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What is the mean of a set of measurements (xi) which have different
uncertainties (si)? The more accurate values are more significant
than the less accurate ones. Accordingly we calculate a mean as
before but with each value weighted by the inverse of its variance: 1/(si)2. Weighted mean
  Put
in 10 values for xi and si
(hit Autofill, then Plot).
If the si
are consistent, we expect approx two thirds of the points to
lie within their si values of  . Note,
if the si values are equal ( i.e. si =
s), the formula becomes  as
for the sample mean. |
and if si = s
(equal uncertainties) this formula becomes 
as
for the sample mean.
