A familiar situation
Estimate a plausible range for a population mean from a sample summary and chosen confidence level.
How to use this calculator
- Enter sample mean, sample standard deviation, sample size and the remaining inputs.
- Select Calculate to see the answer and its breakdown.
- Keep a scenario, change an input and compare the results.
Use consistent units and check the assumptions below before applying the result.
How confidence interval is calculated
Interval = x̄ ± t* s/√n with n−1 degrees of freedom. The t critical value is numerically evaluated from the selected confidence level. For mean 50, SD 10, n=25, a 95% interval is approximately 50 ± 4.13, or 45.87 to 54.13.
x̄ ± t* s/√n, with n−1 degrees of freedom.For mean 50, SD 10, n=25, a 95% interval is approximately 50 ± 4.13, or 45.87 to 54.13.
Assumptions & useful context
The result depends on the values you enter and the method described above. Displayed numbers may be rounded; calculations use the unrounded values. Check that this model matches your situation before relying on it.
Frequently asked questions
Does 95% mean this particular interval has a 95% chance of containing the mean?
In repeated sampling, 95% of intervals constructed this way would contain the true mean under the assumptions.
What assumptions matter?
Independent observations and a reasonably suitable sampling distribution; small samples require particular care with skew and outliers.