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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,
The Harmonic Mean is based on the reciprocals of numbers averaged. It is defined as the reciprocal of the arithmetic mean of the reciprocal of the given individual observations. Th
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