I have samples from normal distributions with the same mean but different standard deviations. I know the corresponding standard deviation for each sample. Is there a way to more accurately estimate mean other than taking an average over all the samples?
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Yes. What you want to do is weight the observations with the smaller variances more than those with the larger variances. I'm sure someone here will supply the correct weights for you. – soakley May 09 '14 at 18:34
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In general, your weights are directly inversely proportional to the variances. Suppose you have two random variables. If the first has $\sigma_1^2 = 1$ and the second has $\sigma_2^2=4,$ then the weight on the first will be 80% and the second will get 20%. – soakley May 09 '14 at 18:59