Suppose you have a series of measurements each of which has its own constant error derived from the sensibility of the tool. In this case in order to obtain the average you'd think of using the weighted average which, due to how the error is the same for every measure, is equal to the simple average formula. Regarding the error instead, the weighted error would end up being
$<br /> \sigma_w^2=\frac{\sigma_0^2}{n}<br />$
Where sigma0 is the constant error and n is the number of measurements. The doubt is that this set of measures is not made of means and therefore a "weighted mean" didn't make too much sense to me because I also needed to consider the standard deviation of all the measures, so I ended up thinking that the final error should be
$<br /> \sigma^2=\sigma_s^2+\sigma_w^2<br />$
where sigma s is simply the standard deviation of all the measures, summed in a square sum with the weighted error. Is this actually a correct method?