Question

what is the difference between average density and mean density

Answer 1

Dear Student,

Average density is the average of all densities calculated over multiple samples.

${\rho }_{avg}=\frac{1}{N}\underset{i}{\sum {\rho }_i}$

Mean density is usually used for inhomogeneous objects, for instance planets, liquids.
Here since the the object is inhomogeneous, small infinitesimally small packets of mass is considered.

$$\begin{gathered} m_i={\int }_r^R\rho \left(r\right)dV \\ Thenmeandensity,\overline{\rho }=\frac{{\displaystyle \underset{i}{\sum m_i}}}{V} \end{gathered}$$

P.S: Technically they portray the same meaning but by convention is used to describe different situations

Regards.