Samples and Sampling
Get to grips with samples and sampling using these Foundation and Higher GCSE Maths practice questions. The worksheet focuses on sampling methods and bias, and the accompanying mark scheme breaks down each solution clearly. Suitable for AQA, Edexcel and OCR. Download the questions and answers for free. A good sample is large and random so it represents the population.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.
Topic overview
A sample is a smaller group selected from a population, used because surveying everyone is usually impractical.
A good sample must be representative, so that conclusions drawn from it apply to the whole population. Larger samples generally give more reliable results, but the method of selection matters more than the size.
A random sample gives every member an equal chance of selection, which avoids bias. Bias creeps in when some groups are more likely to be chosen — surveying only at a leisure centre, for example, would over-represent people who exercise.
Revision notes
Why sample at all
Surveying an entire population is usually too slow and expensive.
A well-chosen sample gives reliable conclusions for a fraction of the effort, provided it genuinely represents the population.
Random sampling
Every member of the population must have an equal chance of being chosen.
Numbering the population and using random numbers achieves this. Asking whoever is nearby does not, since it favours some groups over others.
Recognising bias
Bias occurs when the sample is not representative.
Surveying only at a gym over-represents active people; surveying only on a weekday morning misses those at work. Questions often ask you to identify and explain a source of bias.
Key points
- A sample is part of a population.
- Samples save time and money.
- A sample must be representative.
- Random sampling gives everyone an equal chance.
- Bias occurs when some groups are over-represented.
- Larger samples are generally more reliable.
Worked examples
Example 1
Give one reason for using a sample rather than the whole population.
Working
Example 2
A survey about exercise is carried out at a gym. Identify the bias.
Working
Example 3
What makes a sample random?
Working
Common mistakes
Assuming a large sample is automatically good.
A large but biased sample is still unrepresentative. The method matters more than the size.
Calling any convenient sample random.
Asking whoever is nearby favours certain groups, so it is not random.
Not explaining the bias.
Questions want the reason the sample is unrepresentative, not just that it is.
Confusing population with sample.
The population is everyone; the sample is the smaller group surveyed.
Exam tips
- Say who is over-represented when identifying bias.
- Explain why that group differs from the population.
- Remember randomness means an equal chance for everyone.
- Mention both the method and the size when judging a sample.
Key terms
- Population
- The entire group being studied.
- Sample
- A smaller group selected from the population.
- Bias
- A tendency for some groups to be over-represented.
- Random sample
- A sample where everyone has an equal chance of selection.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.