A student's school and school type can be recorded in Student Details (at institutions that enter student data rather than importing it from another database).
School Type sets based on the selected school; it can not be edited independently. If the student's school is unknown, but school type is known, best practice is to add 'Unknown' school options as below. (Select the yellow pencil to add school options.)
Students can then be set to have the 'unknown' school so School Type sets correctly.