5.14. Least-squares calculation of a weighted mean and its standard uncertainty

UncertRadio applies a matrix-based procedure described in Section 5.4:

x = A y.

The single activity values \(A_{i}\ \)are taken as elements of the vector x. The design matrix A = (1,1,…,1)^T in this case has only one column the elements of which all are equal to1; y reduces to a vector consisting of only one value, the desired weighted mean.

For applying this procedure, the quadratic covariance matrix Ux is needed. UncertRadio assembles all the data into the corresponding algebraic elements and calculates also the required elements of the covariance matrix as already described for the weighted mean. The matrix Uy consists of only one element, the variance associated with weighted mean.