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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,
Uses Arithmetic mean is widely used because of the following reasons: Mean is the simplest average to understand and easy to compute. It
Weighted Arithmetic Mean Another aspect to be considered is the importance we assign to each observation. The arithmetic mean as we calculated it so far gives equal
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