(ax + by)/(a + b) = z (ax + by)/(a + b) = z then it will be true that the distances to the mean are inversely proportional to the weights: (z - x)/(y - z) = b/a so that a(z - x) = b(y - z) How can we show this to be true algebraically?
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Pretty straight forward: From (ax+ by)/(a+ b)= z, ax+ by= (a+ b)z= az+ bz. ax- az= a(x- z)= bz- by= b(z- y) (x- z)/(z- y)= b/a
Many Thanks