Stratified Sampling - Worksheets, Questions and Revision

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F11 Stratified Sampling

EDEXCEL 1ST0 · Calculator allowed · about 75 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Which of these correctly calculates the number of people to include from one group in a stratified sample?
  • A) group size + sample size
  • B) (group size / total population) x sample size
  • C) (total population / group size) x sample size
  • D) group size x total population
(Total for Question 1 is 1 mark)
2
Redbourne Leisure Centre has 350 members split across three fitness classes.
ClassYogaSpinPilates
Members140105105

The centre manager wants to take a stratified sample of 50 members, split across the three classes in proportion to their membership.
(a)Write down the fraction of members who attend the Yoga class.(1)
(b)Work out the number of Yoga members that should be included in the sample of 50.(2)
(c)Work out the number of Spin members that should be included in the sample of 50.(2)
(Total for Question 2 is 5 marks)
3
For each statement about stratified sampling, write down whether it is True or False.
(i)In stratified sampling, the population is first split into separate, non-overlapping groups.(1)
(ii)A well-conducted stratified sample gives every member of the population, whichever group they are in, the same chance of being chosen overall.(1)
(iii)Stratified sampling can only be used when the population is split into exactly two groups.(1)
(Total for Question 3 is 3 marks)
4
A mobile phone company has 2000 customers split across four regions.
RegionNorthSouthEastWest
Customers900600300200

The company wants to survey a stratified sample of 100 customers across the four regions.
(a)Work out the number of North customers that should be included in the sample.(2)
(b)Work out the number of South customers that should be included in the sample.(1)
(c)Work out the number of East customers that should be included in the sample.(1)
(d)Show that the four regional sample sizes add up to the total sample of 100.(1)
(Total for Question 4 is 5 marks)
5
The bar chart shows the number of residents living on each of four housing estates in a town.
0 200 400 600 800 Elm Oak Pine Birch Housing estate Number of residents
(a)Write down the number of residents living on Pine Estate.(1)
(b)Work out the total number of residents living across all four estates.(2)
(c)A stratified sample of 50 residents is to be chosen across the four estates. Work out the number that should be chosen from Elm Estate.(2)
(d)Work out the number that should be chosen from Oak Estate.(1)
(Total for Question 5 is 6 marks)
6
A charity has 500 volunteers. 40% work in fundraising, 35% work in events, and the rest work in admin.
(a)Work out the number of volunteers who work in admin.(2)
(b)The charity wants a stratified sample of 40 volunteers. Work out the number of fundraising volunteers that should be included in the sample.(2)
(Total for Question 6 is 4 marks)
7
A researcher wants to survey students at a college. The college has three departments of very different sizes: Engineering, Business and Art.
(a)Explain why the researcher should use stratified sampling rather than a simple random sample chosen from the whole college.(2)
(b)Explain how stratified sampling makes sure the overall sample is representative of the whole college.(2)
(Total for Question 7 is 4 marks)
8
Give one way in which stratified sampling is similar to simple random sampling, and one way in which it is different.
(a)Give one way stratified sampling is similar to simple random sampling.(1)
(b)Give one way stratified sampling is different from simple random sampling.(1)
(Total for Question 8 is 2 marks)
9
A theatre group has 120 members, split by age group and role, as shown in the table.
GroupUnder-18, CastUnder-18, CrewAdult, CastAdult, Crew
Members24166020

The group's director wants to select a stratified sample of 30 members, split across the four groups in proportion to their size.
(a)Work out the sampling fraction that gives a sample of 30 from a population of 120.(1)
(b)Work out the number of Under-18 Cast members to include in the sample.(1)
(c)Work out the number of Under-18 Crew members to include in the sample.(1)
(d)Work out the number of Adult Cast members to include in the sample.(2)
(e)Show that the four sample sizes total 30, given that 5 Adult Crew members should be included.(1)
(Total for Question 9 is 6 marks)
10
A supermarket has 120 employees, split by contract type and department, as shown in the table.
GroupFull-time, TillsFull-time, WarehousePart-time, TillsPart-time, Warehouse
Employees45301530

A stratified sample of 24 employees is needed, split across the four groups in proportion to their size.
(a)Work out the sampling fraction that gives a sample of 24 from a population of 120.(1)
(b)Work out the number of full-time Tills employees to include in the sample.(2)
(c)Work out the number of full-time Warehouse employees to include in the sample.(1)
(d)Work out the number of part-time Tills employees to include in the sample.(1)
(e)The number of part-time Warehouse employees needed is 6. Show that the total sample across all four groups is 24.(1)
(Total for Question 10 is 6 marks)
11
A music academy has 180 students, split by instrument group and grade band, as shown in the table.
GroupJuniorSenior
Strings3624
Woodwind3018
Brass4230

The academy wants a stratified sample of 30 students, split across all six groups in proportion to their size.
(a)Work out the sampling fraction that gives a sample of 30 from a population of 180.(2)
(b)Work out the number of Junior Strings students to include in the sample.(1)
(c)Work out the number of Senior Woodwind students to include in the sample.(1)
(d)Work out the number of Junior Brass students to include in the sample.(1)
(e)The remaining three sample sizes are 4 (Senior Strings), 5 (Junior Woodwind) and 5 (Senior Brass). Show that the six sample sizes total 30.(2)
(Total for Question 11 is 7 marks)
12
A youth club has 18 members in its Under-14 age group, numbered 1 to 18 in the register. A stratified sample requires 4 members to be chosen from this age group.

To choose them fairly, the youth leader generates random numbers and works through them in order, ignoring any number greater than 18 and ignoring any number that has already been chosen:

7, 23, 7, 2, 15, 31, 9, 18, 4
(a)Explain why the numbers 23 and 31 are ignored.(1)
(b)Explain why the second 7 is ignored.(1)
(c)Write down the register numbers of the 4 members selected for the sample.(2)
(d)Give one advantage of using random numbers to choose the sample within this age group, rather than the youth leader picking members herself.(1)
(Total for Question 12 is 5 marks)
13
A survey of a company's staff uses stratified sampling. From the Sales department, which has 400 staff, a sample of 20 staff was taken.
(a)Work out the sampling fraction used for this survey.(2)
(b)The total sample taken across the whole company was 60 staff. Work out the total number of staff in the company.(2)
(c)The Marketing department has 180 staff. Use the sampling fraction to work out the sample size for Marketing.(1)
(Total for Question 13 is 5 marks)
14
A national retailer is deciding whether to use stratified sampling to survey its staff.

Give one disadvantage of stratified sampling compared with simple random sampling.
(Total for Question 14 is 2 marks)
15
A student wants to find out how students at their college spend their weekly travel money. The college has 1200 students across three faculties: Science (480 students), Arts (360 students) and Business (360 students). The student plans to use stratified sampling.
(a)Plan: Give one reason why stratified sampling is a better choice for this survey than simply asking the first 60 students who arrive at college one morning.(1)
(b)Collect: The student wants an overall sample of 60 students. Work out how many students should be sampled from each of the three faculties.(4)
(c)Process: Describe how the student should choose the actual 24 Science students to survey from the full list of Science students.(1)
(d)Interpret: The mean weekly travel spend in the sample was £14.50 for Science students and £9.20 for Business students. Give one possible reason, other than the amount of travel money itself, why these two means might differ.(1)
(Total for Question 15 is 7 marks)
16
A cinema has 250 staff: 150 full-time and 100 part-time. A stratified sample of 20 staff is required.

A trainee manager's working is shown below.

Sampling fraction = 20/250 = 0.08
Full-time sample = 150 x 20 = 3000
Part-time sample = 100 x 0.08 = 8
(a)Identify the error in the full-time calculation.(1)
(b)Work out the correct full-time sample size.(2)
(c)Check that the corrected full-time sample size and the part-time sample size given (8) together total the required sample of 20.(1)
(d)The cinema decides to double the overall sample to 40, keeping the same proportion of full-time and part-time staff. Work out the new full-time sample size.(2)
(Total for Question 16 is 6 marks)
17
An orchestra has 87 members: 52 string players, 20 wind players and 15 percussion players. A stratified sample of 25 members is required. Because 87 does not divide exactly, each sample size should be rounded to the nearest whole number.
(a)Work out the number of string players to include in the sample, giving your answer to the nearest whole number.(2)
(b)Work out the number of wind players to include in the sample, giving your answer to the nearest whole number.(1)
(c)Work out the number of percussion players to include in the sample, giving your answer to the nearest whole number.(1)
(d)Show that your three rounded sample sizes give a total sample of 25.(1)
(Total for Question 17 is 5 marks)
Mark scheme · F11 Stratified Sampling

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17