The Arithmetic_Mean = (Sum Xi)/n, and therefore n*Arithmetic_Mean= Sum Xi. This fact motivates me to define a Weighted_Total = n*Weighted_Arithmetic_Mean, where Weighted_Arithmetic_Mean=(Sum Wi*Xi)/Sum(Wi).
The Geometric_Mean = (Prod Xi)^(1/n), and therefore Prod Xi = Geometric_Mean^n. This fact motivates me to define a Weighted_Product = n*Weighted_Geometric_Mean, where Weighted_Geometric_Mean = (Prod Xi^Wi)^(1/Sum Wi).
My first question is do you see anything silly in what I am doing?
And my second is how can I do the same for the Harmonic Mean? That is, how can we define some interesting Weighted Total based on the Harmonic Mean?
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