  The stochastic nature of star formation and photon propagation in
high-redshift galaxies can result in sizable galaxy-to-galaxy scatter in their
properties. Ignoring this scatter by assuming mean quantities can bias
estimates of their emissivity and corresponding observables. We construct a
flexible, semi-empirical model, sampling scatter around the following mean
relations: (i) the conditional halo mass function (CHMF); (ii) the
stellar-to-halo mass relation (SHMR); (iii) galaxy star formation main sequence
(SFMS); (iv) fundamental metallicity relation (FMR); (v) conditional intrinsic
luminosity; and (vi) photon escape fraction. In our fiducial model, ignoring
scatter in these galaxy properties overestimates the duration of the EoR,
delaying its completion by up to $\Delta z$ ~ 2. We quantify the relative
importance of each of the above sources of scatter in determining the ionizing,
soft-band X-ray and Lyman Werner (LW) emissivities as a function of scale and
redshift. We find that scatter around the SFMS is important for all bands,
especially at the highest redshifts where the emissivity is dominated by the
faintest, most "bursty" galaxies. Ignoring this scatter would underestimate the
mean emissivity and its standard deviation computed over 5 cMpc regions by
factors of up to $\sim$2-10 at $5< z < 15$. Scatter around the X-ray luminosity
to star formation rate relation is important for determining X-ray emissivity,
accounting for roughly half of its mean and standard deviation. The importance
of scatter in the ionizing escape fraction depends on its functional form,
while scatter around the SHMR contributes at the level of ~10-20%. Although
scatter does flatten the UV luminosity functions, shifting the bright end by
1-2 magnitudes, the level of scatter in our fiducial model is insufficient to
fully explain recent estimates from JWST photometry (consistent with previous
studies).
