where is the -th quantile of the chi-square distribution with degrees of freedom, and is the confidence level. This is equivalent to the following:

With , and . The reciprocals of the square roots of these two numbers give us the factors 0.45 and 31.9 given above.

A larger population of has 9 degrees of freedom for estimating the standard deviation. The same computations as above give us in this case a 95% CI running from to . So even with a sample population of 10, the actual SD can still be almost a factor 2 higher than

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