Sampling Methods
Sampling methods are the different ways of choosing a smaller group (a sample) from a larger population so that the sample can be used to make conclusions about the whole population without surveying everyone. Common methods include random sampling (every member has an equal chance of selection), systematic sampling (selecting every nth member) and quota sampling (selecting a fixed number from each category). Choosing an appropriate, unbiased method is essential so the sample fairly represents the population.
Method
- Identify the population you want to study and, if possible, obtain a sampling frame (a list of every member of the population).
- Decide on a sample size that is large enough to be representative but practical to collect.
- For simple random sampling, number every member of the sampling frame and select using random numbers (e.g. from a random number table or generator).
- For systematic sampling, work out the sampling interval (population size divided by sample size), then select every nth member starting from a random point.
- For quota sampling, decide how many people to select from each category (e.g. age group) and then select non-randomly (e.g. the first people who fit each category) until each quota is filled.
- State any bias or limitations in the chosen method, such as a sampling frame that is out of date or a non-random element in quota sampling.
Worked example
A head teacher wants to survey 40 students out of a school of 800 students using systematic sampling. Explain how she should select the sample.
- Find the sampling interval: population divided by sample size = 800/40 = 20.
- Obtain a numbered list of all 800 students (the sampling frame).
- Choose a random starting point between 1 and 20, for example using a random number generator; say the number 7 is chosen.
- Select the 7th student, then every 20th student after that: the 27th, 47th, 67th, and so on, until 40 students have been selected.
- Final answer: sampling interval = 20; select a random start between 1 and 20, then every 20th student on the list after that.
Practice questions
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Q1A population has 200 members and a sample of 20 is needed using systematic sampling. Find the sampling interval.Show answer
Answer: 10 (200/20 = 10)
Q2State one advantage of random sampling.Show answer
Answer: Every member of the population has an equal chance of being chosen, which reduces bias (accept any valid reason)
Q3A researcher wants a sample of 50 from a population of 500 using systematic sampling, with a random start of 4. List the first three people selected.Show answer
Answer: 4, 14, 24 (interval = 500/50 = 10, so start at 4 then add 10 each time)
Q4State one disadvantage of quota sampling.Show answer
Answer: It is not random, so it can introduce bias (e.g. the researcher may choose people who are easiest to approach)
Q5A school of 600 students wants a sample of 30. A teacher decides to only survey students in her own class of 30. State one problem with this method.Show answer
Answer: It is not representative of the whole school (it is a convenience/biased sample, not random)
Q6A gym has 900 members. A sample of 45 is needed using systematic sampling, with a random start of 12. Find the 4th person selected.Show answer
Answer: 72 (interval = 900/45 = 20; selections are 12, 32, 52, 72)
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
A population has 350 members. A sample of 35 is required using systematic sampling. Find the sampling interval and state the rule used to select members after the random starting point.
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A council wants to find out residents' opinions on a new park. They decide to only survey people walking through the park on a sunny Saturday afternoon. (a) State the sampling method used. (b) State one way this sample could be biased. (c) Suggest one improvement to the sampling method.
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A factory produces 1200 items per day and wants a systematic sample of 24 items to check for faults. (a) Find the sampling interval. (b) If the random starting point is item number 15, list the first four items selected. (c) State one advantage of systematic sampling over simple random sampling in this context.
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Free printable worksheet
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This topic is chapter 7 of GCSE Statistics Foundation Workbook 1 and chapter 7 of GCSE Statistics Higher Workbook 1, the whole course as one free printable PDF.
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