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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,
Use the given information to find the P-value. The test statistic in a two-tailed test is z = 1.49 P-value = (round to four decimal places as needed)
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Calculation for Continuous Series or Grouped Data = where, m = mid-point of class =
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