Confidence Interval Calculator for Standard Deviation
Easily calculate the confidence interval for population standard deviation using the chi-square distribution. Input sample standard deviation, sample size, and confidence level for instant results.
Results
Confidence Interval: (, )
Chi-Square Distribution Visualization
This plot shows the Chi-Square distribution for your sample's degrees of freedom. The green and red dashed lines indicate the Chi-Square values corresponding to the lower and upper bounds of your chosen confidence level.
Understanding Confidence Intervals for Standard Deviation
A confidence interval for the standard deviation estimates a range within which the true population standard deviation is likely to fall. It's based on your sample data and a chosen confidence level, like 95%, indicating the reliability of the estimate.
We use the chi-square (χ²) distribution because the sample standard deviation's distribution relates to chi-square, especially when data is normally distributed. The formula involves chi-square values corresponding to your confidence level and degrees of freedom (sample size minus 1).
For example, if you calculate a 95% confidence interval for standard deviation to be (10, 15), it means you are 95% confident that the true population standard deviation lies between 10 and 15. This tool is useful in quality control, finance, and research to understand the variability in a population.
Learn more about Confidence Intervals and Chi-Square Distribution.