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.
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 question from a sheet like this one, worked a step at a time — with a sentence saying what just happened and why.
The margin of error is 1 ÷ √n, as a percent. Work it out for each.
1
10,000 households were asked about recycling. What is the margin of error?
%
2
2,500 readers were asked about the book. What is the margin of error?
%
3
400 households were asked about recycling. What is the margin of error?
%
4
625 readers were asked about the book. What is the margin of error?
%
5
100 shoppers were asked about the new label. What is the margin of error?
%
6
25 students were asked about walking to school. What is the margin of error?
%
Margin of error · The margin from the sample sizeAnswer key
1. 10,000 households were asked about recycling. What is the margin of error? → 1% (1 ÷ √10,000 = 1 ÷ 100 = 1%)2. 2,500 readers were asked about the book. What is the margin of error? → 2% (1 ÷ √2,500 = 1 ÷ 50 = 2%)3. 400 households were asked about recycling. What is the margin of error? → 5% (1 ÷ √400 = 1 ÷ 20 = 5%)4. 625 readers were asked about the book. What is the margin of error? → 4% (1 ÷ √625 = 1 ÷ 25 = 4%)5. 100 shoppers were asked about the new label. What is the margin of error? → 10% (1 ÷ √100 = 1 ÷ 10 = 10%)6. 25 students were asked about walking to school. What is the margin of error? → 20% (1 ÷ √25 = 1 ÷ 5 = 20%)
