Browse Sampling

22 questions at your level

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

Populations & samples

11 questions

LessonNot started

A head teacher wants to know how the

900

students at her school travel to school. She asks

50

of them. What name is given to (a) the

900

students,
(b) the

50

●●●●●Level 12 marksStart

Give one reason why someone might take a sample instead of asking the whole population.

●●●●●Level 11 markStart

A factory makes

40\,000

batteries each day.

To check quality, a random sample of

50

batteries is taken and each one is run until it stops working.

(a) Write down the population in this investigation.

(b) Explain why the factory tests a sample of batteries rather than carrying out a census.

(c)

3

50

batteries tested lasted less than the advertised time.

Estimate how many of the

40\,000

batteries made that day would last less than the advertised time.

●●●●●Level 24 marksStart

A conservation group wants to estimate the number of newts in a pond.

They catch

40

newts, mark each one and return them to the pond.

A week later they catch

25

8

of these newts are marked.

Work out an estimate for the number of newts in the pond.

●●●●●Level 33 marksStart

A company employs

1200

people at three sites.

Site	Number of employees
Leeds	$420$
Bristol	$330$
Cardiff	$450$

A stratified sample of

80

employees is to be taken.

(a) Work out the number of employees from Leeds that should be in the sample.

(b) The sample is to contain

22

employees from Bristol.

Work out the number of employees from Cardiff that should be in the sample.

●●●●●Level 34 marksStart

A town council wants to estimate how many of the town's

24\,000

residents use the town library.

They take a random sample of

300

54

of these residents use the library.

(a) Use the sample to estimate the number of residents in the town who use the library.

(b) The council repeats the survey using a new random sample of

1200

residents.

Explain why the estimate from this larger sample is likely to be more reliable.

●●●●●Level 33 marksStart

A scientist wants to estimate the number of fish in a lake.

She catches

40

fish, tags them and returns them to the lake. Later she catches

50

fish and finds that

8

of them are tagged.

(a) Estimate the number of fish in the lake. [2]

(b) State one assumption she has made. [1]

(c) Give one reason why asking her friends which fish they had seen would NOT be a good way to sample. [1]

●●●●●Level 34 marksStart

A wildlife group is estimating the number of deer in a large forest.

They catch

32

deer, fit each one with a tag and release them.

Two weeks later they catch

48

12

of these deer have a tag.

(a) Work out an estimate for the number of deer in the forest.

(b) State one assumption you have made in working out your estimate.

●●●●●Level 44 marksStart

500

Group	Number of students
Year 12	$236$
Year 13	$153$
Adult learners	$111$

Rosa takes a stratified sample of

25

of these students.

Work out how many students from each group should be in Rosa's sample.

You must show that your three numbers add up to

25

●●●●●Level 44 marksStart

Priya is estimating the number of frogs in a nature reserve.

She catches

60

frogs, marks each one and releases them.

Later she catches

45

frogs and uses her results to estimate that there are

300

frogs in the reserve.

(a) Work out how many of the

45

frogs in Priya's second catch were marked.

(b) In fact the marked frogs stayed close to the pool where Priya released them, and Priya made her second catch at that same pool.

Explain what effect this has on her estimate of

300

●●●●●Level 54 marksStart

A sports club has

840

members. Each member belongs to exactly one section.

Section	Number of members
Football	$288$
Netball	$168$
Athletics	$240$
Swimming	$144$

A stratified sample of the members is taken. The sample contains

14

members from the Netball section.

(a) Work out the total number of members in the sample.

(b) Work out how many members from the Athletics section are in the sample.

(c) Of the members in the sample,

42

said they train more than twice a week.

Use this to estimate the number of the

840

club members who train more than twice a week.

●●●●●Level 56 marksStart

Bias & sampling methods

11 questions

LessonNot started

Tom wants to find out how often people in his town go swimming. He asks people leaving the swimming pool. Explain why this sample is biased.

●●●●●Level 11 markStart

A council wants to find out what people in the town think about a new bus route.

The council asks

30

people waiting at the bus station one Monday morning.
(a) Give one reason why this sample may be biased. (1 mark)
(b) Suggest one way the council could improve the sample. (1 mark)

●●●●●Level 12 marksStart

Priya wants to find out how much time students at her school spend on homework each week. She asks the 20 students in her own maths class.

(a) Write down the type of sample Priya has taken.

(b) Explain why her sample may be biased.

●●●●●Level 22 marksStart

Describe how to choose a random sample of

20

students from a year group of

200

●●●●●Level 22 marksStart

A gym is writing a questionnaire for its members. This is one question from it.

How many hours do you exercise?

0 – 2
2 – 4
4 – 6

(a) Write down two things that are wrong with this question.

(b) Write an improved version of the question. You must include suitable response boxes.

●●●●●Level 34 marksStart

A factory employs 480 workers. They are shown on a staff list, numbered 1 to 480. A manager wants a sample of 60 workers. She chooses worker number 8, then worker number 16, then worker number 24, and so on, taking every 8th worker on the list.

(a) Write down the name of this type of sampling.

(b) Explain why the manager's sample is not a random sample.

(c) Give one advantage of this method over choosing 60 workers at random from the whole list.

●●●●●Level 33 marksStart

A school has 1000 students. Three teachers each choose a sample of 50 students.

Mr Ahmed numbers every student on the school register from 1 to 1000 and uses a random number generator to pick 50 numbers.
Mrs Bell splits the students into their five year groups and picks students at random from each year group, so that each year group is represented in proportion to its size.
Mr Clarke asks the first 50 students to arrive at school one morning.

(a) Write down the name of the sampling method each teacher has used.

(b) Explain why Mr Clarke's sample is likely to be biased.

●●●●●Level 34 marksStart

A town council wants to find out what the town's residents think about a plan to build a new car park in the town centre. A researcher stands outside the town's largest supermarket between 10 am and midday on a Wednesday and asks 100 shoppers for their views.

(a) Give two reasons why this sample may not represent the views of all the town's residents.

(b) The researcher says: "I will ask 500 shoppers instead of 100. Then the sample will represent the town." Explain why he is wrong.

(c) Describe a better method the council could use to choose its sample.

●●●●●Level 44 marksStart

A school council is writing a questionnaire about the new school dinners. This is one question from it.

Most students think the new school dinners are excellent. Don't you agree?

Yes
No

(a) Write down two criticisms of this question.

(b) Rewrite the question so that it is suitable for the questionnaire. You must include suitable response boxes.

●●●●●Level 44 marksStart

A charity wants to estimate the mean number of hours per week that adults in a city spend doing voluntary work. The charity emails a questionnaire to the 4000 adults on its mailing list. 300 of them reply.

(a) Explain why the mean found from these 300 replies is likely to be too high. Your answer must say who is over-represented and who is left out.

(b) A trustee suggests emailing all 4000 people on the list a second time, to collect more replies. Explain whether this would remove the problem described in part (a).

(c) Describe a sampling method that would give the charity a more reliable estimate. You must say how the people in the sample would be chosen.

●●●●●Level 55 marksStart

A company has 500 employees. Its staff list is arranged in departments. Every department contains exactly 10 employees, and within each department the manager is listed first, followed by the 9 other employees of that department.

A researcher takes a systematic sample of 50 employees: she picks one of the first 10 names at random, then takes every 10th name after it.

(a) Explain why her sample may be very unrepresentative, even though her starting name was chosen at random.

(b) The researcher repeats her method on a longer staff list of 1000 employees, arranged in exactly the same way, to get a sample of 100. Explain why this does not fix the problem.

(c) Describe how she could instead choose a sample of 50 that represents managers and other employees fairly.

●●●●●Level 55 marksStart