We prepare static granular beds under gravity in different stationary states by tapping the system with pulsed excitations of controlled amplitude and duration. The macroscopic state|defined by the ensemble of static configurations explored by the system tap after tap|for a given tap intensity and duration is studied in terms of volume, V, and force moment tensor, &Sgr;. In a previous paper [Pugnaloni et al., Phys. Rev. E 82, 050301(R) (2010)], we reported evidence supporting that such macroscopic states cannot be fully described by using only V or &Sgr;, apart from the number of particles N. In this work, we present an analysis of the fluctuations of these variables that indicates that V and &Sgr; may be sufficient to define the macroscopic states. Moreover, we show that only one of the invariants of &Sgr; is necessary, since each component of &Sgr; falls onto a master curve when plotted as a function of Tr(&Sgr;). This implies that these granular assemblies have a common shape for the stress tensor, even though it does not correspond to the hydrostatic type. Although most results are obtained by molecular dynamics simulations, we present supporting experimental results.