The weighted averaged of $N$ vectors $x_j$ with covariance matrices $W_j$ (with $j$, integers from $1$ to $N$) is:
$$\bar x = \left(\sum_{j=1}^{N}W_j^{-1}\right)^{-1}\left(\sum_{j=1}^{N}W_j^{-1}x_j\right).$$
If $(\bar x)_i$ is the $i^{th}$ element of the vector $\bar x$, can $(\bar x)_i$ be out of the range of all the $(x_j)_i$ values?
e.g $\bar x_i > \max[(x_j)_i]$ or $\bar x_i <\min[(x_j)_i]$.