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Mathematical Properties
The sum of deviations of the items from the arithmetic mean (taking signs into account) is always zero, i.e. = 0.
The sum of the squared deviations of the items from arithmetic mean is less than the sum of the squared deviations of the items from any other value, i.e. is less than where A is any other point, different from .
Since, = , (N x ) = .
If we have the arithmetic mean and number of items of two or more than two groups, we can compute combined average of these groups, by applying the following formula:
where,
Cluster Analysis could be also represented more formally as optimization procedure, which tries to minimize the Residual Sum of Squares objective function: where μ(ωk) - is a centr
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First Moment of Dispersion or Mean Deviation Mean deviation or the average deviation is the measure if dispersion which is based upon all the items in a variable .It is the a
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