Statistics & probability
Confidence interval for a mean
Estimate a mean interval using a sample and Student’s t distribution.
A clear answer. Here’s how.
Uses sample standard deviation (n−1), standard error s/√n and a two-sided Student t critical value with n−1 degrees of freedom. Requires at least two independent observations and a suitable normal/large-sample model; outliers or dependent data can invalidate coverage. A zero sample variance yields a degenerate interval and does not establish zero population variance.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Values, separated by commas or new lines
- 2, 4, 4, 4, 5, 5, 7, 9
- Two-sided confidence level (%)
- 95
Example result
- Sample mean
- 5
- Interval lower bound
- 3.21251208176
- Interval upper bound
- 6.78748791824
- Margin of error
- 1.78748791824
- Sample size
- 8
- Critical t value
- 2.36462425159
Student t interval; sampling and distribution assumptions apply.