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Confidence Interval Calculator

Calculate a confidence interval for a sample mean.

How this is calculated
CI = sample mean ± Z × (standard deviation ÷ √n)

Assumptions used in this calculation

  • Z-distribution: Uses the Z (normal) distribution critical values rather than the t-distribution, which is a reasonable approximation for larger sample sizes but less precise for small samples.

About this calculator

Calculates a confidence interval for a sample mean from the sample's standard deviation, sample size, and chosen confidence level.

Worked example

Mean 50, sd 10, n=100, 95% confidence

Result: CI = 48.04 to 51.96

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