(1) The board of a school district other than a primary school district may establish 1 or more ungraded schools for the instruction of certain pupils classified in subsection (2). The board may require the pupils to attend an ungraded school or a department of the school as the board directs.

  (2) A child aged 7 to his or her sixteenth birthday, or his or her eighteenth birthday if the child turns age 11 on or after December 1, 2009 or is age 11 before that date and enters grade 6 in 2009 or later, who resides in the school district and who meets 1 or more of the following is considered a juvenile disorderly person and in the judgment of the proper school authorities may be assigned to the ungraded school or department:

  (a) Except for a child described in section 1561(5), a child who is habitually truant from the school in which he or she is enrolled as a pupil.

  (b) A child who, while attending school, is incorrigibly turbulent, disobedient, and insubordinate, or who is immoral in conduct.

  (c) A child who is not attending school and who habitually frequents streets and other public places, having no lawful business, employment, or occupation.