Sampling and the enquiry cycle

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What this lesson covers

  • The enquiry cycle has five stages: problem, plan, data, analysis, conclusion.
  • A random sample avoids choosing people in a biased way.
  • Samples vary, so any estimate carries uncertainty.
Key idea

Population and sample

  • The population is the whole group you care about.
  • The sample is the part you measure.
  • A statistic describes the sample and a parameter describes the population.
Key idea

The enquiry cycle

  • Problem: write a clear question about a population.
  • Plan: decide what to measure and how to sample.
  • Data: collect and clean it.
  • Analysis: draw graphs and find statistics.
  • Conclusion: answer the question for the population.
Worked example

A good question

  • Compare these two questions about a school.
WeakStrong
How much do students sleep?What is the median sleep on a school night for Year 12 students at this school?
Do boys sleep more?Do Year 12 boys at this school tend to sleep longer than Year 12 girls?

Common mistakes

  • Asking your friends and calling it a sample of the school.
    Use a random method, such as numbering the roll and using random numbers.
  • Talking about the sample in the conclusion only.
    An inference is about the population.

Your turn

  • 1. Name the population in: what is the median travel time for Year 12 students at this school?
  • 2. Why is surveying one maths class a weak plan?
Show answer

1. All Year 12 students at this school 2. One class may not represent the year, so the sample could be biased

Summary

What to take away

  • State the population before anything else.
  • Random sampling is what makes an inference fair.

More in AS 91264

Sampling and the enquiry cycleNotesBox plots and informal confidence intervalsNotesComparing two samplesNotesMaking and justifying an inferenceNotes

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