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I've got a bit of a problem with estimating the overall error in measurement of a function which I have sampled at sixteen independent points and have calculated the associated error bar with each point. The problem is I'm not sure how to combine all the sixteen errors into a single average error for all my measurements in one go.

At the moment I am simply using this method: √(1/[itex]\sum[/itex](1/weights

*)) where the weights are 1/[itex]\sigma[/itex]*

*^2. The problem is this is not giving me a value for the total standard deviation that I expect therefore I do not trust it but is this the correct method? Are there any others?*

It might be important to point out that the errors on f(x) vary as approximately as x^2 + C, e.g. they are large when approaching 0 and large when x is large. Therefore I needed to use weighted methods to estimate the total standard deviation as an unweighted average will change depending on the range of x I sample over, e.g. the error goes to infinity if I average over infinity.

Thanks for any help physics forum!It might be important to point out that the errors on f(x) vary as approximately as x^2 + C, e.g. they are large when approaching 0 and large when x is large. Therefore I needed to use weighted methods to estimate the total standard deviation as an unweighted average will change depending on the range of x I sample over, e.g. the error goes to infinity if I average over infinity.

Thanks for any help physics forum!