Confidence Interval Calculator

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Calculate the confidence interval for a population mean given sample data.

Sample Data

Sample Mean (x̄)

Sample Standard Deviation (s)

Sample Size (n)

Confidence Level (%)

Confidence Interval

Lower Bound48.0400

Upper Bound51.9600

Margin of Error± 1.9600

About this calculator

Understanding Confidence Intervals

A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data. If you were to repeat your sample many times, 95% of the calculated intervals would contain the true population mean.

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Pro Tips

Common confidence levels are 90% (Z=1.645), 95% (Z=1.96), and 99% (Z=2.576).
Increasing the sample size decreases the margin of error, making the interval narrower (more precise).
Higher confidence levels (e.g. 99%) result in wider intervals.

Fun Facts

"The concept was introduced by Jerzy Neyman in 1937."
"A 95% confidence interval does NOT mean there is a 95% probability the true mean lies within the specific interval calculated; it relates to the long-run frequency of the method."

Formula: CI = x̄ ± Z * (s / √n)