Weighted average that takes error into account?

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My data consists of values with an error (from non-linear curve fitting), for example:
value#1=2.3322e-10 error#1=8.7707e-13
value#2=2.3257e-10 error#2=1.2317e-12
What would be the most appropriate way to produce an average of the values that would take the error of each value into account?
For example, value#2 has a larger error so it would have less "weight" in the total average.
Thanks.
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Walter Roberson
Walter Roberson 2019-11-9
Then it is really up to you. There are circumstances where the weighting should be inverse linear. There are circumstances where it should be . There are circumstances where the relationship should be exponential.

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回答(1 个)

Star Strider
Star Strider 2019-11-9
It depends on what you mean by ‘error’. In regressions, data are commonly weighted by the inverse of the variance, so the larger the variance, the smaller the weight.
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