Confidence Interval

This calculator helps you determine the confidence interval for a population mean when you have sample data. It provides the range within which the true population mean is likely to fall, based on your chosen confidence level.

Sample Mean (X̄)

The average value of your sample data.

Sample Standard Deviation (s)

The spread of values in your sample.

Sample Size (n)

The number of observations in your sample.

Confidence Level (%)

Common levels are 90, 95, or 99. Enter as a percentage (e.g., 95).

How it works

This calculator helps you determine the confidence interval for a population mean when you have sample data. It provides the range within which the true population mean is likely to fall, based on your chosen confidence level.

The Formula

Confidence Interval (CI) = Sample Mean ± Z * (Sample Standard Deviation / √Sample Size)

Worked Example

Example: Student Test Scores
A school takes a random sample of 100 students' test scores. The sample mean score is 78, with a sample standard deviation of 12. To find the 95% confidence interval for the true mean test score of all students, you'd input: Sample Mean: 78 Sample Standard Deviation: 12 Sample Size: 100 Confidence Level: 95 The calculator would then output the lower and upper bounds of the interval.

Tips, Assumptions & Limitations

A larger sample size generally leads to a narrower confidence interval, meaning a more precise estimate.
A higher confidence level (e.g., 99% vs. 95%) will result in a wider interval, as you're more certain to capture the true mean.
This calculator uses Z-scores, which are appropriate for large sample sizes (typically n > 30) or when the population standard deviation is known.

FAQ

A confidence interval is a range of values, derived from sample data, that is likely to contain the true value of an unknown population parameter (like the population mean). It's always associated with a confidence level, such as 95% or 99%.

If you calculate a 95% confidence interval, it means that if you were to take many samples and calculate a confidence interval for each, approximately 95% of those intervals would contain the true population mean. It does NOT mean there's a 95% chance the true mean is within your specific interval.

This calculator uses Z-scores, which are generally appropriate when your sample size is large (typically n > 30) or if you know the population's standard deviation. For smaller sample sizes and when only the sample standard deviation is known, a t-distribution (and t-score) is more accurate, but requires more complex calculations.