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This is a phrase that’s often used by pollsters. When you carry out a poll, you usually analyse it by assuming that your sampling method picks people perfectly at random – that is, everyone in the population is equally likely to be picked. Under these conditions, there is a predictable amount of randomness in the results of the poll, depending on the sample size – if you carry out exactly the same poll again you will typically get slightly different results just by chance, but this effect is more pronounced with smaller sample sizes. The margin of error quoted by pollsters is a measure of how big this variation is. Specifically, about 95% of the time, the results of the poll will be within the margin error of the true result. And the margin of error is roughly 1/sqrt(sample size).
However, in a real life poll there are additional sources of error. Your sampling method might be much more likely to pick some people than others, some people will refuse to participate, and some people will fail to give accurate answers. Instead of adding randomness to the results, these effects skew the results in certain directions. But it’s very difficult to measure or predict these effects, so the quoted “margin of error” generally doesn’t include any of them.
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