Work out confidence interval for variance instantly with clear inputs, formula shown and shareable results.
Because (n − 1)s²/σ² follows a chi-square distribution with n − 1 degrees of freedom, the interval for σ² is ((n−1)s²/χ²_upper, (n−1)s²/χ²_lower). Note the interval is asymmetric.
Variance interval
((n−1)s² / χ²₁₋α/₂, (n−1)s² / χ²α/₂) with n − 1 degrees of freedom
The chi-square bounds on 19 df are about 32.85 and 8.91, giving a variance interval of roughly 14.46 to 53.31.
The chi-square distribution is right-skewed, so the two tail cut-offs are not symmetric about the sample variance.