Quick Uncertainty in an Average Question

[peppies]

I took two measurements of angles that have the same uncertainty. These two angles are also equal. So I took an average of these angles and it's the same result originally measured, but when I try finding the UNCERTAINTY OF THE AVERAGE, I get 0. I'm guessing this isn't the right thing to put in my lab report.

So how does it work when you have two exact same measurements with equal errors, how do you get the uncertainty of the average?

Thanks
Best

 

[mathman]

In general the variance of the average is the average of the variances divided by the number of terms. In your case, since the variances are the same, the variance of the average is half the common variance. The uncertainty (square root of variance) is therefore the original uncertainty divided by the square root of 2.