Samples, populations and data collection

A population is the whole group we want to learn about. Collecting data from every member is a census. A census gives complete information, but it can be slow, expensive or impossible — for example, you cannot test every match in a box to see if it lights, because testing destroys them.

Usually we collect data from a sample — a smaller group — and use it to make conclusions about the population. For this to work, the sample must be representative: it should look like the population in the ways that matter.

The best way to get a representative sample is to choose it randomly, so every member of the population has an equal chance of being picked (for example, drawing names from a hat). The sample should also be large enough — results from 5 people vary much more than results from 100.

Bias happens when the way data is collected favours some results. Common causes:

• Convenience samples: asking whoever is easiest to reach, such as your friends or the first people you meet.
• Wrong place or time: asking people at a gym how often people exercise.
• Voluntary responses: only people with strong opinions bother to reply.
• Leading questions: “Don't you agree the new park is a waste of money?” pushes people towards one answer.

To compare samples, use a measure of centre — the mean (add the values, divide by how many) or the median (the middle value when sorted) — and a measure of spread — the range (highest − lowest). Two samples from the same population usually give slightly different results; this natural difference is called sampling variation.