Granular temperature underpins the kinetic theory of granular flows as well as models for heat transfer, segregation, erosion, attrition, and aggregation in various granular systems. It is generally thought that granular temperature in vibrated granular systems scales with the square of the peak vibrational velocity. However, careful diffusing wave spectroscopy experiments and statistical analysis of data obtained from these for a three-dimensional vibrated bed of monodisperse glass particles reveals that the granular temperature is also significantly correlated with other vibrational parameters. Reexamination of previously published data obtained by others using alternative methods further supports our thus far unremarked upon observation reported here.