Sampling and Margin of Error

A poll never asks everyone. It asks a sample and uses that sample to estimate what the whole population thinks. Margin of error tells you how far off that estimate could reasonably be, just from the luck of who got picked. A quick approximation: margin of error is about 100 divided by the square root of the sample size, in percentage points. A sample of 1,000 gives a margin of error near 3 points, because 100 divided by √1000 is about 3.

That square root is the whole story of why bigger polls get expensive fast for not much payoff. Go from 100 people to 400 people, four times the sample, and the margin of error drops from about 10 points to about 5, cut in half, not to a quarter. Go from 400 to 1,600, another quadrupling, and it halves again to about 2.5. Each doubling of precision costs four times the people. That is why pollsters settle for samples around 1,000: past that point, paying for more interviews buys very little extra accuracy.

Margin of error also explains why close polls get called statistical ties. If Candidate A sits at 48 percent and Candidate B at 45 percent with a 3-point margin of error, A's true support could run anywhere from 45 to 51, and B's from 42 to 48. Those ranges overlap, so the poll cannot confirm A is actually ahead. But margin of error only captures random sampling luck. It says nothing about a bad sample, leading questions, or people lying to pollsters, which is why a poll can have a tiny margin of error and still be wrong.