Use this free Confidence Limits for Mean Calculator to quickly determine the statistical range within which the true population mean is likely to fall. Input your sample mean, standard deviation, sample size, and desired confidence level to get instant results, perfect for academic research and data analysis.
Formula:
The confidence interval for the mean is typically calculated using one of two formulas, depending on whether the population standard deviation is known and the sample size. For this calculator, we use the Z-score method, which is appropriate for large sample sizes (n > 30) or when the population standard deviation is known:
Confidence Interval = X̄ ± Z * (s / √n)
- X̄ (X-bar) = Sample Mean
- Z = Z-score corresponding to the desired confidence level (e.g., 1.96 for 95% CI)
- s = Sample Standard Deviation
- n = Sample Size
- √n = Square root of the Sample Size