Data, sampling and averages Problem set A Answers

1. (a) Stratified sampling
2. (b) 8

1. (a) Simple random sampling
2. (b) Systematic sampling
3. (c) Quota sampling

1. (a) 54
2. (b) 19, 28, 7
3. (c) 15.5 ≤ t < 16.5

1. (a) mean 8.86, median 9, mode 9
2. (b) mean 23.1, median 22, mode 22

1. (a) x = 8
2. (b) x = 6

1. (a) 98.4 seconds
2. (b) 82.7 seconds

1. (a) 30
2. (b) 7
3. (c) 2.53
4. (d) 1.43

1. (a) 20
2. (b) y = 12

1. (a) 66
2. (b) 1.5 ≤ m < 2.0
3. (c) 1.75 kg

5.24 minutes

1. (a) 3320
2. (b) 70

1. (a) 90%
2. (b) Only 120 of the 5000 customers (2.4%) replied, and people who are pleased with the phone are more likely to reply. The company also gains from a good result.
3. (c) Take a random sample of customers and follow up everyone who does not reply, asking a neutral question.

1. (a) 3.06 kg
2. (b) 3, 4, 4, 3, 1
3. (c) 3.08 kg
4. (d) The grouped estimate uses midpoints; the actual values in each class are not all at the midpoint.

1. (a) 72.3
2. (b) 72
3. (c) 61
4. (d) 10.8

1. (a) Convenience sampling
2. (b) People at the bus station use buses, so they are more likely to support a bus route; the sample is not representative.
3. (c) Use a random sample of residents, for example chosen from the electoral register, or a stratified sample by area.