Giving Each Group Its Share of the Sample

Mathematics · Data & Statistics · ages 14-15

Name ______________________ Date ____________

A choir has 400 members and 120 of them are sopranos. Which calculation gives the sopranos' share of the choir?
- 400 / 120
- 120 / 400
- 120 / 280
- 400 / 520
After working out how many to take from each group, the people inside each group should still be chosen at random.
Circle one: True False
Why does stratified sampling split the population into groups first?
- To make the total bigger
- To ask fewer questions
- To avoid random numbers
- To keep each group's fair share
A group holds 3/10 of a population. A stratified sample takes 50 people. How many come from this group?
Answer: ______________
After rounding group samples to whole pupils, the total must be rechecked against the planned sample size. Is this right?
Circle one: True False
A club has 120 juniors and 80 seniors. A stratified sample of 30 is taken. How many seniors are picked?
Answer: ______________
A gym has 700 members: 260 come in the morning and 440 in the evening. For a stratified sample of 40, how many morning members are needed once the figure is rounded?
Answer: ______________
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
The crew wants to know what members think of the opening hours. Which way of splitting the members into groups would help least?
- by which membership type they hold
- by the first letter of their surname
- by how often they visit the site
- by which day of the week they usually come
A sample stratified by membership type does not guarantee the right share of members who work weekends.
Circle one: True False

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

120 / 400 · A share is the group divided by the whole, so it is 120 / 400 = 0.3. Dividing by 280 would compare sopranos with the rest of the choir instead of with all of it.
True · Stratifying fixes how many come from each group, not which people. If the 16 plot holders are the 16 easiest to find, the sample is convenient again with tidier numbers on top.
To keep each group's fair share · Grouping guarantees small groups are not crowded out by chance.
15 · 3/10 of 50 is 15.
True · Rounding can shift the total by one or two, so rechecking is required.
12 · Seniors hold 80/200 = 2/5, and 2/5 of 30 is 12.
15 · 260 / 700 x 40 comes to about 14.86, which rounds to 15. The evening group gives about 25.14, which rounds to 25, and 15 + 25 = 40.
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.
by the first letter of their surname · Strata are worth having when the groups tend to answer differently. Surnames have nothing to do with opening hours, so those groups would all hold much the same mix of opinions.
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.