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. |