Sampling variation

Understand that repeated random samples from the same population give different estimates (sampling variation), and that increasing the sample size (e.g. from 30 to 100 to 1000) reduces the amount of variation and gives a more reliable estimate.

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Te reo Māori terms

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Learning objective overview

Master Teaching Guide coverage for this objective.

Resources

  • CensusAtSchool NZ - Sampling variation: developing big ideas for sample-to-population inferencesQuestions PDF · Answers

Terminology

  • Sample
  • Population
  • Sampling variation
  • Sample size
  • Random sample
  • Estimate
  • Sampling distribution

Task goals

  • Explain what sampling variation is: repeated random samples from the same population give different (but not wildly different) estimates.
  • Compare the expected amount of sampling variation for sample sizes of 30, 100, and 1000, and explain why larger samples give more stable estimates.
  • Judge whether a difference between two sample results is consistent with ordinary sampling variation, or suggests a problem with the sampling process.
  • Explain why a single sample result should not be treated as the exact population value.
  • Distinguish sampling variation (natural spread between random samples) from bias (a systematic error in how a sample is selected).
  • Reason about a set of repeated sample results to judge the underlying sample size or the reliability of an estimate.

Key skills

  • Sampling
  • Variation

Quick stats

  • 81 total questions
  • 3 difficulty levels
  • Answers included