Page 12 - Statistics presented by Dr. Sara Ismail Aborass

9/8/2023

Measures of Dispersion

Three terms are widely used to describe the dispersion
(precision) of a set of replicate data:
standard deviation, variance, and coefficient of variation.
These three are functions of how much an individual result xi
differs from the mean, called the deviation from the mean di.

Note that deviations from
the mean are calculated
without regard to sign.
(modulus)

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Measures of Dispersion

Population Standard Deviation σ Sample Standard Deviation s

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

where N is the number of data points nn IMP
making up the population. where the quantity (xi – x)
The quantity (xi – µ) is the deviation of represents the deviation di of value
data value xi from the mean µ of a xi from the mean ഥ .
population; compare with equation for a
sample of data. Note that the equation differs from
sample equation in two ways. First,

the sample mean, ഥ, appears in the
numerator in place of the population

mean, µ. Second, N in population
equation is replaced by the number of
degrees of freedom (n – 1).

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