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- Discussion on the Relative to correct position grading type
### Discussion on the Relative to correct position grading type

# Discussion on the

**Relative to correct position**grading typeOut of the nine different grading types, the

**Relative to correct position**is the only grading type where the lowest possible score for the question is not 0%. (The highest score for the question is 100% when all draggable items are in the correct order).The lowest possible score for the question varies depending on the number of draggable items displayed to the student, ranging from 33% for 3 and 4 items and tending to 50% for an infinite number of items. The table below shows the lowest possible score,

*lps*, for the question for different numbers of items:*n*, number of items3 4 5 6 7 8 9 10 ∞ *lps*, lowest possible score for the question33% 33% 40% 40% 43% 43% 44% 44% 50% The lowest possible score occurs when both halves of the set of draggable items are reversed.

For an

*even*number of items, there are of these cases, i.e. when the student answer is, for example if there are 6 draggable items:perm[4,5,6] perm[1,2,3]

where perm[1,2,3] and perm[4,5,6] are any permutation of items 1,2,3 and 4,5,6, respectively.

For an

*odd*number of items, the lowest possible score occurs when the student answer is, for example if there are 5 draggable items:perm[4,5] perm[1,2,3]

and

perm[3,4,5] perm[1,2]

where some sets perm[4,5] perm[1,2,3] = perm[3,4,5] perm[1,2], that is when the center item, 3, is placed at the center of student answer set.

Note that for both even and odd numbers of items, the set where all items are reversed, for example [6,5,4,3,2,1] or [5,4,3,2,1], always gives the lowest possible score.

For an

*even*number of draggable items displayed to the student,*n*, the lowest possible score for the question,*lps*, is given by:For example, if , the lowest possible score is equal to:

For an

*odd*number of draggable items displayed to the student, the lowest possible score for the question is given by:For example, if , the lowest possible score is equal to:

The fact the lowest possible score for the question is not zero and that is varies with the number of draggable items displayed to the student, is not consistent with the other grading types and may not be adequate for some teachers.

The score for the question, which ranges from

*lps*to 100%, can easily be adjusted to range from 0% to 100% by doing the following operation: