Calculating stratified sample sizes

Calculate the number of individuals to sample from each stratum in a stratified sample, given the stratum sizes and total sample size.

6 questions · Easy -1.5

2.01c Sampling techniques: simple random, opportunity, etc
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OCR MEI Paper 2 2024 June Q9
4 marks Easy -1.8
9 A teacher is investigating how pupils travel to and from school each day. Pupils can either travel by bus, train, car, bicycle or walk. The teacher decides to collect a sample of size 60 for the investigation.
  1. The teacher lives in a village 10 miles away from the school. Explain how collecting a sample which just consists of pupils who live in the same village as the teacher might introduce bias. The table below shows how many students there are in each year.
    Year 7Year 8Year 9Year 10Year 11
    86105107101101
  2. The teacher decides to use the method of proportional stratified sampling. Calculate the number of pupils in the sample who are in Year 9. The teacher generates a sample of 10 pupils from the 86 in Year 7 by listing them in alphabetical order and selecting the first name on the list and every ninth name thereafter.
  3. Explain whether this method will generate a simple random sample of the pupils who travel in Year 7.
Edexcel S3 2006 January Q1
7 marks Easy -1.2
  1. A school has 15 classes and a sixth form. In each class there are 30 students. In the sixth form there are 150 students. There are equal numbers of boys and girls in each class. There are equal numbers of boys and girls in the sixth form. The head teacher wishes to obtain the opinions of the students about school uniforms.
Explain how the head teacher would take a stratified sample of size 40.
(7)
Edexcel S3 2004 June Q1
6 marks Easy -2.0
  1. There are 64 girls and 56 boys in a school.
Explain briefly how you could take a random sample of 15 pupils using
  1. a simple random sample,
  2. a stratified sample.
Edexcel S3 2013 June Q1
3 marks Easy -1.8
  1. A gym club has 400 members of which 300 are males.
Explain clearly how a stratified sample of size 60 could be taken.
Edexcel S3 2013 June Q3
7 marks Easy -1.2
3. A college manager wants to survey students' opinions of enrichment activities. She decides to survey the students on the courses summarised in the table below.
CourseNumber of students enrolled
Leisure and Sport420
Information Technology337
Health and Social Care200
Media Studies43
Each student takes only one course.
The manager has access to the college's information system that holds full details of each of the enrolled students including name, address, telephone number and their course of study. She wants to compare the opinions of students on each course and has a generous budget to pay for the cost of the survey.
  1. Give one advantage and one disadvantage of carrying out this survey using
    1. quota sampling,
    2. stratified sampling. The manager decides to take a stratified sample of 100 students.
  2. Calculate the number of students to be sampled from each course.
  3. Describe how to choose students for the stratified sample.
Edexcel S3 Q1
4 marks Easy -1.2
  1. A Veterinary Surgeon wishes to survey a stratified sample of size 100 from those people who have pets registered at her surgery. The list below shows the strata to be used and the number in each group.
  • people who own just dogs - 165 ,
  • people who own just cats - 140 ,
  • people who own just small mammals - 105,
  • others, including those who own more than one type of pet - 90 .
    1. Find how many members of each group should be included in the sample.
    2. Give two advantages of using stratified sampling.