= Solution
The population <variance> is $\sigma^2=\operatorname E[(X-\operatorname EX)^2]$, and the population <standard deviation> is $\sigma=\sqrt{\sigma^2}$. For a sample, the usual unbiased estimate of population <variance> is
$$
s^2=\frac1{n-1}\sum_{i=1}^n(x_i-\bar x)^2,\qquad s=\sqrt{s^2}.
$$
The 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 $\pm1\sigma$ entries are interpreted as sample <standard deviations> for the calculations below, rather than <standard errors> of the mean.
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