Sampling
How and why we study a subset of a population to draw conclusions about the whole.
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 â 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.
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 â 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 â the results reflect that particular crowd, not the country.
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 â because its sample was drawn from car owners and telephone subscribers, who were wealthier and more Republican than the general population.
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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