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Margin of error worksheets

Every report of a poll prints a margin of error and almost none of them explain it. These free printable worksheets work it out from the sample size — one over the square root of it, as a percent — and then use it to turn a single figure into the range it really stands for.

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Margin of error
Margin of error worksheet — Whole margins, 25 to 10,000 asked, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

The sample sizes are chosen so the margin comes out whole and nothing rounds: 25 people asked gives 20%, 100 gives 10%, 400 gives 5%, 625 gives 4%, 2,500 gives 2% and 10,000 gives 1%. Reading that list downwards is the lesson. Sixteen times as many people buys four times the precision, not sixteen — which is why national polls stop at about a thousand, and why a survey of twenty-five tells you almost nothing.

Why this sheet works

The small samples are here on purpose for that reason. A margin of twenty points is not a silly answer to leave out; it is the honest arithmetic that explains why nobody reports a poll of twenty-five people.

How this one works

One over the square root of how many were asked

n=10,000
√10,000=100
1 ÷ 100=1%
1%
  1. 10,000 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.
  2. Take the square root first: 100 × 100 = 10,000, so √10,000 is 100.
  3. Then one over it, as a percent: 1 ÷ 100 = 1%.
  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.

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