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Systematic Sampling

FoundationHigherAQAEdexcel

Practise Systematic Sampling for GCSE Statistics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA and Edexcel. Systematic sampling selects members at regular intervals from an ordered list, after a random start.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA and Edexcel specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

In systematic sampling, members are selected at regular intervals from an ordered list.

The sampling interval is found by dividing the population size by the sample size. A random starting point is then chosen within the first interval, and every subsequent member at that interval is selected.

For a population of 800 and a sample of 40, the interval is \(800 \div 40 = 20\), so every 20th member is chosen after a random start between 1 and 20. The advantage is that it is quick and simple. The disadvantage is that if the list has a repeating pattern matching the interval, the sample will be biased.

Revision notes

Finding the interval

Sampling interval \(= \frac{\text{population size}}{\text{sample size}}\).

For a population of 800 and a sample of 40, the interval is \(800 \div 40 = 20\), so every 20th member is selected.

The random start

A random starting point must be chosen within the first interval.

For an interval of 20, pick a random number between 1 and 20, then select that member and every 20th one after it. Without a random start the method is not fair.

Advantages and disadvantages

Advantage: quick, simple, and spreads the sample evenly through the list.

Disadvantage: if the list has a repeating pattern that matches the sampling interval, the sample will be biased. A sampling frame is also required.

Key points

  • Members are selected at regular intervals.
  • Interval = population size ÷ sample size.
  • A random starting point is needed.
  • The start must be within the first interval.
  • The method is quick and simple.
  • A repeating pattern in the list causes bias.

Worked examples

Example 1

A sample of 25 is taken from a population of 500 using systematic sampling. Work out the sampling interval. [2 marks]

Working

\(500 \div 25\)divide the population size by the sample size
\(= 20\), so every 20th member is chosenwork out the interval

Example 2

Explain why a random starting point is used in systematic sampling. [2 marks]

Working

Without a random start, the same positions in the list would always be selectedstate the problem
so the method would not give every member a chance of selection and could be biasedexplain the consequence

Example 3

Give one disadvantage of systematic sampling. [1 mark]

Working

If the list has a repeating pattern matching the sampling interval, the sample will be biasedgive the disadvantage

Common mistakes

  • Forgetting the random starting point.

    It is essential for the method to be fair.

  • Dividing sample size by population size.

    The interval is population ÷ sample, giving a number greater than 1.

  • Choosing a start outside the first interval.

    The random start must fall within the first interval.

  • Saying systematic sampling is always unbiased.

    A repeating pattern in the list can introduce bias.

Exam tips

  • Show the division clearly for the interval.
  • Always mention the random starting point.
  • State the repeating-pattern problem as the disadvantage.
  • Check the interval is population ÷ sample.

Key terms

Systematic sampling
Selecting members at regular intervals from a list.
Sampling interval
Population size divided by sample size.
Random start
A randomly chosen starting position within the first interval.
Periodic pattern
A repeating pattern in the list that can cause bias.

Related topics

Written and reviewed against the current AQA and Edexcel specifications. Spotted an error? Let us know.