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A school has four year groups: 360 students in Year 9, 300 in Year 10, 300 in Year 11 and 240 in…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A school has four year groups: 360 students in Year 9, 300 in Year 10, 300 in Year 11 and 240 in Year 12. The head wants a stratified sample of 60 students, shared in proportion to the size of each group. How many students are chosen from each year group?
Need a reminder? The key ideaShow
Systematic: step and a random start. Stratified: a simple random sample inside each stratum; proportional allocation gives stratum the share . Cluster: whole groups chosen at random. An estimate from strata weights each stratum by its share of the population.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The total. students.
Step 2. The shares. Each group gets , which is :
- Year 9: ;
- Year 10: ;
- Year 11: ;
- Year 12: .
Answer: 18, 15, 15 and 12.
Check. .
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