Systematic and quota sampling, and choosing a method

Systematic sampling

1. Number the population (sampling frame) of size N.

2. Find the interval k = N ÷ n.

3. Choose a random starting point between 1 and k.

4. Then take every k th member.

Example: N = 1200, n = 60, so k = 20; a random start of 7 gives 7, 27, 47, ...

Examiners want the random start explained: it gives every member an equal chance of selection and so reduces bias. Keep the start (a random number from 1 to k) separate from the interval k.

Quota sampling

The interviewer is told how many people of each type to ask (for example 30 men and 20 women aged over 60) and stops people until each quota is filled.

It is not random: the interviewer chooses who to ask, which can introduce bias, and non-responders are simply replaced. But it needs no sampling frame, is quick and cheap, and is used widely in market research.

Comparing methods

Judge in context.

Worked example

Describe how to take a systematic sample of 60 from 1200 numbered customers.

1. k = 1200 ÷ 60 = 20.
2. Choose a random number from 1 to 20 as the start, say 7.
3. Take customers 7, 27, 47, ... up to 1187.

Answer: Random start from 1 to 20, then every 20th customer.

Check yourself

1. A systematic sample of 60 is to be taken from 1200 numbered items. Find the sampling interval.
   Show answer

   20. k = 1200/60 = 20.

2. In a systematic sample the interval is 20 and the random start is 7. What is the number of the 4th item chosen?
   Show answer

   67. 7, 27, 47, 67: the 4th is 67.

3. Why should the starting point in a systematic sample be chosen at random?
   • So that the interval k is a whole number
   • So that the sample size is exactly n
   • So that the list does not need numbering
   • So that every member of the population has an equal chance of being selected
   Show answer

   So that every member of the population has an equal chance of being selected. A random start between 1 and k makes each member's chance equal to 1/k, which reduces bias.

4. Which is a disadvantage of quota sampling?
   • It is not random, so the interviewer's choices can bias the sample
   • It needs a complete sampling frame
   • It is very expensive
   • It cannot represent different groups
   Show answer

   It is not random, so the interviewer's choices can bias the sample. The interviewer picks who to approach, so the sample may not be representative.

5. A market researcher in a shopping centre has no list of shoppers. Which method is most suitable?
   • Simple random sampling
   • Systematic sampling from a list
   • Quota sampling
   • Stratified sampling with numbered strata
   Show answer

   Quota sampling. Only quota sampling works without a sampling frame.

6. A systematic sample takes every 10th house on a street plan, where every 10th house happens to be a corner house. What is the problem?
   • The list has a repeating pattern, so the sample is biased
   • The interval is too small
   • Quota sampling should have been used
   • The start was random
   Show answer

   The list has a repeating pattern, so the sample is biased. A periodic pattern matching k gives an unrepresentative sample.

7. A manager chooses 10 staff by taking the first 10 names on an alphabetical list. Why is this not a random sample?
   • The list is a sampling frame
   • 10 is too small a sample
   • Staff later in the alphabet have no chance of being chosen
   • Alphabetical lists cannot be numbered
   Show answer

   Staff later in the alphabet have no chance of being chosen. Only names near the start can be chosen, so not every member has an equal chance.

Practise with instant feedback Print this lesson

Sources

• Pearson Edexcel International Advanced Level in Mathematics specification (issue 3), Unit S3
• Pearson Edexcel IAL Statistics S3 (WST03) examiners' report, June 2025
• Pearson Edexcel IAL Statistics S3 (WST03) mark scheme, June 2024

Last updated 8 November 2026. Spotted a mistake? Tell us.