Page 39 - Pharmaceutical Analytical Chemistry III

Measures of Dispersion

Population Standard Deviation σ Sample Standard Deviation s

The population standard deviation, which is The sample standard deviation s is
given by the equation:
a measure of the precision of the

population, is given by the equation

where N is the number of data points nn
making up the population.
where the quantity (xi – x) represents
The quantity (xi – m) is the deviation of data the deviation di of value xi from the
value xi from the mean m of a population; mean x.

compare with equation for a sample of data. Note that the equation differs from
sample equation in two ways. First, the

sample mean, , appears in the
numerator in place of the population
mean, m. Second, N in population
quation is replaced by the number of
degrees of freedom (N – 1).