Mean Confidence Interval
Build a two-sided t interval from sample mean, sample deviation and size.
Your numbers
Lower confidence limit
Assumes independent observations and a suitable sampling model; small samples need approximately normal observations.
Scenario comparison
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Formula
Use m±t_c s/√n. m is sample mean, s is sample standard deviation, n is sample size, and t_c is the two-sided Student critical value for the chosen confidence and n−1 degrees of freedom.
Build a two-sided t interval from sample mean, sample deviation and size.
Worked example
- Sample mean
- 10
- Sample standard deviation
- 4
- Sample size
- 16
- Confidence level (%)
- 95
- Lower confidence limit
- 7.86855045444
- Upper confidence limit
- 12.1314495456
- Margin of error
- 2.13144954556
- Degrees of freedom
- 15
Scope and limitations
Assumes independent observations and a suitable sampling model; small samples need approximately normal observations.
Inputs are checked for missing values and allowed ranges. A result outside the finite numeric range is not displayed. Rounding affects display, while the calculation uses the model’s numeric precision.
Check your units and assumptions before relying on a result. Changing a label does not convert a currency or physical unit.
Formula version: bb918c55cb8e · Example checked: