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Secondary 2 Mathematics · Samples, populations and data collection

Name: ______________________

Date: ____________

1. Which of these is a census?
- ☐ (a) Asking 50 students at a school of 800 about lunch
- ☐ (b) Asking every student in a class of 25 about their favourite sport, to describe that class
- ☐ (c) Testing 10 light bulbs from a batch of 10 000
- ☐ (d) Phoning 1000 voters before an election
2. Why does a battery company test a sample rather than every battery it makes?
- ☐ (a) A sample is always more accurate
- ☐ (b) Testing how long a battery lasts uses it up
- ☐ (c) Censuses are not allowed
- ☐ (d) Samples need no planning
3. Which method is most likely to give a representative sample of students at a school?
- ☐ (a) Ask the first 20 students to arrive in the morning
- ☐ (b) Ask students in the chess club
- ☐ (c) Draw 40 names at random from the full school list
- ☐ (d) Ask your friends
4. The survey question “Don't you agree that the new park is a waste of money?” is an example of:
- ☐ (a) a random sample
- ☐ (b) a leading question
- ☐ (c) a census
- ☐ (d) an outlier
5. Find the mean of the sample 3, 8, 9, 12, 18.
6. Find the median of the sample 15, 4, 9, 22, 7, 11.
7. Find the range of the sample 31, 18, 45, 27, 22.
8. Samples of 20 apples are weighed from two orchards. Orchard A: mean 152 g, range 40 g. Orchard B: mean 150 g, range 12 g. Which orchard's apples are more consistent in size? Answer A or B.

Answer sheet

1. Asking every student in a class of 25 about their favourite sport, to describe that class — Only the class survey collects data from every member of the population (the class).
2. Testing how long a battery lasts uses it up — Testing a battery until it runs out destroys it, so testing every battery would leave none to sell.
3. Draw 40 names at random from the full school list — A random selection from the whole school gives every student an equal chance of being chosen.
4. a leading question — The wording pushes people towards agreeing, so it is a leading question that causes bias.
5. 10 — 3 + 8 + 9 + 12 + 18 = 50, and 50 ÷ 5 = 10.
6. 10 — Sorted: 4, 7, 9, 11, 15, 22. The two middle values are 9 and 11, so the median is (9 + 11) ÷ 2 = 10.
7. 27 — Highest − lowest = 45 − 18 = 27.
8. B — Orchard B has a much smaller range, so its apple masses are less spread out and more consistent. The means are almost the same.