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Measurement uncertainty: Standard uncertainty of the mean

  1. Oct 26, 2014 #1
    1. The problem statement, all variables and given/known data
    Hi,

    I am doing some basic X-ray analysis and trying to quantify the measurement uncertainty associated with my determined value for the K-α line of copper. I have obtained the x-ray spectrum from a copper target using a detector and multichannel analyzer (No. of pulses/pulse height as a function of energy in keV). I have identified and isolated the K-α peak. I have fitted a Gaussian/Normal distribution curve to the data, computed the mean value in keV and have computed the sample standard deviation. I now need to compute the standard uncertainty of the mean and I’m unsure of the correct method. As far as I know the standard uncertainty of the mean (u) is given by [1] below where N is the number of measurement readings taken in order to determine the mean value and sigma n-1 is the computed sample standard deviation.


    2. Relevant equations

    U=σn-1/N [1]





    3. The attempt at a solution
    The multi-channel analyzer effectively sorts and counts incident voltages of different magnitudes. I have an array of x-axis data in keV. e.g. x=[2 3 4 5 4 3 2] I am wondering is N the length of the array (=7) or the sum of the array (23)
     
  2. jcsd
  3. Oct 27, 2014 #2

    haruspex

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    Shouldn't that be ##\sigma_{n-1}/\sqrt n##?
     
  4. Oct 27, 2014 #3
    Yes it should be ##\sigma_{n-1}/\sqrt N##
    But what value is N
     
  5. Oct 27, 2014 #4

    haruspex

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    N is the number of values (which is why I wrote n; it's the same n as in σn−1).
     
  6. Oct 27, 2014 #5
    Sorry i was referring to my lecture notes, n makes a lot more sense, thanks
     
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