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R, 49 bytes

function(l)Reduce(function(x,y)(x+y)/2,l)-mean(l)

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Pretty straightforward implementation. Reduce(mean,l)-mean(l) would be nice, but mean is not a binary function. Alas.

R, 51 bytes

function(l,L=sum(l|1))sum(l*2^(c(1,1:(L-1))-L)-l/L)

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This approach is perhaps more amenable to an improvement that I have overlooked.