Past exam of the year 2 of the earth sciences (geology) course of the University of Oxford / 2023 / Paper 1 / 9 / b / Solution

The population variance is ${\sigma }^2=E[(X-EX{)}^2]$, and the population standard deviation is $\sigma =\sqrt{{\sigma }^2}$. For a sample, the usual unbiased estimate of population variance isThe sample standard deviation measures scatter in the original concentration units; variance has squared units. Both are nonnegative, but the sample standard deviation itself is not generally an unbiased estimator of $\sigma$. The table's $\pm 1\sigma$ entries are interpreted as sample standard deviations for the calculations below, rather than standard errors of the mean.