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 village hall has 700 members. The committee asks 84 of them about a new roof. How many members are in the population?

    Answer: ______________

  2. Dee grows her survey from 200 forms to 400 forms, all collected at the same Saturday gate. What happens to the bias?

    • It halves, because the sample is twice as big
    • It stays, because the same gate reaches the same kind of member
    • It vanishes once a sample passes 300
    • It drops, because 400 replies average out the odd answers

  3. Which survey method is biased?

    • Drawing names from a hat
    • Asking only people leaving a gym about exercise
    • Rolling a die to pick classes
    • Numbering pupils and using random numbers

  4. A school of 800 pupils surveys 80 of them. What percentage of pupils is in the sample?

    Answer: ______________

  5. A weekday 10am phone poll fairly represents all adults. Is this right?

    Circle one:   True   False

  6. A year group of 240 pupils picks 60 by lottery. What fraction of the year is picked? Give a decimal.

    Answer: ______________

  7. Leo says his sample is random because he made no plan: he stopped whoever walked past the cafe. Why is that not random?

    • It is random, since he chose nobody himself
    • It would become random if he stopped more people
    • Who walks past the cafe is decided by the cafe, so members who never go there have no chance
    • Random means the answers cannot be predicted, so he is right

  8. 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

  9. Which sample would you trust most to describe what a town's 20,000 adults think?

    • 800 adults who phoned in to a radio show
    • 3,000 shoppers asked outside one supermarket
    • 500 people who follow the town council online
    • 60 adults picked at random from a full list of the town's adults

  10. 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
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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. 700 · The population is the whole group the claim is about, which is all 700 members. The 84 are the sample.
  2. It stays, because the same gate reaches the same kind of member · More paper from one gate is more of the same voice. The members who never come on a Saturday still had no chance at 400 forms.
  3. Asking only people leaving a gym about exercise · Gym leavers exercise more than most, so the method favours one answer.
  4. 10 · 80 out of 800 is 80/800 = 10%.
  5. False · It is wrong: workers and students are missed, so the sample is biased.
  6. 0.25 · 60/240 simplifies to 1/4, which is 0.25.
  7. Who walks past the cafe is decided by the cafe, so members who never go there have no chance · Unplanned is not the same as equal chance. The cafe door quietly does the choosing, and it favours cafe users every time.
  8. 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.
  9. 60 adults picked at random from a full list of the town's adults · The other three each come through one gate: listeners who phone in, one supermarket's customers, council followers. Only the random 60 is drawn from a list holding every adult, so any of the 20,000 could have landed in it.
  10. 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.
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