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Two well studied compounds $Sr_{3} Cr_{2} O_{8}$ and $Ba_{3} Cr_{2} O_{8}$ are insulating dimerized antiferromagnets with magnetic ions. These ions are located in hexagonal bilayers with a strong intradimer antiferromagnetic interaction, that leads to a singlet ground state and gapped triplet states We report on the effect on the structural and magnetic properties of the spin-$\frac{1}{2}$-dimer system, $Sr_{3} Cr_{2} O_{8}$, by introducing chemical disorder. Two large single crystals of $Ba_{3-x} Sr_{x} Cr_{2} O_{8}$ were grown. The structural and magnetic properties of these compounds were studied by magnetization, heat-capacity and inelastic neutron scattering measurements. These results show a noticeable change in the magnetic properties by a random substitution effect.