What is the mean of a set of measurements (x_{i}) which have ** different**
uncertainties (s_{i})? 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/(s_{i})^{2}. Weighted mean
Put
in 10 values for x_{i} and s_{i
}(hit **Autofill**, then **Plot**). If the s_{i}
are consistent, we expect approx two thirds of the points to
lie within their s_{i } values of . Note,
if the s_{i } values are equal ( i.e. s_{i} =
s), the formula becomes as
for the sample mean. |