Working with block groups, I've noticed discrepancies between the households by size and the household population, for example, suppose I have a block group with the following:

- population in occupied households: 1454

- households by household size:

- 1: 89
- 2: 273
- 3: 72
- 4: 97
- 5: 31
- 6: 0
- 7+: 0

To get household population by household size, I would think that I could take each household count for sizes 1-6, and multiply them by the corresponding household size. The pop for 7+ households would then be the total household population minus the sum of the calculated populations for household sizes 1-6. So for this case:

- 1: 89
- 2: 546
- 3: 216
- 4: 388
- 5: 155
- 6: 0
- total pop for household sizes 1 - 6: 1394
- remaining for 7+: 89

Note the inconsistency here: we have 0 7+ plus households, but we to match the household population we would theoretically need to have 89 in this group. I've also noticed cases where the inverse is true: there are 7+ households, but adding the implied total across 1-6 household size groupings is larger than the entire household population for the block group (i.e. the pop in 7+ households would then be negative).

So I guess I'm looking for suggestions as to why this is occurring and on how to make this more consistent.

My first inclination is to scale the population variables so that they match the implied population in the household sizes, but am curious if anyone has dealt with this differently.