What is a sample?
Think subset.
A sample is part of a population.
Sampling
Sampling involves selecting a group from a population to collect data. Choosing the correct method ensures results are fair and reliable.
Overview
In statistics, it is often not practical to ask or measure everyone.
Instead, we choose a smaller group called a sample.
Sample = a smaller group chosen from a larger population
A good sample should represent the whole population fairly.
If the sample is biased, the results may be misleading.
What you should understand after this topic
- Understand what population and sample mean
- Understand why samples are used
- Identify what makes a sample fair or biased
- Know common sampling methods
- Comment on whether a sample is reliable
Key Definitions
Population
The whole group being studied.
Sample
A smaller group chosen from the population.
Bias
When the sample is unfair and does not represent the population properly.
Random Sample
A sample chosen so everyone has an equal chance of being selected.
Stratified Sample
A sample chosen in the same proportions as the population groups.
Representative
Accurately reflecting the population.
Key Rules
Choose fairly
A good sample should not favour one group unfairly.
Use enough people
Larger samples are often more reliable than very small ones.
Match the population
The sample should reflect the population structure.
Avoid bias
Biased questions or biased selection can distort results.
Quick Good vs Bad Check
Good sample
Random, large enough, and representative.
Poor sample
Too small, unfair, or taken from only one type of person.
How to Solve
Step 1: Understand why samples are used
A sample is used when it is too slow, expensive or difficult to collect data from everyone.
Sampling makes data collection quicker.
Exam tip: A good sample should represent the whole population.
Step 2: Know population and sample
Population = everyone of interest.
Sample = people or items selected from that population.
Population
The full group being studied.
Sample
The smaller group actually chosen.
Step 3: Know what makes a good sample
Representative
Similar to the population overall.
Large enough
More reliable than a very small sample.
Unbiased
Does not unfairly favour one group.
Relevant
Chosen from the correct population.
Step 4: Random sampling
In random sampling, every member of the population has an equal chance of being chosen.
Why this matters: Random sampling helps reduce bias.
- Number everyone in the population.
- Use a random method to choose numbers.
- Select the people or items with those numbers.
Step 5: Stratified sampling
Stratified sampling keeps the same group proportions as the population.
\( \text{Number in sample} = \dfrac{\text{Group size}}{\text{Population size}} \times \text{Sample size} \)
Exam thinking: Use stratified sampling when the population has clear groups.
Sampling is often used when collecting data for bar charts or pie charts.
Step 6: Identify biased samples
A sample is biased if it does not fairly represent the population.
Biased
Asking only sporty students about PE lessons.
Better
Ask students from different classes and groups.
Step 7: Common causes of bias
Too small
Not enough data to be reliable.
One group only
Does not represent everyone.
Self-selecting
Only people who choose to reply are included.
Leading question
Question influences the answer.
Step 8: Exam method summary
See questionnaires for designing fair survey questions.
- Identify the population.
- Identify the sample.
- Decide if the sample is representative.
- Check for bias.
- Suggest a fairer sampling method if needed.
Example Questions
Edexcel
Exam-style questions inspired by Edexcel GCSE Mathematics, focusing on populations, samples and bias.
Edexcel
A school wants to find out whether students like the new lunch menu.
The headteacher asks 20 students who are waiting in the lunch queue.
Explain why this sample may be biased.
Edexcel
A company wants to survey its customers.
Explain why the company might use a sample instead of asking every customer.
Edexcel
A student says, "A random sample means choosing people you know."
Tick one box. Correct ☐ Incorrect ☐
Give a reason for your answer.
AQA
Exam-style questions based on the AQA GCSE Mathematics specification, focusing on random samples and reliability.
AQA
A survey asks 5 people whether they use the local library.
Explain why this sample may not give a reliable estimate for the whole town.
AQA
A school has 900 students. A sample of 90 students is chosen at random.
What fraction of the school is in the sample?
AQA
A researcher wants a fair sample of people in a town.
Describe one way the researcher could choose a random sample.
OCR
Exam-style questions aligned with OCR GCSE Mathematics, emphasising stratified sampling and proportional reasoning.
OCR
There are 300 students in a school. 180 are girls and 120 are boys.
A stratified sample of 40 students is chosen.
Work out how many girls should be in the sample.
OCR
A population contains 500 people. A sample of 60 people is chosen.
Explain why a larger sample is usually more reliable than a smaller sample.
OCR
A survey about cinema habits is carried out outside one cinema on a Saturday evening.
Explain why this may not be representative of all people in the town.
Exam Checklist
Step 1
Identify the population clearly.
Step 2
Check how the sample was chosen.
Step 3
Decide whether the sample is fair and representative.
Step 4
Comment on size, bias and method if asked.
Most common exam mistakes
Population confusion
Mixing up the full group and the selected group.
Bias ignored
Not noticing that only one type of person was asked.
Small sample overlooked
Forgetting that a very small sample may be unreliable.
Wrong stratified calculation
Using the wrong ratio when working out sample numbers.
Common Mistakes
These are common mistakes students make when working with sampling in GCSE Maths.
Confusing population with sample
Incorrect
A student mixes up the full group with the smaller group tested.
Correct
The population is the entire group being studied, while the sample is a smaller subset used to represent it.
Assuming all samples are fair
Incorrect
A student thinks any sample will give reliable results.
Correct
A good sample must be unbiased and representative. Random sampling is often used to improve fairness.
Ignoring bias
Incorrect
A student does not consider how the sample was chosen.
Correct
Check for bias. For example, asking only one group of people can lead to unfair results.
Using a sample that is too small
Incorrect
A student uses a very small sample and assumes it is reliable.
Correct
Larger samples are generally more reliable, as they better represent the population.
Incorrect stratified sampling
Incorrect
A student does not keep proportions consistent.
Correct
In stratified sampling, each group must be represented in the same proportion as in the population.
Try It Yourself
Practise selecting and evaluating different sampling methods.
Foundation
Foundation Practice
Understand basic sampling methods and identify bias.
What is the whole group being studied called?
Think complete group.
The whole group is the population.
Which is the best type of sample?
Think fairness.
Random samples reduce bias.
If a sample only includes one type of person, it is called a ______ sample.
Think unfair.
This is a biased sample.
A teacher surveys only their own class. What type of issue is this?
Think fairness.
Not representative → biased.
A sample chosen without favouring any group is called a ______ sample.
Think fair selection.
Random sampling reduces bias.
Why is random sampling useful?
Think fairness.
Random = fair representation.
A survey only asks teenagers. What type of issue is this?
Not representative.
This is biased sampling.
Which sample is most representative?
Think variety.
Random sample represents population best.
If a sample reflects the population well, it is called ______.
Think accurate reflection.
Representative samples reflect the population.
Higher
Higher Practice
Evaluate sampling methods and identify bias in real situations.
Which sampling method divides population into groups and samples from each?
Think groups.
Stratified uses subgroups.
Sampling every 10th person is called ______ sampling.
Think pattern.
This is systematic sampling.
Which method is most likely to be biased?
Think limited group.
Friends → biased.
A survey is done online only. What issue may occur?
Not everyone has access.
Online-only may exclude groups.
Why is stratified sampling useful?
Think representation.
Ensures fair group representation.
A sample is too small. What issue does this cause?
Think accuracy.
Small samples are less reliable.
Which method is quickest but often biased?
Think easy access.
Convenience = easy but biased.
A sample misses certain groups. What is this called?
Think unfair selection.
Missing groups causes bias.
Why is a large sample better?
Think reliability.
Large samples improve accuracy.
A method that avoids bias and represents all groups fairly is called ______ sampling.
Think groups.
Stratified ensures fair representation.
Games
Practise this topic with interactive games.
Games coming soon.
Frequently Asked Questions
What is sampling?
Selecting part of a population.
What is random sampling?
Every item has equal chance.
Why is it important?
To avoid bias.