Standard Deviation
The standard deviation is a numerical value used to indicate how widely
individuals in a group vary. If individual observations vary greatly from the
group mean, the standard deviation is big; and vice versa.
It is important to distinguish between the standard deviation of a population
and the standard deviation of a sample. They have different notation, and they
are computed differently. The standard deviation of a population is denoted by
σ and the standard deviation of a sample, by s.
The standard deviation of a population is defined by the following formula:
σ = sqrt [ Σ
( Xi - X )2 / N ]
where σ is the population standard deviation,
X
is the population mean, Xi is the ith element
from the population, and N is the number of elements in the population.
The standard deviation of a sample is defined by slightly different formula:
s = sqrt [ Σ ( xi
- x )2 / ( n - 1 ) ]
where s is the sample standard deviation, x is
the sample mean, xi is the ith element from the sample, and n
is the number of elements in the sample.
And finally, the standard deviation is equal to the square root of the variance.