Does Averaging Numbers Reduce Their Combined Uncertainty?

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lapo3399
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If an average of three numbers with equal uncertainties is taken, does the average have an uncertainty of the sum of the absolute uncertainties of the three numbers?
e.g. (3.0 +/- 0.1) + (6.0 +/- 0.1) + (9.0 +/- 0.1)/3 = 6.0 +/- 0.3?
This makes sense to me because the three in the denominator has no uncertainty.

p.s. I know this may not seem like it belongs in this forum ( :confused: ), though uncertainties are scientific calculations, so...
 
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Take the square root of the sum of the squares of the values.
 
What values, the uncertainties or the numbers? What will that give me? The uncertainty?
 
The uncertainties, it's going to give you the absolute uncertainty.