Margin Of Error
Calculator
Results
- Margin of error
- 4.2
- Standard error
- 2.142857
Statistical results
| Margin of error | 4.2 |
| Standard error | 2.142857 |
formula-map diagram
- Margin of error
- 4.2
- Standard error
- 2.142857
Statistical relationship
Formula
E = z × σ / √n= 4.2
Note
This is a simplified model: it applies the displayed standard formula to the summary values you entered and assumes their underlying conditions (independence, normality, correct sampling) hold. It does not analyse a real data set. Check the assumptions before relying on the result.
More in Statistics and probability
See all →Frequently asked questions
What does margin of error actually represent?+
It's the range above and below a sample estimate within which the true population value is likely to fall, at a stated confidence level. A poll result of 52% with a margin of error of 3 points means the true value is likely between 49% and 55%.
How does confidence level affect the margin of error?+
Higher confidence levels require a wider margin of error, because being more certain that you've captured the true value means casting a wider net. Moving from 90% to 99% confidence increases the margin of error even with the same sample.
Why does a bigger sample size shrink the margin of error?+
Margin of error is proportional to 1/√n, so quadrupling your sample size only halves the margin of error. This diminishing return is why polls rarely use samples larger than a couple thousand people even for national populations.
Does margin of error account for all sources of survey error?+
No, it only accounts for random sampling variability. It does not capture non-response bias, poorly worded questions, or a sample that isn't representative of the population, which can matter far more than the margin of error itself.
What's a common misreading of margin of error in news coverage?+
A frequent mistake is treating a lead within the margin of error as meaningless, but if a candidate leads by more than twice the margin of error over another, the lead can still be statistically meaningful. The margin of error describes uncertainty around a single estimate, not automatically the significance of the gap between two estimates.