Suppose I have a relation Grades(student_id, assignment_id, score). I have 150 students and 20 assignments. I would grade all submissions of one assignment based on the submission order, and then insert the records. As a result, based on my insertion nature, this relation is not sorted on student_id, but sorted on the assignment_id. I choose heap file as my file organization. My page is quite small it can only store 20 records, or 200 bytes in one page. The SearchKeySize is 4 bytes and PointerSize is 2 bytes. My buffer size is also small, 5 pages.

If my most frequent query is to find all scores for an assignment (e.g.,select student_id, score from grades where assignment_id=10;)

What is the average I/O cost if I dont build index for assignment_id? (note: assignment_id is sorted and each assignment_id can appear as many as 150 times in this relation)