Editing Weighted arithmetic mean (section)

===Accounting for correlations===
{{see also|Generalized least squares|Variance#Sum of correlated variables}}
In the general case, suppose that <math>\mathbf{X}=[x_1,\dots,x_n]^T</math>, <math>\mathbf{C}</math> is the [[covariance matrix]] relating the quantities <math>x_i</math>, <math>\bar{x}</math> is the common mean to be estimated, and <math>\mathbf{J}</math> is a [[design matrix]] equal to a [[vector of ones]] <math>[1, \dots, 1]^T</math> (of length <math>n</math>). The [[Gauss–Markov theorem]] states that the estimate of the mean having minimum variance is given by:
:<math>\sigma^2_\bar{x}=(\mathbf{J}^T \mathbf{W} \mathbf{J})^{-1},</math>
and
:<math>\bar{x} = \sigma^2_\bar{x} (\mathbf{J}^T \mathbf{W} \mathbf{X}),</math>

where:

:<math>\mathbf{W} = \mathbf{C}^{-1}.</math>