When you report that 30% of customers prefer an option, you should also say how precise that figure is. The standard error of a proportion is the square root of p times (1 minus p) over n, and multiplying by 1.96 gives the 95% margin of error.
A 50% result on 400 responses has a 2.5% standard error and about a 4.9% margin of error.
The example
Three surveys. Larger samples shrink the margin; proportions near 50% have the widest margin.
| A | B | C | D | E | |
|---|---|---|---|---|---|
| 1 | Case | Proportion | Sample n | Std error | Margin |
| 2 | Survey A | 50.0% | 400 | 2.5% | 4.9% |
| 3 | Survey B | 30.0% | 1,000 | 1.4% | 2.8% |
| 4 | Survey C | 8.0% | 250 | 1.7% | 3.4% |
The formula
The standard error uses the proportion itself; the margin multiplies it by 1.96:
How it works
Here is the logic, one piece at a time:
B2*(1-B2)is the variance of a single yes/no response./C2divides by the sample size.SQRT(...)converts to a standard error.1.96*...turns it into a 95% margin.
Report the proportion with its margin, for example 30% plus or minus 2.8%.
Try it: interactive demo
Enter the survey proportion and sample size.
Variations
Confidence interval low
Lower bound.
Confidence interval high
Upper bound.
Pitfalls & errors
Enter the proportion as a decimal or a percent-formatted cell. Entering 30 instead of 0.30 produces nonsense.
This normal approximation is weak for very small samples or proportions near 0 or 1.
Use the larger-sample rule: n*p and n*(1-p) should both be above 10.
Practice workbook
Frequently asked questions
What does 1.96 mean?
How do I get a 99% margin?
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