However, the spatial distribution of population and dwelling density is not uniform. Following figures show how population and dwelling density vary as we move away from city center. I drew multiple 10 km rings in ArcGIS overlaid on top the mesh block and population data. Population and dwellings in each ring are counted and divided by the sum of mesh block areas to get the densities.
Dwelling densities vary from more 1800 dwellings/sq-km to near zero. Similarly, population densities vary from more than 4000 persons/sq-km to near zero. Obviously, the average densities decrease as we go farther out from the city center. However, this does not necessarily mean a neighborhood in the middle of the city is always denser than a neighborhood in an outer suburb. One reason that outer suburbs have much average lower density is the existence of vast amount of undeveloped (or non-residential) lands between blocks/neighborhoods.
* UPDATE (03/07/2014)
I have also plotted "ring maps" of dwelling and population density in Melbourne. Starting from a point in CBD, several rings with radius incrementally increasing by 5 km are overlaid on population and dwelling data from Census. The following ring maps may provide a better picture of the spatial distribution of density in Melbourne.