Calculate a mean interval with known population deviation or a Wilson interval for a proportion, with clear model assumptions.
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1 – 1000000000
-1000000000 – 1000000000
0 – 1000000000
95% confidence interval for the mean
48.0400–51.9600
Use only when population standard deviation is known and the normal model is appropriate. An estimated sample standard deviation generally calls for a Student t interval, which this mode does not compute.
Standard error = known population standard deviation ÷ √sample size.
Interval = sample mean ± normal critical value × standard error.
For a mean with known population standard deviation σ, use x̄ ± zσ/√n. For a proportion use the Wilson score interval, which remains between 0 and 1.
A mean of 50, known population deviation 10 and sample size 100 give a 95% interval of approximately 48.0400–51.9600.
Mean mode assumes population deviation is known. If it is estimated from the sample, a Student t interval is generally appropriate instead.
Last updated . Results are estimates for informational purposes only.