A confidence interval pairs a point estimate with model-based uncertainty. Repeated samples produce different intervals.
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Confidence Interval for a Mean. A confidence procedure adds model-based uncertainty around an estimate. Wider confidence levels and noisier or smaller samples generally produce wider intervals.
1Compute the sample estimate2Calculate its standard error3Apply the stated confidence procedure
Method used
x̄±t* s/√n.
Repeated intervals produced by this method achieve the selected long-run coverage when assumptions hold.
What the result cannot establish
A 95% confidence interval does not mean there is a 95% probability that a fixed parameter lies inside this realized interval. The 95% describes long-run coverage of the procedure under its assumptions.
Assumption: Observations should be independent and the sampling distribution of the mean should be adequately modeled by the t procedure.
Quick guide
How to use this calculator
Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the confidence interval for a mean calculator works
x̄±t* s/√n.
Repeated intervals produced by this method achieve the selected long-run coverage when assumptions hold.
Worked example
Confidence Interval for a Mean example
Mean 50, s=10, n=25 at 95% gives an interval of roughly 45.87 to 54.13.
x̄±t* s/√n.
Supported inputs
Precision and limits
Model and design
Observations should be independent and the sampling distribution of the mean should be adequately modeled by the t procedure.
Numerical scope
Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.
Interpretation
Repeated intervals produced by this method achieve the selected long-run coverage when assumptions hold.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
Privacy
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