  In this paper we analyze the behavior of the daily Sunspot Number from the
Sunspot Index Data Center (SIDC), the mean Magnetic Field strength from the
National Solar Observatory/Kitt Peak (NSO/KP) and Total Solar Irradiance means
from Virgo/SoHO, in the context of the $q$--Triplet which emerges within
nonextensive statistical mechanics. Distributions for the mean solar Magnetic
Field show two different behaviors, with a $q$--Gaussian for scales of 1 to 16
days and a Gaussian for scales longer than 32 days. The latter corresponds to
an equilibrium state. Distributions for Total Solar Irradiance also show two
different behaviors (approximately Gaussian) for scales of 128 days and longer,
consistent with statistical equilibrium and $q$--Gaussian for scales $<$ 128
days. Distributions for the Sunspot Number show a $q$--Gaussian independent of
timescales, consistent with a nonequilibrium state. The values obtained
("$q$--Triplet"$\equiv$$\{$$q$$_{stat}$,$q$$_{sen}$,$q$$_{rel}$$\}$)
demonstrate that the Gaussian or $q$--Gaussian behavior of the aforementioned
data depends significantly on timescales. These results point to strong
multifractal behavior of the dataset analyzed, with the multifractal level
decreasing from Sunspot Number to Total Solar Irradiance. In addition, we found
a numerically satisfied dual relation between $q_{stat}$ and $q_{sen}$.
