Trying to calcualte the uncertainty

[lavster]

if i have two repeat measuremetns, A and B, is the following correct? I am trying to calculate the uncertainty... I know there are easier ways to do this but i need to have the uncertainty of the mean in terms of δ(A-B).

from pairs of measurements A and B at each setting we have:
δ(A-B)=〖(〖δA〗^2+〖δB〗^2)〗^(1/2)
=√2 δA
(since δA=δB).

Rearrangement of this equation gives the uncertainty of a single measurement:

δA=(δ(A-B))/√2

Now considering the mean of each pair of measurements:

δ((A+B)/2)=δA/√2=(δ(A-B))/2

In particular, is is correct to have the √2 in the denominator in the last line?

Thanks

 

[mfb]

It is correct, but I would not replace δB with δA even if they are equal, that is just confusing.
You can get the same result without the detour of δ(A-B), as δ(A+B)=δ(A-B) and δ(X/2)= (δX)/2 for all X.

 

[lavster]

Thanks :) is this just differentiation? So delta F(A) = da times dF/da ?

 

[mfb]

Where do you see differentiation?

So delta F(A) = da times dF/da ?

No.