# Error Calculation on an Average of Errors

Recently I have done an experiment with diffraction grating. I had to calculate 'N' (number of lines per meter) from the equation sin($${\theta}$$)=pN$${\lambda}$$. I then required an average N to use in another calculation.

I had 4 different average results for each angle (2 per each order, p=1 and p=2).

With those 4 average angles, I calculated the uncertainty with std:

Angle 1(p=1): 20.283° +/- 0.00882°
Angle 2(p=1): 21.280° +/- 0.29006°
Angle 3(p=2): 43.393° +/- 0.00667°
Angle 4(p=2): 45.540° +/- 0.01000°

However, using the equation I took those 4 angles for 4 different N values and then I found the average N to use for another calculation.

How do I calculate the error on the average N?

I know how to propagate my error with the equation. I just am not sure how to find the error on my average N based off 4 uncertainties.

Any help would be appreciated. Thanks.