Data, sampling and averages Problem set B Answers

1. (a) Stratified sampling
2. (b) 12

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

1. (a) 52
2. (b) 16, 30, 6
3. (c) 454.5 ≤ l < 455.5

1. (a) mean 16.3, median 14, mode 14
2. (b) mean 7, median 7.5, mode 8

1. (a) x = 7
2. (b) x = 6

1. (a) 66.9 g
2. (b) 59.9 g

1. (a) 29
2. (b) 12
3. (c) 2.34
4. (d) 1.51

1. (a) 20
2. (b) y = 14

1. (a) 50
2. (b) 14.5 ≤ h < 16.5
3. (c) 15.7 cm

4.57 minutes

1. (a) 345 seconds
2. (b) 11.3 seconds

1. (a) 80%
2. (b) Only 150 of the 6000 users (2.5%) replied, and people who like the shampoo are more likely to fill in the form. The company also gains from a good result.
3. (c) Choose users at random, ask a neutral question and follow up everyone who does not reply.

1. (a) 17.9 s
2. (b) 4, 7, 3, 1
3. (c) 17.8 s
4. (d) The grouped estimate uses midpoints; the actual values in each class are not all at the midpoint.

1. (a) 65.4
2. (b) 64
3. (c) 55
4. (d) 11.9

1. (a) Convenience sampling
2. (b) Members who come on Monday morning may be keen early visitors, so they may want longer hours more (or less) than other members; the sample is not representative.
3. (c) Use a random sample from the full membership list, or a stratified sample by age group or by visit time.