I have $N$ rulers that each have a different but known level of accuracy, e.g. one's a meterstick, one's a yard stick, etc.
I measure the length of my table using each ruler.
How do I combine those $N$ measurements? If I simply take the mean and standard deviation of all the measurements, does that neglect the (known) systematic uncertainty of each measurement?
I would assume it does, so I would assume I would want to take a weighted mean and a weighted standard deviation with weights 1/$\sigma$, where $\sigma$ is the uncertainty from each ruler. Is that right?
If each ruler has a different uncertainty, is it possible to create a histogram or density plot of the results? How would I obtain, say, the 86% percentile?