In public opinion polls, how can a few thousand people possibly represent the millions of people in a country?
Surprising as it may seem, polls can estimate the proportion of people with a certain trait or opinion to within a few percent, just by asking a few thousand individuals out of a population of millions. The so-called “margin of error” in a poll is about 1 divided by the square root of the number of people asked; so for instance, with 1600 people the margin of error is 1/40 or 2.5%. Think about it this way: Suppose you wanted to know what proportion of adults are left-handed. You observe what you think is a representative sample, perhaps people signing credit card receipts at stores. Suppose you spent the time to watch 1600 people, and noticed that 163 (10.2%) were writing with their left hand. Do you really think that observing more people would change that percentage much? It’s not the size of the population that matters, but rather how much information you have from a representative sample.
