function [mean,stdev] = ewmean(values,errors);
% [Mean, Stdev] = ewmean(values,errors) returns the error-weighted
% mean of the data. values and errors have to be the same size.
%
% The error-weighted mean is Sigma(Wi * Xi) / Sigma(Wi)
% where Xi are the values and Wi are the weights, such that
% Wi = 1/(errori ^2).
%
% The uncertainty is given by 1/sqrt(Sigma(Wi)).
%
weights = 1./(errors.^2);
mean = (sum(sum(weights.*values)))./(sum(sum(weights)));
stdev = 1./sqrt(sum(sum(weights)));