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Uncertainties of averages

  1. Sep 17, 2010 #1
    Hi

    Ok, we all know that if a quantity T is measured N times, then all measurements have the same standard deviation (SD). Now, with this assumption one can derive the width of the average to get SD/sqrt(N).

    I have often encountered a dataset D, where each measurement has been assigned no SD. Then one finds the SD for the whole dataset, and then the author uses SD/sqrt(N) to find the width of the average of D.

    My question is: In these cases, then what justifies that SD found from the whole dataset D can be assumed to be valid for each single measurements, such that one can use SD/sqrt(N)?

    I hope you understand.

    Best,
    Niles.
     
  2. jcsd
  3. Sep 17, 2010 #2

    statdad

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    "In these cases, then what justifies that SD found from the whole dataset D can be assumed to be valid for each single measurements"

    The assumption that all the values in the data set come from the same population - one having a constant standard deviation.
     
  4. Sep 18, 2010 #3
    Thanks, that makes sense.

    Best wishes,
    Niles.
     
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