Upon qualifying in the manner prescribed in section 71.160, the census supervisor shall appoint such enumerators as may be necessary to assist in taking such census, each of whom shall take the same oath as heretofore prescribed for such supervisor, before some officer authorized to administer oaths. Such supervisor and enumerators shall immediately proceed to take a census of such city or town, for the sole purpose of determining the population of such city or town, and no other information shall be taken by such supervisor and enumerators. Upon the completion of such census, the supervisor shall certify the result thereof to the secretary of state, and, from and after the date of the filing of such certificate with the secretary of state, the population of such city or town, as given in such certificate of the supervisor, shall be the legal census and population of such city or town, for all purposes whatsoever, under the constitution and laws of the state.