Stratified Sampling · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Giving Each Group Its Share of the Sample

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

  1. A sports centre has 300 swimmers, 450 runners and 150 cyclists. In a stratified sample of 60, which group gets the most places?

    • the swimmers
    • the cyclists
    • all three get 20
    • the runners

  2. In a stratified sample, every group contributes the same number of people.

    Circle one:   True   False

  3. A school has 1,200 students and 400 of them are in Year 10. In a stratified sample of 90, how many Year 10 students should be picked?

    Answer: ______________

  4. A plain random sample of 50 from a club of 500 could come back with 3 juniors when the juniors' share is 10. What does stratifying do about that?

    • It makes the sample bigger, which evens things out
    • It removes the need to pick anybody at random
    • It sets each group's number in advance, so the shares cannot come out wrong
    • It picks the juniors first, before the other groups

  5. A club has 300 juniors, 100 coaches and 200 adults. Dee suggests taking 20 from each group for a sample of 60, because that treats the groups equally. What is wrong with it?

    • Coaches are a sixth of the club but a third of the sample, so their view counts double
    • Nothing, since taking the same number from each group is the fairest way
    • The sample should be 30 from each group instead
    • Groups of different sizes cannot be sampled at all

  6. Three groups in a club sit in the ratio 5:2:3. Which split of a stratified sample of 40 matches that ratio?

    • 5, 2, 3
    • 13, 13, 14
    • 20, 8, 12
    • 16, 10, 14

  7. Four groups give 7.2, 9.8, 11.6 and 21.4 places for a sample of 50. Sam rounds every figure up and writes 8, 10, 12 and 22. What has gone wrong?

    • He should have rounded all four down instead
    • Rounding all four up puts the total at 52, two more people than he planned to ask
    • Nothing, since rounding up is always the safe direction
    • The shares must have been worked out wrongly to start with

  8. A stratified sample takes 12 people from a group of 300, out of a population of 1,500. What was the total sample size?

    • 25
    • 125
    • 300
    • 60

  9. A sample stratified by membership type does not guarantee the right share of members who work weekends.

    Circle one:   True   False

  10. Three groups give 8.6, 12.5 and 18.9 places for a sample of 40. Rounded, they read 9, 13 and 19, which is 41. Which figure should give up the extra place?

    • the 12.5, because rounding it up added the most
    • the 18.9, because it is the biggest group
    • the 8.6, because it is the smallest group
    • none of them, report the sample as 41
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Answer key

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

Giving Each Group Its Share of the Sample W1-mt_CWzOOk0609-s1

  1. the runners · The centre has 900 members, so runners get 450 / 900 x 60 = 30 places, swimmers get 20 and cyclists get 10. The biggest group takes the biggest share.
  2. False · Each group gets places in proportion to its size, so a bigger group gets more. Equal numbers from unequal groups would hand the small group too much of the sample.
  3. 30 · Year 10 is 400 / 1,200 of the school, which is a third. A third of 90 places is 400 / 1200 x 90 = 30 students.
  4. It sets each group's number in advance, so the shares cannot come out wrong · A fair random draw can still wobble, because chance does not know which members are juniors. Stratifying decides the juniors get 10 places before anyone is picked, so the wobble has nowhere to happen.
  5. Coaches are a sixth of the club but a third of the sample, so their view counts double · The club is 600 people, so coaches are 100 / 600 = a sixth of it. Giving them 20 of 60 places makes them a third of the sample, twice the weight they have in the club.
  6. 20, 8, 12 · 5 + 2 + 3 = 10 parts, and 40 / 10 = 4 people per part. That gives 20, 8 and 12, which adds to 40 and keeps the ratio 5:2:3.
  7. Rounding all four up puts the total at 52, two more people than he planned to ask · 8 + 10 + 12 + 22 = 52, and the sample was meant to be 50. Rounding each figure to the nearest whole number gives 7, 10, 12 and 21, which totals 50.
  8. 60 · 12 out of 300 is 1 in 25, and the same fraction was used on every group, so the sample is 1,500 / 25 = 60. The 25 is the fraction, not the sample, and 300 is the group it came from.
  9. True · Stratifying fixes the shares of the groups you chose. Weekend workers were never a group, so they are spread through the other strata and nothing protects their share.
  10. the 12.5, because rounding it up added the most · Rounding added 0.4, 0.5 and 0.1 to the three figures. The 12.5 gained most, so cutting it back to 12 gives 9 + 12 + 19 = 40 with the least damage to the shares.
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