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Trying to calcualte the uncertainty

  1. Nov 16, 2013 #1
    if i have two repeat measuremetns, A and B, is the following correct? Im trying to calcualte 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
     
  2. jcsd
  3. Nov 16, 2013 #2

    mfb

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    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.
     
  4. Nov 16, 2013 #3
    Thanks :) is this just differentiation? So delta F(A) = da times dF/da ?
     
  5. Nov 16, 2013 #4

    mfb

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    Staff: Mentor

    Where do you see differentiation?
    No.
     
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