Stratified Sampling - Worksheets, Questions and Revision

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H12 Stratified Sampling

EDEXCEL 1ST0 · Calculator allowed · about 85 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
A youth orchestra has 240 members. The strings section has 96 members. A stratified sample of 30 members is to be taken from the whole orchestra.

Which calculation correctly gives the number of strings players to include in the sample?
  • A) 96/240 x 30
  • B) 30/96 x 240
  • C) 96/30 x 240
  • D) 240/96 x 30
(Total for Question 1 is 1 mark)
2
Cranmoor Golf Club has 260 members: 156 are full members and 104 are social members. A stratified sample of 40 members is needed for a satisfaction survey.
(a)Write down the fraction of members who are full members.(1)
(b)Work out the number of full members to include in the sample.(2)
(c)Work out the number of social members to include in the sample.(2)
(Total for Question 2 is 5 marks)
3
A researcher is planning a stratified sample of secondary school pupils.

Which of these variables would be LEAST suitable to use when deciding the strata?
  • A) Year group (Year 7 to Year 11)
  • B) Gender
  • C) The pupil's favourite colour
  • D) Whether the pupil has school dinners or a packed lunch
(Total for Question 3 is 1 mark)
4
A dance school has 180 students split across three age groups, as shown in the table.
Age groupUnder 1010-1314+
Students726345

A stratified sample of 20 students is needed for a feedback survey.
(a)Write down the sampling fraction for this sample.(1)
(b)Work out the number of Under 10 students to include in the sample.(2)
(c)Work out the number of 10-13 students to include in the sample.(1)
(d)The 14+ group should contribute the rest of the sample. Work out this number, and show that the three sample sizes add up to 20.(2)
(Total for Question 4 is 6 marks)
5
A supermarket employs 400 staff across three sections: Grocery, Fresh Produce and Bakery. 50% of staff work in Grocery, 30% work in Fresh Produce, and the rest work in Bakery. A stratified sample of 40 staff is required for a training review.
(a)Work out the number of staff who work in Bakery.(2)
(b)Work out the number of Grocery staff to include in the sample.(2)
(c)Work out the number of Fresh Produce staff to include in the sample.(1)
(d)Show that the three sample sizes total 40, given that 8 Bakery staff should be included.(1)
(Total for Question 5 is 6 marks)
6
For each statement about stratified sampling, write down whether it is True or False.
(i)If a population is divided into strata by age group, everyone within the same age group must be identical in every other way.(1)
(ii)The sampling fraction used for one stratum must be the same fraction used for every other stratum.(1)
(iii)Stratified sampling can be combined with random number generation to choose the actual sample members within each stratum.(1)
(iv)The size of a stratum's sample depends only on how many strata there are, not on the size of the stratum itself.(1)
(Total for Question 6 is 4 marks)
7
The bar chart shows the number of employees in each of four departments at Northgate Retail Ltd.
0 25 50 75 100 125 150 175 200 Sales Marketing IT Operations Department Number of employees
(a)Write down the number of employees in the IT department.(1)
(b)Work out the total number of employees at the company.(2)
(c)A stratified sample of 50 employees is required across the four departments. Work out the number that should come from Marketing.(2)
(d)Work out the number that should come from Operations.(1)
(e)Show that all four department sample sizes add up to 50, given that Sales contributes 20 and IT contributes 5.(1)
(Total for Question 7 is 7 marks)
8
Elmsworth Borough Council wants to survey residents about a new recycling scheme. The borough is split into 12 wards with very different population sizes, from 1200 residents in the smallest ward to 9800 in the largest.
(a)Explain why the council should use stratified sampling by ward, rather than a simple random sample taken from the whole borough's electoral register.(2)
(b)Give one advantage of stratified sampling over simple random sampling, other than making sure every ward is fairly represented.(2)
(Total for Question 8 is 4 marks)
9
The Premium tier at one branch of a gym chain has 84 members, numbered 01 to 84 in the membership register. A sample of 5 Premium members is required from this branch.

To choose them, the branch manager reads the following string of random digits in pairs:

40 91 07 40 66 12 84
(a)Explain why 91 is not used as a member number.(1)
(b)Explain why the second appearance of 40 is skipped.(1)
(c)Write down the register numbers of the 5 members selected.(2)
(d)Give one reason why using random digits, rather than the manager simply choosing 5 members she knows, produces a fairer sample within this stratum.(1)
(Total for Question 9 is 5 marks)
10
A gym chain wants to run a satisfaction survey of its 3000 members nationwide. Its membership database records each member's age, gender, home town, membership tier (Standard, Premium, or Family), and how long they have been a member.
(a)The gym wants a stratified sample that reflects the very different sizes of the three membership tiers. Identify the variable that should be used to define the strata for this purpose, and give one reason for your choice.(2)
(b)Explain why home town would usually be a less suitable single variable to stratify by for this national survey than membership tier.(2)
(c)Give one other variable in the database (other than membership tier) that could reasonably be used to define strata, and state one thing that would need to be true about the data for this to work well.(2)
(Total for Question 10 is 6 marks)
11
A regional bus operator is planning several surveys. For each scenario, name the most appropriate sampling method from: stratified, systematic, quota, or cluster, and justify your choice.
(a)Interviewers approach passengers at every 10th stop along a long bus route, starting from a randomly chosen first stop.(1)
(b)Interviewers are told to keep stopping people until they have spoken to 20 men and 20 women, but they can choose which 20 of each to approach.(1)
(c)The operator wants to survey only 6 of its 40 depots (chosen at random), interviewing every driver based at those 6 depots.(1)
(d)Give one key difference between cluster sampling and stratified sampling.(2)
(Total for Question 11 is 5 marks)
12
A stratified sample is taken from a company's 900 employees, split across three departments. The sampling fraction used is 1/15.
(a)Work out the total size of the stratified sample.(1)
(b)The Finance department contributed 12 employees to the sample. Work out the number of employees in the Finance department.(2)
(c)The remaining two departments, Operations and Support, have a combined 720 employees. Work out how many of the 60 sample places should come from Operations and Support combined.(2)
(d)Support has 240 employees. Work out the number of Support employees in the sample.(1)
(Total for Question 12 is 6 marks)
13
A hospital trust has 175 nurses across five wards, as shown in the table.
WardA&EMaternityPaediatricsSurgeryElderly Care
Nurses4035304525

A stratified sample of 40 nurses is required, with each ward's sample size rounded to the nearest whole number.
(a)Work out the sampling fraction, giving your answer as a fraction in its simplest form.(2)
(b)Work out the number of nurses to sample from A&E, to the nearest whole number.(2)
(c)Work out the number to sample from Surgery, to the nearest whole number.(1)
(d)Work out the number to sample from Elderly Care, to the nearest whole number.(1)
(e)Given that Maternity contributes exactly 8 nurses and Paediatrics rounds to 7, show that the five rounded sample sizes total 40.(1)
(Total for Question 13 is 7 marks)
14
A college has 1500 students. The two-way table shows the percentage of all students in each combination of study mode and faculty.
Study modeScienceHumanities
Full-time38%22%
Part-time12%28%

A stratified sample of 150 students is required, split across all four groups in proportion to their size.
(a)Work out the number of students in the Full-time Science group.(1)
(b)Work out the number of Full-time Science students to include in the sample.(2)
(c)Work out the number of Part-time Humanities students to include in the sample.(1)
(d)Work out the number of Full-time Humanities students and the number of Part-time Science students to include in the sample, and show that all four sample sizes add up to 150.(3)
(Total for Question 14 is 7 marks)
15
A trainee analyst is asked to take a stratified sample of 45 delegates from a conference of 900 delegates, split into three categories: Speakers (60), Exhibitors (240), and Attendees (600).

The trainee's working is shown below.

Sampling fraction = 45/900 = 1/20
Speakers sample = 60 - 1/20 = 59.95, rounded to 60
Exhibitors sample = 240 x 1/20 = 12
Attendees sample = 600 x 1/20 = 30
(a)Identify the error in the trainee's calculation for the Speakers sample.(1)
(b)Work out the correct Speakers sample size.(2)
(c)Using the corrected Speakers figure, show that the three sample sizes total 45.(1)
(d)The trainee's incorrect method gave a Speakers sample of 60, effectively every speaker at the conference. Explain one practical problem this error would have caused if it had not been spotted.(2)
(Total for Question 15 is 6 marks)
16
A gym chain took a stratified sample of its members 6 months ago, based on the membership tier sizes at that time. It now wants to repeat the survey, using the same stratum sample sizes as before, without checking current membership numbers.
(a)Explain why simply reusing the same stratum sample sizes could now give a biased sample.(2)
(b)Describe what the gym chain should do before taking the new sample, to make sure the stratified sample remains representative.(2)
(Total for Question 16 is 4 marks)
17
A researcher is investigating how much time students spend on homework each week, at a secondary school of 1000 students across three year groups: Year 9 (400 students), Year 10 (350 students) and Year 11 (250 students). The researcher plans to use stratified sampling to select an overall sample of 100 students.
(a)Plan: Give one reason why a stratified sample across the three year groups is more appropriate here than a cluster sample of 2 whole tutor groups.(1)
(b)Collect: Work out how many students should be sampled from each year group.(3)
(c)Process: Describe how the researcher should select the actual 40 Year 9 students from the full list of Year 9 students.(1)
(d)Interpret: The mean weekly homework time in the sample was 5.4 hours in Year 9, 6.8 hours in Year 10, and 8.1 hours in Year 11. Use these sample means, weighted by the sample sizes from part (b), to estimate the mean weekly homework time across the whole sample of 100 students.(3)
(e)Interpret: Give one reason why this weighted estimate is likely to be a better estimate of the true whole-school mean than simply averaging the three year-group means (5.4, 6.8 and 8.1) without weighting.(2)
(Total for Question 17 is 10 marks)
18
A charity is planning a stratified sample of its 3000 donors, split into three donor bands: Bronze (2400 donors), Silver (480 donors) and Gold (120 donors). Because Gold donors are few in number but give very large amounts, the charity decides to include all 120 Gold donors in the sample, and to sample Bronze and Silver proportionally from the remaining sample places. The overall sample size is 300 donors.
(a)Work out how many sample places remain for Bronze and Silver combined, after all 120 Gold donors are included.(1)
(b)Bronze and Silver donors together number 2880. Work out the number of Bronze donors to include in the sample, sampling proportionally from these 2880 donors.(2)
(c)Work out the number of Silver donors to include in the sample.(1)
(d)Show that the full sample (Bronze + Silver + Gold) totals 300.(1)
(e)Give one reason why the charity chose to include all Gold donors, rather than sampling them proportionally like Bronze and Silver.(2)
(Total for Question 18 is 7 marks)
Mark scheme · H12 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

Question 18