An extract from a vehicle database contains 800 cars, grouped by make as shown below.
| Make | Number of cars |
|---|---|
| P | 100 |
| Q | 100 |
| R | 100 |
| S | 500 |
Theo wants a sample of 60 cars in which each make is represented in proportion to its size in the extract. He calculates the number required from each make and rounds each one to the nearest whole number.
Show that Theo's rounded numbers give a sample of 62 cars, not 60.
Suggest how Theo could adjust his numbers so that the sample size is exactly 60.
Explain why this difficulty does not arise when a sample of 60 is taken by simple random sampling.
28 exam-style questions on AQA A Level Maths 2.1 K: Statistical sampling, covering 2.1.1 Populations, samples and sampling techniques. Each one has a worked solution and a mark scheme showing where the marks go.