How to phrase a list that continually refers to the first word in the list

To write succinctly, we can use

The census shall provide the total number, structure and spatial distribution of the population.

The census shall describe the population: its count, structure and geographical distribution.

I substitute 'describe' for 'provide', since what the census provides is not the elements enumerated but an account of them. You could say "population's count, structure, &c"; my construction is just a tad more formal.

'Total' is superfluous, and creates an ambiguity respecting which terms it modifies.

I say 'geographical' distribution because 'spatial' implies that there will be some account of which story various demographics occupy!