A-level · Statistical sampling

Populations, samples and the large data setExam-style questions

What a population, a census and a sample actually are; the sampling units and the sampling frame; why you would sample rather than take a census (and when a census is impossible); and how a sample can be unrepresentative — including the trap of combining overlapping samples.

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7 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 2Level 3
  1. 1
    In the context of sampling, explain what is meant by
    (a) a sampling unit, and (b) a sampling frame.
    Level 3 · 2 marksTry it
  2. 2
    A factory tests the lifetime of its light bulbs by running each one until it fails. Explain why a sample, rather than a census, must be used.
    Level 3 · 1 markTry it
  3. 3
    A researcher wants to know the average height of 1616-year-olds in a city. Identify the population and a suitable sampling unit.
    Level 3 · 2 marksTry it
  4. 4
    Give two reasons why an organisation might choose to take a sample rather than carry out a census.
    Level 3 · 2 marksTry it
  5. 5
    A hospital employs about 4000 staff. The hospital's travel planner is preparing a report on how long staff take to travel to work.
    (a) Give one reason why the planner might prefer to use a sample, instead of asking every member of staff.

    (1 mark)
    (b) The staff live in several different towns. A manager proposes a stratified sample, with the towns in which the staff live as the strata.

    Give one advantage, in this context, of this method compared with taking a simple random sample.

    (1 mark)

    The planner chooses a random sample of 80 members of staff and records the time, in minutes, that each of them took to travel to work on one Monday. Summary statistics for these times are shown in the table.
    MeanStandard deviationMedianLower quartileUpper quartile
    34.614.531.026.039.0
    (c) A nurse who was not in the sample took 61 minutes to travel to work on that Monday.

    Discuss briefly whether this time should be treated as an outlier.

    (3 marks)
    Level 3 · 5 marksTry it