Comprehensive Calculator Guide
This calculator gives the sample proportion p̂, its standard error, the margin of error and a 95% confidence interval. 520 of 1,000 is 52% ± 3.1%, so the true share is likely 48.9% to 55.1%. Because the interval includes 50%, a majority cannot be claimed.
From sample to population
SE = √(p̂(1 − p̂)/n); margin = 1.96 × SE. Halving the margin takes four times the sample. The interval assumes a random, representative sample.
How to Use
- Enter the successes.
- Enter the sample size.
- Press “Calculate” to see p̂, the margin and the interval.
Formula Used
p̂ = x/n | SE = √(p̂(1 − p̂)/n) | Margin = 1.96 × SE
Practical Examples
- Example 1
- 520/1,000: 52% ± 3.1%.
- Example 2
- 36/120: 30% ± 8.2%.
Important Tips
- Quote the margin and n.
- No majority if the interval spans 50%.
- Plan n in advance.
Common Mistakes to Avoid
- Generalising from a non-random sample.
- Ignoring the margin.
- Doubling n to halve the margin.
Frequently Asked Questions
- What does ±3% mean?
- The true share is likely within 3 points.
- How big a sample?
- About 1,067 for ±3%.
- Why 1.96?
- 95% of a normal lies within 1.96 SDs.