|You are working with the text-only light edition of "H.Lohninger: Teach/Me Data Analysis, Springer-Verlag, Berlin-New York-Tokyo, 1999. ISBN 3-540-14743-8". Click here for further information.
In addition to the measures of location for describing the position
of the distribution of a variable, one has to know the spread of the
distribution (and, of course, about its form). Maybe you want to have
a look at the following in
order to see some examples of common means but different spreads.
The spread of a distribution may be described using various parameters,
of which variance is the most common one. Mathematically speaking, the
variance v is the sum of the squared deviations from the mean divided by
the number of samples less 1:
Examination of this formula should lead to at least three questions:
Please note the notation concerning the variance and the standard deviation:
it is depicted as s² (or s, respectively) if it has been calculated
from a sample. If it is computed from a population the standard deviation
is depicted by the Greek letter s
Why take the sum of squares and not, for example, the sum of absolute deviations
from the mean? The answer to this is quite simple: the mathematical analysis
is simpler, if the sum of squares is used.
Why is the sum divided by n-1; wouldn't it be more logical to take just
n? Here again, the answer is simple, but requires the introduction of
the concept of the degree of freedom.
What about the s² in the formula? The parameter s which is apparently
the square root of the variance is called the standard
The variance of some data is closely related to the precision
of a measuring process, as can be seen in the following .
Last Update: 2006-Jšn-18