On 10/10/2013 22:35, James Waldby wrote: > On Thu, 10 Oct 2013 22:15:46 +0200, Cristiano wrote: > >> In this link: >> http://en.wikipedia.org/wiki/Weighted_arithmetic_mean#Statistical_properties >> >> there is the formula sigma(x_bar) = sqrt(...). >> I need to find the n w's which give the smallest possible sigma(x_bar). >> Please, could somebody help me? > > Your question might not be well-posed. If you are given a set of > sigma_i values and want to minimize their weighted sum of squared > values, and weights add up to 1, find the minimum sigma_j, > set w_j = 1, and set w_i = 0 for i other than j. If weights don't > have to add up to 1, set them all to zero, which gives sigma(x_bar)=0.
The additional constraint is that all the w's must be greater than 0.