  We study the 10 fast radio bursts (FRBs) detected in the far side-lobe region
of the CHIME telescope from 2018 August 28 to 2021 August 31. We find that the
far side-lobe events have on average $\sim$500 times greater fluxes than events
detected in CHIME's main lobe. We show that the side-lobe sample is therefore
statistically $\sim$20 times closer than the main-lobe sample. The median
dispersion measure (DM) excess, after removing the Galactic disk component
using the NE2001 for the free electron density distribution of the Milky Way,
of the 10 far side-lobe and 471 non-repeating main-lobe FRBs in the first
CHIME/FRB catalog is 183.0 and 433.9 pc\;cm$^{-3}$, respectively. By comparing
the DM excesses of the two populations under reasonable assumptions, we
statistically constrain that the local degenerate contributions (from the Milky
Way halo and the host galaxy) and the intergalactic contribution to the excess
DM of the 471 non-repeating main-lobe FRBs for the NE2001 model are
131.2$-$158.3 and 302.7$-$275.6 pc cm$^{-3}$, respectively, which corresponds
to a median redshift for the main-lobe FRB sample of $\sim$0.3. These
constraints are useful for population studies of FRBs, and in particular for
constraining the location of the missing baryons.
