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Confidence Interval Calculator

Estimate a range in which the true population mean is likely to fall, based on a sample.

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Precision Estimate

Confidence Interval & Marginal Error Analysis

About the Confidence Interval Calculator

Estimate a range in which the true population mean is likely to fall, based on a sample.

How to use the Confidence Interval Calculator

  1. Enter the Sample Mean (x̄), the Population σ / Sample S and the Sample Size (n).
  2. Choose the Confidence Level: 90%, 95%, 98% or 99%.
  3. Press Calculate Interval.

Formula and method

CI = x̄ ± z × (σ ÷ √n), with z = 1.645 (90%), 1.96 (95%) or 2.576 (99%).

Worked example

A sample of 100 with a mean of 50 and standard deviation of 10 gives a 95% interval of 50 ± 1.96 × 1 = 48.04 to 51.96.

Tips

  • A larger sample gives a narrower interval.
  • A higher confidence level gives a wider interval.

Frequently asked questions

What does 95% confidence mean?
If you repeated the sampling many times, about 95% of the intervals would contain the true mean.