Sampling Theory
The mathematical foundation of polling: why a sample of 1,000 can represent 330 million people, and the conditions that make it work.
The Logic of Sampling
The idea that 1,000 people can represent 330 million seems counterintuitive, but the mathematics is well-established. The Central Limit Theorem states that a randomly drawn sample will have a mean close to the population mean, and that this approximation improves as the sample grows. With a truly random sample of 1,000, you can estimate a population proportion with a margin of error of roughly +/- 3 percentage points, 95% of the time.
The critical word is 'random.' The mathematical guarantee depends on every member of the population having an equal chance of being selected. In practice, perfectly random sampling is impossible: you cannot reach people without phones, people who never answer unknown numbers, or people who refuse to participate. Every deviation from randomness introduces potential bias, which is why the art of polling is as important as the science.