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

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In summary, to find the error in a mean value when given the errors of each individual value, you can take the lowest and highest possible numbers for each value, find the mean of those, and then use that to calculate the error. For independent measurements with gaussian uncertainties, the variance of the sum is equal to the sum of the variances. This means that for finding the error in the mean, you would take the square root of the sum of the variances of each individual value. It is also important to note that this method may result in an over-estimate of the error.
  • #1
Pandabasher
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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.
 
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  • #2
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.
 
  • #3
for independent measurements, with gaussian uncertainties: the variance of the sum is the sum of the variances.
so for:

[itex]z=x_1+x_2[/itex] means [itex]\sigma_z=\sqrt{\sigma_1^2 + \sigma_2^2}[/itex]

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?
 

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