Every court ruled in favor of the House of Representatives. At least for now statistical sampling will not substitute for enumeration for purposes of apportionment. By requiring an actual enumeration, the Framers intended to avoid political controversy that would surely accompany a more lax accounting protocol. What is not generally appreciated is that apportionment is related to, but not equivalent to redistricting. Apportionment is the distribution of Representatives among the states.
Every state is entitled to at least one, but the actual number increases with population.
The record of the case presented to the Court suggested that if sampling were used instead of enumeration, perhaps three states would loose representatives to other states. Redistricting, by contrast, is the division of a state into Congressional districts. Creative delineation of districts can group constituents to maximize the number of representatives for a political party. The Constitution does not mandate that Census numbers be used for redistricting. Moreover, Federal Court review mitigates flagrant political use of the redistricting process and would probably give little weight to the use of population figures other than Census Bureau numbers.