Confidence Range for Mean

Build two-sided t interval from sample mean, sample deviation and size.

Your numbers

Lower end of confidence range

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E assume independent observations and suitable sampling model; small samples need observations wey approximately follow normal distribution.

Formula

Use m±t_c s/√n. m na sample mean, s na sample standard deviation, n na sample size, and t_c na di two-sided Student critical value for di confidence wey you choose and n−1 degrees of freedom.

Build two-sided t interval from sample mean, sample deviation and size.

Example wey show the calculation

Average of the sample: 10
Di sample standard deviation: 4
How many items the sample get: 16
Di confidence level (%): 95

Lower end of confidence range: 7.86855045444
Upper end of confidence range: 12.1314495456
Size of error margin: 2.13144954556
Di degrees of freedom: 15

Where e fit work and limits

E assume independent observations and suitable sampling model; small samples need observations wey approximately follow normal distribution.

We check inputs for missing values and allowed ranges. Result wey pass the finite numeric range no go show. Rounding affect wetin display, while calculation use the model numeric precision.

Check your units and assumptions before you rely on result. Changing label no convert currency or physical unit.

Version of di formula: bb918c55cb8e · Example don get check: 2026-10-30

Method