Confidence Interval Calculator
The confidence interval for a mean: mean ± z·(SD/√n).
Result
Margin of error
5.37
Lower bound
94.63
Upper bound
105.37
How it works
A confidence interval turns a single estimate into a range: mean ± z × (σ ÷ √n). Rather than claiming the average is exactly 52, it says the true value plausibly lies between 49 and 55. The 95% is often misread. It does not mean there is a 95% chance the true value sits in your particular interval — the true value is fixed, your interval is what varies. It means that if you repeated the study many times, 95% of the intervals produced would contain the true value. Width is driven by three things: more data narrows it as √n, more variability widens it, and higher confidence widens it too. That last trade-off is unavoidable — a 99% interval is more likely to be right precisely because it claims less, and an interval wide enough to be certain says nothing useful.
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Frequently asked questions
What does 95% confidence mean?
If you repeated the sampling many times, about 95% of the intervals would contain the true mean.
How do I narrow the interval?
Increase the sample size or lower the confidence level — both shrink the margin of error.
What does it mean if the interval contains zero?
When the interval is for a difference, containing zero means "no difference" remains plausible — the data cannot rule it out at that confidence level. It is the interval version of a result that is not statistically significant.
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