Use this guide with a free ScanScore resource
- MCQ difficulty calculator — Find the proportion of students who answered a question correctly.
After a test, one question often stands out: almost nobody got it right. Was the question hard, badly worded, or wrongly keyed? The first number to look at is the facility index — the proportion of students who answered a question correctly. The MCQ difficulty calculator works it out from response counts.
The formula
Facility index = number who answered correctly ÷ number who attempted. If 24 of 40 students got a question right, the index is 0.60, or 60%.
Reading the number
| Index | Usually means |
|---|---|
| Above about 0.80 | Easy — most students got it |
| About 0.30 to 0.80 | A reasonable spread |
| Below about 0.30 | Hard — or something is wrong |
These bands are a common rule of thumb, not a law; a diagnostic test may want some very easy and very hard items on purpose.
When a low number is a warning
- Check the key first. A wrong answer key is the most common cause of a question nobody gets right.
- Check the wording. Ambiguity makes strong students miss too.
- Check the teaching. If the key is right, the class may not have met the idea yet.
If a question was wrong, fix the key and re-mark. ScanScore can re-mark every saved sheet after a key change, and a question can be marked wrong for everyone. See setting and fixing the answer key.
Getting the numbers without counting
The calculator suits a single question. In ScanScore the class view lists the questions the most students missed automatically after you scan, so you do not count by hand. See class result analysis and subject-wise analysis.
For a spreadsheet version, use the class result analysis template, and explore the negative marking calculator guide.