The school board of any Class I, II, III, or IV school district shall establish a permanent and continuing census or enumeration of school children in the school district. The list in writing of the names of the children and taxpayers shall not be required to be reported, but the names of all of the children belonging to such school district, from birth through twenty years of age, shall instead be kept in a depository maintained by such school district and subject to inspection at all times. Such record shall not or need not include the names of all the taxpayers in the district.