A sample is a smaller group chosen from a larger population to represent it. Good sampling methods give every member of the population a fair chance of being selected; poor methods produce a biased sample that does not represent the population accurately. Choosing the right method is the first step in a reliable statistical investigation.
What is the difference between a population and a sample?
The population is the entire group you are interested in — for example, all 800 students in a school, or all adults in the UK. It is usually impractical to collect data from every member of a population, so you take a sample — a manageable subset — and use it to draw conclusions about the whole.
A good sample is representative: its characteristics reflect those of the population. An unrepresentative sample leads to conclusions that appear valid but are actually misleading.
Example: You want to know the average number of hours per week KS3 students at your school spend reading. The population is all KS3 students (say, 300 students). Taking a sample of 30 gives you manageable data to work with.
What is random sampling?
In simple random sampling, every member of the population has an equal probability of being selected, and selections are independent of each other.
How to do it:
- List all members of the population (the sampling frame).
- Assign each member a number.
- Use a random number generator or draw numbers from a hat to select the required sample size.
Advantages:
- No bias is introduced by the person choosing.
- Results can be generalised to the population.
Disadvantages:
- Requires a complete list of the population (not always available).
- Can be time-consuming for large populations.
What is systematic sampling?
In systematic sampling, you select every nth member from a list, starting from a random point.
How to do it:
- Decide the sample size k and the population size N.
- Calculate the sampling interval: n = N ÷ k. Round to the nearest whole number.
- Choose a random starting point between 1 and n.
- Select every nth member after that starting point.
Example: Population of 200 students, sample size 20. Interval = 200 ÷ 20 = 10. Choose a random start between 1 and 10 — say, 4. Sample: members 4, 14, 24, 34, ... 194.
Advantages: Quick and easy once the list is prepared.
Disadvantages: Can introduce bias if the list has a repeating pattern that coincides with the interval (for example, a list of houses alternating "detached/terraced" with an interval of 2).
What is convenience sampling?
Convenience sampling (also called opportunity sampling) selects whoever is easiest to reach — the first students you see in a corridor, members of your own form group, or people passing a particular location.
Advantages: Very quick and cheap.
Disadvantages: Almost always biased. People who are convenient to sample are rarely representative of the whole population.
Example of bias: Asking only the students in your form group about revision habits to represent all KS3 students. Your form group may have unusually high or low revision habits — there is no guarantee they are typical.
How do you identify and describe bias?
A sample is biased if certain groups in the population are systematically over-represented or under-represented.
| Scenario | Type of bias |
|---|---|
| Surveying only students in one subject set about preferred teaching styles | Ability bias |
| Surveying students only at lunchtime on a Tuesday | Time bias (misses students absent that day) |
| Posting an online survey | Response bias (only tech-engaged students reply) |
| Asking your friends | Selection bias (not random) |
When asked to "explain a possible source of bias," state which group is over- or under-represented and why that would skew the results.
How should you choose a sampling method?
| Method | Use when... |
|---|---|
| Random | You need unbiased results and have a complete population list |
| Systematic | You have an ordered list and need a quick, reasonably unbiased sample |
| Convenience | Speed matters more than reliability (e.g. a quick pilot study) |
In GCSE and beyond, stratified sampling is used when the population contains distinct groups (strata) of different sizes, and you want each group to be proportionally represented. At KS3, you are expected to know random, systematic, and convenience — and to recognise bias.
Frequently asked questions
Why can't I just ask everyone in my class?
Using only your class is convenience sampling. Your class is a very small, self-selected group within the school — its characteristics (age, subject choices, friendship groups) may not match those of the broader student population you are investigating. Results from your class cannot be reliably generalised.
What is a sampling frame?
A sampling frame is the complete list of all members of the population from which you draw your sample. Without a sampling frame, true random sampling is impossible. For a school survey, the sampling frame might be the school roll. For a national survey, it might be the electoral register or a postcode database.
How large should my sample be?
At KS3, exam questions typically specify the sample size. In practice, larger samples give more reliable results, but they cost more time and money to collect. A common rule of thumb is that a sample of at least 30 individuals is needed for basic statistical analysis to be meaningful.
Can I combine sampling methods?
Yes. In practice, researchers often combine methods — for example, using systematic sampling within randomly chosen groups. At KS3, you are not expected to design complex multi-stage samples, but you should understand why simple convenience sampling is insufficient for reliable conclusions.
For Socratic KS3 statistics and sampling practice with Professor Pi, see aitutors.me.