“Population” and “rate” defined.

(1) "Population" for the purpose of distributing revenues among cities, villages, townships, and counties means population according to the last and each succeeding statewide federal census, or a special statewide census as provided by law, whichever is later. Corrections to the statewide federal census that are published by the bureau of the census, United States department of commerce, and that occur during the period July 1, and ending June 30, shall become effective for the purpose of revenue distributions on the next July 1. Fifty percent of the total number of persons who are wards, patients, or convicts committed to or domiciled in a city, village, or township institution located outside the boundaries of the city, village, or township or committed to or domiciled in a county, state, or federal tax-supported institution, if the persons were included in the federal census, or any special census as provided by law, shall be excluded from the computation. The population of a township is its population outside the corporate limits of villages in the township. The population data used in determining distributions under this act in a year in which a federal decennial statewide census, federal mid-decade statewide census, or special statewide census provided by law is conducted shall become effective for distributions made on and after October 1 of the year for which the respective census is conducted. Once the official population data from a federal decennial statewide census, federal mid-decade statewide census, or special statewide census provided by law is certified and published, the department of management and budget shall calculate any overpayment or underpayment made to a local unit of government since the effective date of the respective census and make adjustments in future distributions to the local unit of government to correct these overpayments or underpayments of revenue distributed pursuant to this act. (2) "Rate" means a figure determined each May 15 by the department of management and budget pursuant to this act from applicable tax data for the preceding calendar year as reported to it by the department of treasury and applicable to payments made during the succeeding period of July 1 to June 30.