A population in statistics means the entire group being studied — every item, person or measurement of interest. Because surveying a whole population is often impossible or too costly, we instead take a sample: a smaller, representative subset from which we draw conclusions about the whole.
What is a statistical population?
In statistics, a population is the complete set of individuals, objects or measurements about which you want to draw conclusions. The population is defined by the question being asked.
Examples of populations:
- All Year 9 pupils in a school (if you are studying Year 9 behaviour at that school)
- Every car produced at a factory in one week
- All adult residents in a town
- Every shoe size purchased at a shop last month
Notice that "population" does not always mean people — it is any complete set of the items being investigated.
What is a sample?
A sample is a subset of the population that is selected for study. Rather than collecting data from every member of the population, you collect data from the sample and use those findings to make inferences about the whole population.
| Feature | Population | Sample |
|---|---|---|
| Definition | Every member of the group | A subset of the group |
| Size | Often very large | Smaller, manageable |
| Data collection | Complete — no one left out | Partial — a selection only |
| Conclusions | Exact (no inference needed) | Estimates (with possible error) |
Why do we use a sample instead of the whole population?
There are four main reasons:
- Cost. Surveying every person in the UK would cost millions of pounds; a sample of a few thousand is far cheaper.
- Time. Collecting and analysing data from an entire population can take years. A sample gives results quickly.
- Practicality. Some populations are so large or spread out that a full census is impossible.
- Destructive testing. To test whether a batch of light bulbs lasts 1000 hours, you must use them until they fail. Testing every bulb destroys the entire batch; a sample test leaves most bulbs intact for sale.
What makes a good sample?
A good sample must have two key properties:
1. Representative. The sample should reflect the characteristics of the population in proportion. If a school has 60% girls and 40% boys, a representative sample of 50 pupils should contain approximately 30 girls and 20 boys.
2. Sufficiently large. Larger samples are more reliable. A sample of 3 from a school of 1000 could easily produce misleading results. In general, the larger the sample, the closer the sample statistics are to the true population values.
What is sampling bias?
Bias occurs when the method of selecting the sample systematically favours some members of the population over others. A biased sample does not represent the whole population and can lead to inaccurate conclusions.
Examples of biased sampling:
- Asking only your friends about their favourite music (convenience/opportunity sampling — only a specific social group is represented)
- Carrying out a telephone survey at 2 pm on a weekday (people at work cannot respond — retired and unemployed people are over-represented)
- Posting an online questionnaire about internet use (non-internet users cannot participate)
How to reduce bias:
- Use a random sampling method so every member of the population has an equal chance of selection.
- Ensure the sample is large enough relative to the population.
- Collect data in a way that reaches all subgroups.
What are the main types of sampling?
| Method | Description | Potential issue |
|---|---|---|
| Simple random | Every member equally likely to be chosen | Requires a complete list of the population |
| Systematic | Choose every kth member from an ordered list | Can introduce patterns if the list itself has a regular structure |
| Stratified | Population divided into groups (strata); sample proportionally from each | Requires knowledge of the population's composition |
| Convenience/opportunity | Select whoever is easiest to reach | Highly likely to be biased |
At KS3, you are expected to know that samples should be random and representative, and to identify sources of bias in a given sampling method.
How do sample size and reliability connect?
The larger the sample, the more reliable the estimate. A sample of 10 from a class of 30 gives less reliable results than a sample of 20 from the same class. This is because a larger sample is less likely to accidentally over-represent any unusual member of the population.
However, even a large sample can be unreliable if it is biased — a sample of 10 000 people, all from one city, will not reliably represent the national population.
Frequently asked questions
What is the difference between a census and a sample?
A census collects data from every member of the population. The UK National Census, held every 10 years, attempts to count every person in the country. A sample collects data from only part of the population. Censuses give exact results but are expensive and slow; samples are cheaper and faster but produce estimates.
How do I decide how large a sample should be?
At KS3, there is no fixed rule, but larger is generally better. As a rough guide: for a school population of a few hundred, a sample of 30–50 is often adequate for an investigation. For a very small population (say, a class of 30), a sample of 10 or more covers a third of the group and is reasonably reliable.
Can a sample ever be larger than the population?
No — by definition, a sample is a subset of the population and cannot exceed it. If you collect data from every member of the group, you have conducted a census, not a sampling exercise.
Why do opinion polls sometimes give the wrong result?
Opinion polls use samples to estimate population views. They can fail for three main reasons: sampling bias (the sample is not representative), response bias (people do not answer truthfully), or sampling variation (even a perfectly random sample can differ from the population by chance, especially if the sample is small relative to the population).
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