  We analyze, analytically and numerically, the position, momentum, and in
particular the angular-momentum variance of a Bose-Einstein condensate (BEC)
trapped in a two-dimensional anisotropic trap for static and dynamic scenarios.
The differences between the variances at the mean-field level, which are
attributed to the shape of the BEC, and the variances at the many-body level,
which incorporate depletion, are used to characterize position, momentum, and
angular-momentum correlations in the BEC for finite systems and at the limit of
an infinite number of particles where the bosons are $100\%$ condensed.
Finally, we also explore inter-connections between the variances.
