  Asteroseismic scaling relations are often used to derive stellar masses and
radii, particulaly for stellar, exoplanet, and Galactic studies. It is
therefore important that their precisions are known. Here we measure the
intrinsic scatter of the underlying seismic scaling relations for $\Delta\nu$
and $\nu_{\rm max}$, using two sharp features that are formed in the H--R
diagram (or related diagrams) by the red giant populations. These features are
the edge near the zero-age core-helium-burning phase, and the strong clustering
of stars at the so-called red giant branch bump. The broadening of those
features is determined by factors including the intrinsic scatter of the
scaling relations themselves, and therefore it is capable of imposing
constraints on them. We modelled Kepler stars with a Galaxia synthetic
population, upon which we applied the intrinsic scatter of the scaling
relations to match the degree of sharpness seen in the observation. We found
that the random errors from measuring $\Delta\nu$ and $\nu_{\rm max}$ provide
the dominating scatter that blurs the features. As a consequence, we conclude
that the scaling relations have intrinsic scatter of $\sim0.5\%$ ($\Delta\nu$),
$\sim1.1\%$ ($\nu_{\rm max}$), $\sim1.7\%$ ($M$) and $\sim0.4\%$ ($R$), for the
SYD pipeline measured $\Delta\nu$ and $\nu_{\rm max}$. This confirms that the
scaling relations are very powerful tools. In addition, we show that standard
evolution models fail to predict some of the structures in the observed
population of both the HeB and RGB stars. Further stellar model improvements
are needed to reproduce the exact distributions.
