A-level · Statistical sampling

Random sampling — simple, systematic and stratifiedExam-style questions

The three sampling methods that use chance: simple random sampling (every sample equally likely), systematic sampling (every kth unit after a random start), and stratified sampling (proportional allocation across groups), with how to carry each out and the advantages and drawbacks that examiners ask for.

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12 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3

1
Describe how to take a simple random sample of $5$ students from a class of $30$ .
Level 2 · 2 marksTry it
2
SECTION B: STATISTICS

A college has $1200$ students: $500$ in Year $12$ and $700$ in Year $13$ . A researcher wants to select a sample of $60$ students, stratified by year group.
(a) Explain briefly how the researcher should select the sample. (2 marks)
(b) Find the number of Year $12$ students that should be in the sample. (2 marks)
(c) Give one advantage of using a stratified sample rather than a simple random sample in this situation. (2 marks)
Level 2 · 6 marksTry it
3
The manager of a leisure centre wants to find out how often, each week, the centre's members use its swimming pool.

For her investigation, she takes a sample consisting of every 25th member on the centre's membership list.
(a) Identify the population in the investigation.

(1 mark)
(b) (i) State the name of this method of sampling.

(ii) Describe one advantage of this sampling method.

(2 marks)
Level 2 · 3 marksTry it
4
A library keeps a list, in alphabetical order, of the names of its $3840$ members.

Describe briefly how to use random numbers to choose a sample of $25$ of these members.

(3 marks)
Level 2 · 3 marksTry it
5
The head of a science department needs to choose one of the 9 teachers in the department, at random, to attend a training course. The teachers are labelled A to I. She spins a fair spinner twice; the spinner has five equal sectors, numbered 1 to 5. She adds the two scores and uses the following table.
Total of the two scores 2 3 4 5 6 7 8 9 10
Teacher chosen A B C D E F G H I
(a) Show that this sampling method is not random.

(2 marks)

A colleague suggests a different method. The spinner is spun twice and the teacher is chosen from the table below, in which the rows give the score on the first spin and the columns give the score on the second spin.
1 2 3 4 5
1 A B C D E
2 F G H I –
3 – – – – –
4 – – – – –
5 – – – – –
The head of department points out that the colleague's method does not always lead to a teacher being chosen.
(b) (i) Write down an additional instruction that would complete the colleague's method.

(ii) Using the completed method, state the probability that teacher H is chosen.

(2 marks)
Level 2 · 4 marksTry it

	1	2	3	4	5
1	A	B	C	D	E
2	F	G	H	I	–
3	–	–	–	–	–
4	–	–	–	–	–
5	–	–	–	–	–

	1	2	3	4	5
1	A	B	C	D	E
2	F	G	H	I	–
3	–	–	–	–	–
4	–	–	–	–	–
5	–	–	–	–	–

	1	2	3	4	5
1	A	B	C	D	E
2	F	G	H	I	–
3	–	–	–	–	–
4	–	–	–	–	–
5	–	–	–	–	–