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Choosing how to sample

Mathematics · Data & Statistics · ages 16-17

Name ______________________ Date ____________

A college has 600 full time and 300 part time students. How many of each belong in a stratified sample of 90?
- 60 full time and 30 part time
- 45 full time and 45 part time
- 90 full time and 0 part time
- 30 full time and 60 part time
A school roll lists 900 names. How do you draw a systematic sample of 90?
- Take the first 90 names on the roll
- Ask for 90 volunteers
- Pick a random start from 1 to 10, then take every 10th name
What does a census give that no sample can?
- A smaller workload than any sample
- Data on every member, so there is no sampling error
- Freedom from nonresponse
A college has 600 full time and 300 part time students. How many of each belong in a stratified sample of 90?
- 60 full time and 30 part time
- 45 full time and 45 part time
- 90 full time and 0 part time
Dee takes the first 90 names on the roll and calls it a fair sample because it was quick. Is Dee right?
Circle one: True False
You must survey station commuters cheaply but fairly across rush hour and midday travellers. Which method do you defend?
- Stratified sampling by time band, because the two crowds differ
- Opportunity sampling of your friends, because it is cheapest
- Interviewing one commuter, because all commuters agree
- Sampling only drivers, because they are easiest to stop
A school roll lists 900 names. How do you draw a systematic sample of 90?
- Pick a random start from 1 to 10, then take every 10th name
- Take the first 90 names on the roll
- Ask for 90 volunteers
- Take every 9th name with no random start
A systematic sample is drawn from a class list ordered by tutor group. What could go wrong?
- A hidden pattern in the list can line up with the interval and skew the sample
- The sample is always too large to use
- Systematic samples always favour one gender
A school wants views from each year group, and the years differ in size and views. Which plan do you defend?
- Stratified sampling by year, keeping each year share of the sample
- Opportunity sampling at the school gate at lunch
- Surveying one tutor group in depth
Dan takes every 9th name from 900 pupils for a sample of 90, with no random start. Is Dan right?
- No, the interval must be 10 and the start must be random
- Yes, every 9th with any start works
- No, he should take the first 90 names

Answer key

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Choosing how to sample W1-mt_aSsRQvnKa6-s1

60 full time and 30 part time · Two thirds of the college are full time, and two thirds of 90 is 60, leaving 30 part time.
Pick a random start from 1 to 10, then take every 10th name · 900 divided by 90 is 10, so the interval is 10, and the random start keeps it fair.
Data on every member, so there is no sampling error · Asking everyone removes the luck of the draw, though not the cost.
60 full time and 30 part time · Two thirds of the college are full time, and two thirds of 90 is 60.
False · Quick is not fair: the front of the list may hold one kind of pupil only.
Stratified sampling by time band, because the two crowds differ · Rush hour and midday crowds differ, so sampling within each band guarantees both appear in fair shares.
Pick a random start from 1 to 10, then take every 10th name · 900 divided by 90 is 10, so the interval is 10, and the random start keeps every name equally likely.
A hidden pattern in the list can line up with the interval and skew the sample · If the list repeats on the same cycle as the interval, every pick lands in the same slot.
Stratified sampling by year, keeping each year share of the sample · The years are the groups that differ, so sampling inside each one guarantees every year appears fairly.
No, the interval must be 10 and the start must be random · 900 divided by 90 is 10, not 9, and a fixed start favours some positions.