Browse Statistical sampling

30 questions at your level

DifficultyAllLevel 2Level 3Level 4Level 5

Populations, samples and the large data set

12 questions

LessonNot started
SECTION B: STATISTICS

A college has 12001200 students: 500500 in Year 1212 and 700700 in Year 1313. A researcher wants to select a sample of 6060 students, stratified by year group.
(a) Explain briefly how the researcher should select the sample. (2 marks)
(b) Find the number of Year 1212 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 26 marksStart
The manager of a leisure centre is investigating how many times each week the centre's members use its swimming pool.

The manager selects every 25th member from the centre's membership list for the investigation.
(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 23 marksStart
Explain the difference between a population and a sample.
●●●●●Level 22 marksStart
State one advantage and one disadvantage of taking a census rather than a sample.
●●●●●Level 22 marksStart
A forester measures the heights, X1,X2,…,X25X_1, X_2, \ldots, X_{25}, of a random sample of 2525 trees in a large forest. The mean height of all the trees in the forest is μ\mu, which is unknown.

For each of the following, state whether or not it is a statistic. Give a reason for your answer in each case.
(a) X1+X2+⋯+X2525\dfrac{X_1 + X_2 + \cdots + X_{25}}{25}

(1 mark)
(b) ∑i=125(Xi−μ)2\displaystyle\sum_{i=1}^{25} (X_i - \mu)^2

(1 mark)
(c) The difference between the heights of the tallest tree and the shortest tree in the sample.

(1 mark)
●●●●●Level 23 marksStart

Random sampling — simple, systematic and stratified

12 questions

LessonNot started
Maya has to choose one person at random from the 9 members of a quiz team. Maya makes the choice using a single throw of a fair six-sided dice and a fair four-sided dice, whose faces are numbered 1, 2, 3 and 4, together with the following table.
Total score on the two dice2345678910
Member chosenABCDEFGHI
(a) Show that this sampling method is not random.

(2 marks)

Leo suggests making the choice using a single throw of the same two dice, together with the following table. In each pair of scores, the first number is the score on the six-sided dice and the second number is the score on the four-sided dice.
Scores on the two dice1, 11, 21, 31, 42, 12, 22, 32, 43, 1
Member chosenABCDEFGHI
Maya says that a further instruction is needed to complete the method.
(b) (i) Write a suitable further instruction.

(ii) Using Leo's method, state the probability of choosing member G.

(2 marks)
●●●●●Level 24 marksStart
SECTION B: STATISTICS

A college has 12001200 students: 500500 in Year 1212 and 700700 in Year 1313. A researcher wants to select a sample of 6060 students, stratified by year group.
(a) Explain briefly how the researcher should select the sample. (2 marks)
(b) Find the number of Year 1212 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 26 marksStart
The manager of a leisure centre is investigating how many times each week the centre's members use its swimming pool.

The manager selects every 25th member from the centre's membership list for the investigation.
(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 23 marksStart
Describe how to take a simple random sample of 55 students from a class of 3030.
●●●●●Level 22 marksStart

Non-random sampling — quota and opportunity

10 questions

LessonNot started
Maya has to choose one person at random from the 9 members of a quiz team. Maya makes the choice using a single throw of a fair six-sided dice and a fair four-sided dice, whose faces are numbered 1, 2, 3 and 4, together with the following table.
Total score on the two dice2345678910
Member chosenABCDEFGHI
(a) Show that this sampling method is not random.

(2 marks)

Leo suggests making the choice using a single throw of the same two dice, together with the following table. In each pair of scores, the first number is the score on the six-sided dice and the second number is the score on the four-sided dice.
Scores on the two dice1, 11, 21, 31, 42, 12, 22, 32, 43, 1
Member chosenABCDEFGHI
Maya says that a further instruction is needed to complete the method.
(b) (i) Write a suitable further instruction.

(ii) Using Leo's method, state the probability of choosing member G.

(2 marks)
●●●●●Level 24 marksStart
Describe how a quota sample might be taken when surveying 100100 shoppers.
●●●●●Level 22 marksStart
Explain what is meant by opportunity (convenience) sampling.
●●●●●Level 21 markStart