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Suppose I have the numbers below. Consider them as results of some measurement.

 22.73  +2.15  -1.81
 23.81  +1.77  -1.54
 28.6  +11.4   -6.4 
 29.59  +8.58  -5.43

The numbers on the 2nd and 3rd columns are the errors associated to the values in the 1st one. I would like to know how to calculate an average of those numbers taking the errors in account. According to what I saw on the net, I should use a weighted average, but I was unable to find an example which uses values like those above, i.e. with unequal errors.

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  • $\begingroup$ It is unusual, although certainly not impossible, for errors to be given as two distinct values. Please explain in your question more precisely what those error values mean. How were they obtained? $\endgroup$ – whuber Jan 27 '14 at 20:33
  • $\begingroup$ No, it's common in scientific papers. At least those that I have seen. The measurements are distances in parsecs for the same star but calculated by distinct teams. For example, "22.73 +2.15 -1.81" means (I guess...) that the distance is between 20.92 and 24.88 parsecs in an 1 sigma interval with the average being 22.73. $\endgroup$ – Bruno Alessi Jan 29 '14 at 18:14
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    $\begingroup$ I will not dispute that such a notation might be commonplace within a particular community, but my point still stands: it is not generally understood and may be subject to multiple different interpretations. You will therefore reach far more people who can potentially answer your question,and avoid confusing people who are not part of that community, if you would explain what these numbers mean and how they have been obtained. $\endgroup$ – whuber Jan 29 '14 at 18:19
  • $\begingroup$ Unfortunately I don't know such details, for many things are taken for granted or presupposed in scientific papers... they are not dealing with statistics per se but using it as a (very powerful) tool. That's why I originally posted this question in the Physics forum. $\endgroup$ – Bruno Alessi Jan 30 '14 at 14:11
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Asymmetrical errors usually arise from using the maximum likelihood method, particularly often this is used by particle physicists. If this is such a case, then I recommend this paper.

The author discusses the need for special treatment of those errors and then proposes couple of models to do so. It also links to very useful java application for computing.

Have fun and show it to others - it is not widely known :).

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  • $\begingroup$ Gung, many thanks for the suggestion. I were dealing with star distances and parallaxes, but will read the paper and tell my Lab teacher about it (I asked him this same question) $\endgroup$ – Bruno Alessi Apr 24 '14 at 21:08

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