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Simple question about Error Analysis

  1. Feb 17, 2013 #1
    I'm doing a report on a set of lab data and am supposed to find the mean and mean's standard deviation

    [tex] \bar{x} + \sigma_{\bar{x}} [/tex]

    The mean is given by

    [tex]\displaystyle{ \bar{x} = \sum_{i=1}^{N} w_{i} x_{i} } [/tex]

    Where

    [tex]\displaystyle{ w_{i} = \left( \frac{\sigma}{\sigma_{i}} \right)^2 } [/tex]

    and for the error (mean's standard deviation)

    [tex] \displaystyle{ \sigma_{\bar{x}} = \sigma = \frac{1}{ \sqrt{ \sum_{i=1}^{N} \frac{1}{\sigma_{i}^{2} } } } } [/tex]


    The problem is I can't quite figure it out what the σi would be, is it the standard deviation? This might sound very silly but it's been a long time I've dealt with this.

    Any help is appreciated.
     
  2. jcsd
  3. Feb 17, 2013 #2

    mfb

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    2016 Award

    Staff: Mentor

    σi is the uncertainty (standard deviation*) of data point i.

    *any multiple of it will work as well, if you keep it consistent, as it cancels in the fraction
     
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