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Random Sampling

FoundationHigherAQAEdexcel

Learn Random 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. In simple random sampling every member of the population has an equal chance of being selected.

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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 simple random sampling, every member of the population has an equal chance of being selected.

The method requires a sampling frame. Each member is numbered, then random numbers are generated using a calculator, computer or random number table. The members with those numbers form the sample. If a number repeats, it is ignored and another generated.

The advantage is that it is free from bias, because selection does not depend on any characteristic of the members. The disadvantages are that a sampling frame is needed, it can be time-consuming for a large population, and by chance the sample may not represent all subgroups well.

Revision notes

The method

Number every member of the population using the sampling frame.

Generate random numbers using a calculator, computer or random number table. Select the members with those numbers. Ignore any repeated number and generate another.

Advantages

Every member has an equal chance of selection, so the method is free from bias.

Selection does not depend on any characteristic of the members, which makes it the fairest method in principle.

Disadvantages

A complete sampling frame is required, which is not always available.

It can be time-consuming for a large population. By chance the sample may under-represent some subgroups — a random sample of a school could happen to contain very few Year 7 students.

Key points

  • Every member has an equal chance of selection.
  • A sampling frame is required.
  • Members are numbered before selection.
  • Random numbers are generated to select members.
  • Repeated numbers are ignored.
  • The method is free from bias.

Worked examples

Example 1

A population of 200 is numbered 1 to 200. Describe how to select a simple random sample of 20. [2 marks]

Working

Generate 20 random numbers between 1 and 200describe generating the numbers
and select the members with those numbers, ignoring any repeatsdescribe the selection

Example 2

State one advantage of simple random sampling. [1 mark]

Working

Every member has an equal chance of being selected, so the method is free from biasgive the advantage

Example 3

Give one disadvantage of simple random sampling. [1 mark]

Working

A complete sampling frame is needed, which may not be availablegive a disadvantage

Common mistakes

  • Forgetting to ignore repeated numbers.

    Each member should appear only once in the sample.

  • Saying random sampling guarantees a representative sample.

    It is unbiased, but by chance it may still under-represent some subgroups.

  • Not mentioning the sampling frame.

    Random sampling cannot be carried out without a complete list.

  • Describing the method without numbering first.

    Numbering the population is the essential first step.

Exam tips

  • Always mention numbering the population first.
  • Say random numbers are generated, not chosen.
  • State that repeats are ignored.
  • Give the sampling frame requirement as a disadvantage.

Key terms

Simple random sampling
Sampling where every member has an equal chance of selection.
Random number
A number generated with no pattern or bias.
Equal chance
The defining property of random sampling.
Unbiased
Not systematically favouring any part of the population.

Related topics

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