Populations, Samples and Bias · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Who the Sample Really Speaks For

Mathematics · Data & Statistics · ages 14-15
Name ______________________   Date ____________

  1. A club numbers every member and lets a generator choose 30 of them. A member who has never come to anything has the same chance of being picked as the chair.

    Circle one:   True   False

  2. A magazine asks people leaving a gym how many hours a week they exercise, then reports the figure as the town's average. What is wrong?

    • Nothing, since everyone asked answered honestly
    • Hours of exercise cannot be measured accurately
    • People leaving a gym exercise more than the town does, and anyone who never goes could not be picked
    • The survey should have been run on a different day of the week

  3. Which of these picks 20 members from a list of 500 at random?

    • Ask the first 20 members who walk in on Monday
    • Take the 20 who reply fastest to an email
    • Pick out 20 names nobody on the crew recognises
    • Number all 500 and let a random number generator choose 20

  4. A swimming club has 400 members. The committee asks 50 of them about pool times. Which number is the sample size?

    • 400
    • 50
    • 450

  5. Sam posts 500 forms and 90 come back. He reports those 90 answers as the members' view. What is the risk?

    • The members with strong feelings are the likeliest to have bothered replying, so the 90 need not match the 500
    • None, because 90 is a large enough number to trust
    • The forms were too long to be answered properly
    • Post is always less accurate than asking in person

  6. A properly random sample of 40 members comes out with 26 gardeners, when the site's mix would suggest about 20. What is the best description of that?

    • Bias, because the method must have favoured gardeners
    • Proof that most members really are gardeners
    • Bad luck in one sample, which a fair method can still throw up
    • A reason to abandon random sampling

  7. A survey run only in the school library at lunchtime finds that students study about 3 hours a night. Which conclusion does that sample actually support?

    • Students who are in the library at lunchtime study about 3 hours a night
    • The school's students study about 3 hours a night
    • Students across the town study about 3 hours a night
    • Nothing at all, because a biased sample is worthless

  8. Priya writes: 'We asked 120 dog walkers in the park, so this is what all park users want.' Which part of that sentence is not earned?

    • The number 120, which is too small to report
    • The jump from dog walkers to all park users
    • The word 'want' instead of 'need'
    • Nothing, the sentence is fine

  9. A museum holds 40 diaries written in one town in 1850. What should a historian say about them?

    • They are the whole population of that town's experience
    • They are a sample of the people who could write and whose diaries happened to survive
    • They are random, because nobody chose which ones survived
    • They are useless, since 40 is too few

  10. If a sample is chosen at random, its results will match the population exactly.

    Circle one:   True   False

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Who the Sample Really Speaks For W1-mt_c7knRZy3Vt-s1

  1. True · The list holds every member once and the generator knows nothing about who turns up. Equal chance is decided by the list, not by how involved a member is.
  2. People leaving a gym exercise more than the town does, and anyone who never goes could not be picked · The gym door lets in one kind of member of the town and shuts out the rest. Honest answers from the wrong group still describe the wrong group.
  3. Number all 500 and let a random number generator choose 20 · Random needs every member to have the same chance, decided by something with no opinion. Only the numbered list and the generator manage that.
  4. 50 · The sample is the group actually asked, which is 50. The 400 is the population, and adding the two together describes nothing.
  5. The members with strong feelings are the likeliest to have bothered replying, so the 90 need not match the 500 · Sam picked nobody, but the members picked themselves. Replying takes effort, and the people willing to spend it tend to be the ones who care most either way.
  6. Bad luck in one sample, which a fair method can still throw up · A fair draw wobbles. Landing 26 where 20 was likely is the sort of gap chance throws up now and then. Bias is a lean built into the method, and this method had none.
  7. Students who are in the library at lunchtime study about 3 hours a night · The library at lunchtime reaches students who chose to be there, and they study more than the school average, so 3 hours runs high for the school. The sample still describes itself honestly.
  8. The jump from dog walkers to all park users · Dog walkers were the sample, so the sentence may describe dog walkers. Park users who bring no dog were never in the running.
  9. They are a sample of the people who could write and whose diaries happened to survive · Writing and surviving are both filters. People who could not write left nothing, and damp cellars removed more, so the 40 stand for a selected slice of the town.
  10. False · Random removes the lean, not the wobble. Any one random sample can land a little off, and the gap shrinks as the sample grows.
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