Suppose I administer an exam consisting of 320 multiple-choice questions (i.e., the answer is either correct or incorrect - there's no partial credit). I grade the exams, and now I want to do an analysis of the results where I would like to break the analysis up by how difficult the questions were.
I would like to talk about "the hardest 10% of questions" (i.e., the 32 questions for which the fewest numbers of students got the correct answer), as well as "the second hardest 10% of questions" (i.e., the 32 questions that were hardest for students, besides the ones that were in the hardest 10%), etc.
However, it is cumbersome to talk about "the fifth hardest 10% of questions" or "the eighth hardest 10% of questions". Even "the second hardest 10% of questions" sounds a bit silly.
It feels like there must be a descriptive statistic that gives a pithy name to these quantities, but I haven't been able to find one! Can you please give me some suggestions?
The first one that came to mind for me is percentile, but this isn't quite right, since "questions above the 90th percentile in difficulty" is already a bit long-winded, and describing the "second hardest 20% of questions" seems to require a description like "questions above the 80th percentile in difficult, but below the 90th percentile".
I could describe things in terms of rank, which results in pithy statements (good!) but isn't normalized to the number of questions:
"Question difficulty rank: 1st - 32nd" "Question difficulty rank: 33rd - 64th" "Question difficulty rank: 289th - 320th"