Samples and What They Tell You

Asking everyone is usually impossible, so a smaller group stands in for the whole.

Sample is a smaller group chosen to represent a whole population.

It must be representative

A sample only tells you about the population if it is chosen without favouring anyone.

How samples go wrong

Asking only people leaving a sports shop about exercise will not describe the town.

Scaling up

If 12 of 50 sampled prefer blue, then in 500 you would expect about 120.

Why sample at all

Asking everyone is usually impossible — too many people, too much time, too much cost. A sample lets you learn about a whole population from a part of it. The entire question is whether the part represents the whole.

Random samples are the fair ones

In a random sample every member of the population has an equal chance of being chosen. Randomness is what protects against bias — not carefulness, not good intentions. A thoughtfully chosen sample is usually more biased than a random one.

How samples go wrong

Surveying about sport at a football match, or about internet use by an online poll, samples people already unusual in the relevant way. Bias comes from how the sample was gathered, and no amount of arithmetic afterwards can remove it.

Bigger samples vary less

A larger random sample gives estimates that cluster more tightly around the true value. But a large biased sample is still biased — size fixes variability, not bias. Both matter, and they are separate problems.