read: Standard Deviation
for comparisons of 2 variances, see: f-distribution
Confidence Interval for Population Variance
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A rescaled sample variance [(𝑛-1)𝑠2] / [𝜎2] has Chi-Square density (example on the right)
Solving the inequality for the unknown parameter 𝜎2, we get
A (1 − 𝛼)100% confidence interval for the population variance is obtained
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/ci---1-sample/ci---variance--and--standard-deviation/confidence-interval-variance-1.png)
/ci---1-sample/ci---variance--and--standard-deviation/confidence-interval-variance-2.png)
/ci---1-sample/ci---variance--and--standard-deviation/variance-confidence-interval.png)
/ci---1-sample/ci---variance--and--standard-deviation/example-chi-squared-density-function.png)
Confidence Interval for Population Standard Deviation
A confidence interval for the population standard deviation 𝜎 = √𝜎2 is just one step away
/ci---1-sample/ci---variance--and--standard-deviation/standard-deviation-confidence-interval.png)