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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What values, the uncertainties or the numbers? What will that give me? The uncertainty?