Collecting data
Taking a sample
You cannot weigh every baby born in the country. So you weigh some of them — and how you choose those some decides whether your answer means anything.
Population and sample
Take the prediction: 'Newborn baby boys are heavier than newborn baby girls.' Finding the mass of EVERY baby born would be impossible. So you find the masses of some of them. The POPULATION is every member of the group you are interested in — here, all newborn babies. The SAMPLE is the smaller group you actually collect data from.
Why not use the whole population?
If you can collect data from the whole population, that is best — the answer is then certain. But usually it takes too long, costs too much, or is simply impossible. A sample is a practical compromise: less certain, but achievable.
Sample size
The SAMPLE SIZE is how many are in your sample. A bigger sample generally gives a more reliable result, because one unusual value matters less. A sample of 5 babies could easily mislead you. A sample of 500 is far more trustworthy. But bigger samples take more time and cost more — so you balance reliability against what is practical.
A fair sample
Size is not everything: the sample must also REPRESENT the population. If you want to know what learners in your school think, asking only your own friends gives a biased sample, however many you ask. They are not typical of the whole school. A good sample includes the same kinds of people, in roughly the same proportions, as the population it comes from.
Worked examples
Testing 'newborn boys are heavier than newborn girls'
- Weighing every baby born is impossible.
- So weigh some of them.
Answer: Use a sample
What is the population here?
- The population is everyone you are interested in.
Answer: All newborn babies
A sample of 5 babies or 500?
- A bigger sample makes one unusual value matter less.
Answer: 500 — far more reliable
Asking only your friends about the school
- Your friends are not typical of the whole school.
- Size does not fix that.
Answer: A biased sample, however many you ask
When should you use the whole population?
- If you can collect from everyone, the answer is certain.
- Usually it costs too much or takes too long.
Answer: Whenever it is actually practical
What makes a sample fair?
- It must represent the population.
- The same kinds of people, in roughly the same proportions.
Answer: Representative, not just large
Where you see this in real life
- Opinion polls ask a sample of a few thousand people rather than the whole country — and get close, provided the sample is chosen fairly.
- A factory testing every product it makes would have nothing left to sell, so it tests a sample instead.
Key words
- Population
- every member of the group being studied
- Sample
- the smaller group actually used to collect data
- Sample size
- how many members are in the sample
- Biased sample
- a sample that does not represent the population fairly
- Reliable
- likely to be close to the true value
- Representative
- matching the population it came from
- Bias
- a systematic tilt that makes a sample unfair