The tax commissioner shall order a reappraisal of all real property in each county once in each six-year period. The commissioner may order the commencement of any sexennial reappraisal in sufficient time for the county auditor to complete the reappraisal as required by section 5713.01 of the Revised Code. The commissioner may order a reassessment of the real property or any class thereof in any taxing district or subdivision thereof in the third calendar year following the year in which a sexennial reappraisal is completed if in his opinion such property has been unequally or improperly assessed, so that all classes of property in such district shall be assessed in compliance with law.