An analysis is presented of the generalized weighted mean of a set of quantities, some or all of which may be correlated, and the variance associated with that mean. The cases covered specifically are (a) two correlated quantities, (b) a general number of quantities, two of which are correlated and (c) a general number of quantities, all of which are correlated. For (c), two instances are treated, namely where the quantity variances are equal and unequal. Consistency of the data representing realizations of the quantities concerned is shown to be important in terms of appreciating the results obtained.
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Cox et al. (2006) studied this question.
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