Confidence Interval for Standard Deviation

Exact Confidence Interval

The confidence interval for the population standard deviation σ is given by:

Standard Error Approximation

For large samples, the standard error of the sample standard deviation is:

This can be used to construct approximate confidence intervals: $s \pm z_{\alpha/2} \cdot SE(s)$

Where:

• $n$ is the sample size
• $s$ is the sample standard deviation
• $\chi^2_{(p, n - 1)}$ is the p-th percentile of the chi-square distribution with n-1 degrees of freedom
• $\alpha$ is the significance level (e.g., 0.05 for a 95% confidence interval)
• $z_{\alpha/2}$ is the critical value from the standard normal distribution