Calculating Mean Value Error: Tips for Undergrad Lab Work | Matt's Question

[Pandabasher]

Homework Statement

I'm an undergrad doing labs, and I was wondering how to get the error in a mean value, given that I know the errors of each individual value? This is probably a simple question, but any help is appreciated. Thanks, Matt.

 

[yortzec]

Try looking at the errors of each individual value and find the lowest possible number for each, and find the mean of that. Then do this again for the highest possible number. Then you have the lowest possible mean, and the highest possible mean, and from that you can find the error.

 

[Simon Bridge]

for independent measurements, with gaussian uncertainties: the variance of the sum is the sum of the variances.
so for:

$z=x_1+x_2$ means $\sigma_z=\sqrt{\sigma_1^2 + \sigma_2^2}$

for the mean you have N of them: can you wrok it out now?
(good practice - and it builds character xD)

@yortzec: I would have thought gaussian uncertainties would be more tightly distributed than that - won't that method give an over-estimate?