Samples and the Population

Define population and sample, and identify which is which in simple given scenarios.

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • S4-1
New NZC (2026)
  • NZC26-P4-STA-DKD-K-Y10-03
  • NZC26-P4-STA-DKD-K-Y10-02
  • NZC26-P4-STA-DKD-P-Y10-01
  • NZC26-P4-STA-DKD-K-Y10-01

Resources

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Terminology

    Task goals

    • Foundation: Define population and sample, and identify which is which in simple given scenarios.
    • Proficient: Explain why a sample is used instead of a full population census and identify a stated sampling method (e.g. random, systematic, convenience).
    • Excellence: Evaluate whether a described sample is likely to represent its population well, justifying with reference to sampling method, size, and potential bias.

    Where this fits

    What leads into this objective, and where it goes next.

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    Samples and the Population

    Samples and the Population

    Know

    When sampling from a population, the distribution for a variable varies from sample to sample. To make a reliable inference about what is happening in the population, sample sizes need to be: about 1,000 for categorical variables (with the sample obtained using technology); at least 30 for numerical variables.

    Statement▸
    Year 10 · Statistics · Developing knowledge from data
    NZC26-P4-STA-DKD-K-Y10-03
    Know

    Samples must be taken randomly from the population, otherwise there will be bias in the data, leading to inaccurate and misleading statistics. Samples are ideally chosen using simple random sampling, in which each item of the population has an equal probability of being chosen.

    Statement▸
    Year 10 · Statistics · Developing knowledge from data
    NZC26-P4-STA-DKD-K-Y10-02

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