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Hi Readers,
The correct formula is implemented in several Excel templates that are
posted under Documents on ai-geostats. Its veracity can be proved heuristically
by replacing all variable weights with unity (1), and watch the
weighted average turn into the arithmetic mean, the variance of the weighted
average into the Central Limit Theorem, and the degrees of freedom into the
positive integer df=n-1. The formula applies to area-, count-,
density-, distance-, length, mass and volume-weighted averages.
The variance of the weighted average derives from the properties of
variances. William Volk's Applied Statistics for Engineers, deals
exhaustively with the properties of variances. Amazon.com carries
offers preread copies of Volk's textbook.
Kind regards,
Jan W Merks
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