  We analyze the properties of a sample of long gamma-ray bursts (LGRBs)
detected by the Fermi satellite that have a spectroscopic redshift and good
follow-up coverage at both X-ray and optical/nIR wavelengths. The evolution of
LGRB afterglows depends on the density profile of the external medium, enabling
us to separate wind or ISM-like environments based on the observations. We do
this by identifying the environment that provides the best agreement between
estimates of $p$, the index of the underlying power-law distribution of
electron energies, as determined by the behavior of the afterglow in different
spectral/temporal regimes. At 11 rest-frame hours after trigger, we find a
roughly even split between ISM-like and wind-like environments. We further find
a 2$\sigma$ separation in the prompt emission energy distributions of wind-like
and ISM-like bursts. We investigate the underlying physical parameters of the
shock, and calculate the (degenerate) product of density and magnetic field
energy ($\epsilon_B$). We show that $\epsilon_B$ must be $\ll 10^{-2}$ to avoid
implied densities comparable to the intergalactic medium. Finally, we find that
the most precisely constrained observations disagree on $p$ by more than would
be expected based on observational errors alone. This suggests additional
sources of error that are not incorporated in the standard afterglow theory.
For the first time, we provide a measurement of this intrinsic error which can
be represented as an error in the estimate of $p$ of magnitude $0.25 \pm 0.04$.
When this error is included in the fits, the number of LGRBs with an identified
environment drops substantially, but the equal division between the two types
remains.
