  The dynamics of attractive bosons trapped in one dimensional anharmonic
potentials is investigated. Particular emphasis is put on the variance of the
position and momentum many-particle operators. Coupling of the center-of-mass
and relative-motion degrees-of-freedom necessitates an accurate numerical
treatment. The multiconfigurational time-dependent Hartree for bosons (MCTDHB)
method is used, and high convergence of the energy, depletion and occupation
numbers, and position and momentum variances is proven numerically. We
demonstrate for the ground state and out-of-equilibrium dynamics, for condensed
and fragmented condensates, for small systems and {\it en route} to the
infinite-particle limit, that intriguing differences between the density and
variance of an attractive Bose-Einstein condensate emerge. Implications are
briefly discussed.
