  The energy dependence of the spectral fluctuations in the interacting boson
model (IBM) and its connections to the mean-field structures have been analyzed
through adopting two statistical measures, the nearest neighbor level spacing
distribution $P(S)$ measuring the chaoticity (regularity) in energy spectra and
the $\Delta_3(L)$ statistics of Dyson and Metha measuring the spectral
rigidity. Specifically, the statistical results as functions of the energy
cutoff have been worked out for different dynamical situations including the
U(5)-SU(3) and SU(3)-O(6) transitions as well as those near the AW arc of
regularity. It is found that most of the changes in spectral fluctuations are
triggered near the stationary points of the classical potential especially for
the cases in the deformed region of the IBM phase diagram. The results thus
justify the stationary point effects from the point of view of statistics. In
addition, the approximate degeneracies in the $2^+$ spectrum on the AW arc is
also revealed from the statistical calculations.
