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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,
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Each weekend, Derek either reads a book (B), goes to the cinema (C), visits his local museum (M), or plays squash (S). If he reads a book one weekend, then he will take part in one
worked model
Examples of grouped, simple and frequency distribution data
Features of index numbers
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