An interval for spread itself
Means get confidence intervals constantly; variances deserve them too: how precisely do we know a process's variability? The construction runs through the chi-square distribution: (n−1)s² divided by its two critical values. The result leans visibly right: variance intervals are asymmetric, because a variance cannot fall below zero but can stretch far upward.
Bakery sales again (s² = 22.57, n = 8, df = 7). Chi-square critical values at 95%: 1.690 and 16.013. The variance interval is 9.87 to 93.50; for the SD, 3.14 to 9.67. Compare that width with the mean's tidy interval from the same data: eight observations pin down the centre far better than the spread. Knowing your variability precisely is a luxury bought with large samples.
Trusting this interval on heavy-tailed data. Of all the common intervals, this one leans hardest on normality, with genuinely non-normal samples its real coverage can fall well short of the label. Treat it as exact for near-normal data and indicative elsewhere.
Frequently asked questions
Why is the interval asymmetric?
It inherits the chi-square distribution's right skew. The sample variance can undershoot the truth only so far (it cannot go negative) but can overshoot a long way. The interval mirrors that geometry.
How do I get the SD interval?
Take square roots of the variance interval's endpoints, the page does it for you. No separate calculation is needed, because the square root is monotone.