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Mean Confidence Interval Calculator
Calculate a mean confidence interval using an explicit normal or Student-t model.
Observations, Population standard deviation, Confidence probability, Known mode: positive population sigma
JSON
Browser only
Runs locally in your browser. Your files, pasted content and generated output are not uploaded. Reset clears this tool’s working data.
This tool needs JavaScript. If it does not load, refresh the page and try again.
How to use this tool
- Enter the displayed example values,or choose the local input files requested by the controls. Optional source files take precedence where labelled.
- Choose Calculate result and inspect the complete result and any reported limitations.
- Use Download result and each companion download link to save complete outputs. Reset clears output and restores example controls.
Examples
Observations: [2,4,4,5,7,9]
Population standard deviation: estimated
Confidence probability: 0.95
Known mode: positive population sigma: 2
Limitations
- Calculate a two-sided mean interval using estimated-sigma Student t,or an explicitly entered known population sigma with normal critical values. Confidence is a probability from0.000001 to0.999999. Estimated mode needs two observations; known mode needs one. Constant samples produce zero estimated width but do not prove zero population uncertainty. Assumes independent normal observations or a suitable large-sample approximation. Numeric JSON arrays,at most10,000 observations,each within +/-1e12; no strings,nulls or missing values. Download the complete JSON report. All processing stays in your browser. Combined input limit: 400,000 UTF-8 bytes, 100,000 characters per field; report limit: 4 MiB. Floating-point rounding and probability underflow can occur.
- Complete outputs only. Unsupported or oversized input is refused. Follow the displayed job-specific bounds and format policies.
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