Margin of error, step by step
Every report of a poll prints a margin of error and almost none of them explain it.
The question
625 fans were asked about the match. What is the margin of error?
One over the square root of how many were asked
n=625
√625=25
1 ÷ 25=4%
4%
- 625 people were asked. The margin of error depends on that number and nothing else — not on what they said, and not on how big the country is.
- Take the square root first: 25 × 25 = 625, so √625 is 25.
- Then one over it, as a percent: 1 ÷ 25 = 4%.
- Notice what that means. To halve this margin you would need FOUR times as many people, not twice as many — the root is why a poll of a few thousand is as good as most polls ever get.
How it works.
- 01
625 people were asked. The margin of error depends on that number and nothing else — not on what they said, and not on how big the country is.
- 02
Take the square root first: 25 × 25 = 625, so √625 is 25.
- 03
Then one over it, as a percent: 1 ÷ 25 = 4%.
- 04
Notice what that means. To halve this margin you would need FOUR times as many people, not twice as many — the root is why a poll of a few thousand is as good as most polls ever get.