Let's say there are two research groups that measure some interesting quantity $x$.
Group A measures $x_A = 5.3 \pm 0.4$
Group B measures $x_B = 5.7 \pm 0.6$
Let's assume the uncertainties are standard deviations of normal distributions.
I am interested in what the best estimator for $x$ is? Does one simply calculate a weighted mean with weights $w_i = 1/\Delta x_i$? If so, what is the resulting uncertainty?
