  We report a structural/magnetic investigation by X-ray absorption
spectroscopy (XAS), neutron diffraction, dc-susceptibility ($\chi_{\mbox{dc}}$)
and electron spin resonance (ESR) of the 12R-type perovskite
BaTi$_{1/2}$Mn$_{1/2}$O$_{3}$. Our structural analysis by neutron diffraction
supports the existence of structural trimers with chemically disordered
occupancy of Mn$^{4+}$ and Ti$^{4+}$ ions, with the valence of the Mn ions
confirmed by the XAS measurements. The magnetic properties are explored by
combining dc-susceptibility and $X$-band ($9.4$ GHz) electron spin resonance,
both in the temperature interval of $2\leq T\leq1000$ K. A scenario is
presented under which the magnetism is explained by considering magnetic dimers
and trimers, with exchange constants $J_{a}/k_{B}=200(2)$ K and
$J_{b}/k_{B}=130(10)$ K, and orphan spins. Thus, BaTi$_{1/2}$Mn$_{1/2}$O$_{3}$
is proposed as a rare case of an intrinsically disordered $S=3/2$ spin gap
system with a frustrated ground state.
