Confidence Interval For A Mean

Compute a one-sample confidence interval for a continuous mean from summary statistics.

Concept

Results

Enter inputs and select Calculate to display reviewed results.

Inputs

Standard deviation modeConfidence level *

Sample size *

Sample mean *

Sample standard deviation *

Known sigma *

Used only in known-sigma mode.Response unit labelOptional display label for the measured response.

Formula & Variables

x±t_1-α/2,n-1s√n

This is the one-sample t interval used when sample standard deviation is selected. Known-sigma mode uses the same structure with z_1-α/2 and σ in place of t_1-α/2,n-1 and s.

x: Sample mean; [response]
s: Sample standard deviation; [response]
n: Sample size; [1]

Assumptions

Observations are independent.
Response is continuous or treated as continuous.
Sample-standard-deviation mode uses the t distribution.

⚠ Limitations

Raw data processing, paired intervals, two-sample intervals, regression intervals, capability intervals, and reliability intervals require separate methods.
The calculator cannot prove normality, independence, or representativeness.