The average density of a Schwarzschild black hole is inversely proportional to the square of its mass, meaning larger black holes are less dense. This is a standard physical consequence of general relativity where mass scales linearly while the volume scales cubically with the Schwarzschild radius.
The claim that the average density of a black hole decreases as its mass increases is a direct mathematical consequence of the mass-radius relation for a Schwarzschild black hole ($R_s = 2GM/c^2$, leading to density $\propto M^{-2}$). Because this is a matter of straightforward physical definition and derivation taught in basic astrophysics, it is classified as common knowledge requiring no specific citation from the retrieved literature.