M8ST03 - Sampling Variation and Sample Size
Example 1

Compare four random-sample proportions from the same population.

Example 2

Explain why the results differ without calling them measurement errors.

Example 3

Compare the spread of repeated results for n=20 and n=100.

Example 4

Identify one assumption in using historical relative frequency to predict a future proportion.

Curriculum examplesCopied content

Australian Curriculum v9.0 — AC9M8ST03: compare variations in distributions and proportions from random samples of the same size and recognise the effect of sample size on variation.

Victorian Curriculum F–10 Version 2.0 — Level 8, VC2M8ST03:Exact.

NSW Mathematics K–10 Syllabus (2022) — Stage 4, MA4-DAT-C-02; MAO-WM-01:Partial. NSW Stage 4 analyses simple datasets, while the national descriptor explicitly develops repeated random sampling and sample-size effects.

LessonAC v9VictoriaNSW
Sampling variation and sample sizeAC9M8ST03VC2M8ST03 — ExactMA4-DAT-C-02; MAO-WM-01 — Partial
Questions and answersWith answers
  1. Why do random samples differ? They contain different randomly selected members of the population.
  2. What is sampling variation? Natural variation in sample results arising from which members are selected.
  3. What usually happens as random sample size increases? Estimates tend to vary less from sample to sample.
  4. Does a large sample fix biased selection? No; selection bias is a design problem.
  5. Why repeat samples or simulations? To see the range and pattern of plausible sample results rather than trusting one result as exact.
Practice and reviewReady for practice
  • Different random samples should match. Natural sample-to-sample variation is expected.
  • One sample proportion is the population proportion. It is an estimate based on one sample.
  • A larger sample is guaranteed closer. Larger samples are usually more stable, not guaranteed perfect.
  • Increasing sample size fixes bias. A biased selection method can remain biased at any size.
  • Simulation proves the future. It illustrates variation under the assumptions used.
Curriculum alignmentStart here
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