  We analyze data from several studies of metal-poor stars in the Milky Way,
focusing on both strong (Eu) and weak (Sr) $r$-process elements. Because these
elements were injected in an explosion, we calculate the mass swept up when the
blast wave first becomes radiative, yielding a lower limit for the dilution of
such elements and hence a lower limit on the ejecta mass which is incorporated
into the next generation of stars. Our study demonstrates that in order to
explain the largest enhancements in [Eu/Fe] observed in stars at low [Fe/H]
metallicities, individual $r$-process production events must synthesize a
minimum of $10^{-3.5} M_{\odot}$ of $r$-process material. We also show that if
the site of Mg production is the same as that of Eu, individual injection
events must synthesize up to $ \sim 10^{-3} M_{\odot}$ of $r$-process material.
On the other hand, demanding that Sr traces Mg production results in
$r$-process masses per event of $\sim 10^{-5} M_{\odot}$. This suggests that
the astrophysical sites responsible for the genesis of the strong $r$-process
elements need to operate at a drastically reduced rate when compared to
core-collapse supernovae, while the synthesis of the weak $r$-process material
is consistent with a supernova production site.
