Sampling

How and why we study a subset of a population to draw conclusions about the whole.

Sampling asks a smaller group to stand in for the population
populationrandom samplebiased sample
Population
The full group contains several subgroups.
Representative
Random selection keeps the mix of groups visible.
Biased
A convenient sample can over-represent one group.
Definition

A population is the entire group you want to learn about. A sample is the smaller group you actually measure.

We sample because measuring every member of a population is usually impossible — too expensive, too slow, or literally impossible (you can't test every light bulb a factory will ever make).

A representative sample reflects the diversity of the population. A biased sample systematically over- or under-represents certain groups.

Opinion polls

A polling company wants to know how the whole country will vote. They can't ask all 50 million eligible voters.

Instead they ask 1,000 people — a sample. If those 1,000 are chosen carefully (random selection, diverse regions, ages, incomes), the results will be close to what you'd get from asking everyone.

If they only ask people outside a particular supermarket, the sample is biased — the results reflect that particular crowd, not the country.

Sample size is not the only thing that matters

A large biased sample is worse than a small unbiased one. In 1936, a magazine polled 2.4 million people and wrongly predicted the US election outcome — because its sample was drawn from car owners and telephone subscribers, who were wealthier and more Republican than the general population.

Try it

A school wants to know students' opinions on a new lunch menu. Describe one biased and one unbiased sampling method.

Solution

Biased: Ask the first 20 students who arrive at the canteen. These are likely students who eat there regularly and may already like the food.

Unbiased: Assign every student a number and use a random number generator to select 20. Each student has an equal chance of being chosen regardless of their habits.

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