Weighted average with uneven errors

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Cant seem to find information on this anywhere...

If I want to average two values with errors, say

x1 = 10 +/- 2
x2 = 12 +/- 4

I would do a regular weighted average that would reflect the fact that x1 is a more precise measurement.

But what if my errors are asymmetric? So if I had

x1 = 10 +2/-1
x2 = 12 +3/-4

How would I take the average of those values? My first thought was to somehow "normalize" x1 and x2 such that they have symmetric errors, but I am not sure whether that is valid or how I would do that. Anyone have any ideas? thanks...
 

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  • #2
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Cant seem to find information on this anywhere...

If I want to average two values with errors, say

x1 = 10 +/- 2
x2 = 12 +/- 4

I would do a regular weighted average that would reflect the fact that x1 is a more precise measurement.

But what if my errors are asymmetric? So if I had

x1 = 10 +2/-1
x2 = 12 +3/-4

How would I take the average of those values? My first thought was to somehow "normalize" x1 and x2 such that they have symmetric errors, but I am not sure whether that is valid or how I would do that. Anyone have any ideas? thanks...
What are these values? Assuming they are random sample means from the same population, it's usual to express the uncertainty of the estimate in terms of confidence intervals (CI)which in turn are based on the standard error of the sample mean.

If so, the asymmetry of these intervals suggest the original data was transformed for analysis because the data was not normally distributed. Moreover the CIs should not be this different. Because of this and the lack of other information, I can't recommend any "safe" way to combine the two estimates.

EDIT: To make matters worse, the asymmetry indicates the two samples are skewed in different directions!
 
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