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Standard deviation of the mean
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The standard deviation of the mean of N measurements, each with the same standard deviation s,  is

 

i.e. the more measurements we take the more precise is our estimate of the mean. 

This is as expected. However, it is only true if the measurement uncertainties are independent, i.e. there is no systematic error included in the uncertainty s, such as instrument calibration error, zero offset, etc.

 

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1999, 2000 The University of Liverpool, Department of Physics

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