Magnetospheric standing Alfv¿n waves are guided along the ambient magnetic field, and their frequency depends on the mass density of the plasma distributed along the field lines. These properties allow us to use Alfv¿n waves to map time-dependent phenomena between space and ground and to estimate the mass density. In this paper we present a statistical study of the spatial variation of the fundamental frequency fT1 of toroidal-mode standing Alfv¿n waves in the L range from 6 to 10, where L indicates the maximum geocentric distance on the field line. The data used for this analysis are energetic particle flux anisotropy (proxy of transverse electric field) and magnetic field measurements from the Active Magnetospheric Particle Tracer Explorers /Charge Composition Explorer (CCE) spacecraft. Using CCE data covering 4 years, we obtained ~5000 20-min intervals containing a clear signature of toroidal waves. The median fT1 is 6--10 mHz at L = 7 and decreases to 4--8 mHz at L = 9. The frequency tends to be lower at noon than at midnight. The observed frequencies are compared with numerically derived frequencies using an empirical mass density model <Gallagher et al., 2000> and a magnetic field model <Tsyganenko, 1989>. We found a good agreement for 1200--2400 magnetic local time (MLT) but a large discrepancy near 0300 MLT. This may indicate that the flux tubes at this local time are more heavily loaded than specified in Gallagher et al.'s <2000> model.