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Glossary

What Is Item Difficulty? The Quiz Quality Metric Most Teachers Ignore

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Short answer. Item difficulty (denoted *p*) is the proportion of students who answered a given quiz question correctly. A question that 80% of students got right has *p* = 0.80. The metric is poorly named — *higher* difficulty value = *easier* question — but it's a foundational stat for evaluating quiz quality.

What the values mean

  • p = 1.0: Every student got it right. Either trivially easy, or a freebie. Not useful for distinguishing students.
  • p = 0.80-0.90: Easy. Good for confidence-building, foundational checks.
  • p = 0.50-0.70: Medium. Most useful for assessment — discriminates between students who know and don't know.
  • p = 0.20-0.40: Hard. Good for stretch questions; use sparingly.
  • p < 0.20: Either too hard for the cohort, or a broken question.
  • p = 0: No one got it right. Almost certainly a broken question.
  • How to use it

    For a typical quiz:

  • Aim for an average difficulty of 0.5-0.7 across all items
  • Don't have all easy items (p > 0.85) — the quiz doesn't differentiate
  • Don't have all hard items (p < 0.4) — the quiz frustrates without measuring
  • Mix difficulty levels so the quiz has a discrimination curve
  • Item difficulty + item discrimination

    Item difficulty alone is incomplete. A question with p = 0.50 might be:

  • A great question (top half of class gets it right, bottom half doesn't) — high item discrimination
  • A coin-flip question (every student has 50/50 odds) — low item discrimination
  • A *reverse-discrimination* broken question (bottom half gets it right, top half misses) — negative discrimination
  • Use both metrics together. A good quiz has medium-difficulty items with positive discrimination.

    How modern quiz tools surface this

    Most LMSs and quiz platforms show item difficulty after each quiz administration:

  • Canvas, Blackboard, Moodle: quiz statistics page
  • SimpleQuizMaker: per-question analytics across all submissions
  • After every quiz, scan the difficulty distribution. The items with p > 0.95 (everyone right) and p < 0.15 (almost no one right) are usually the ones to review or rewrite.

    Common mistakes

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  • Confusing the name. Higher value = easier. Not intuitive. Many teachers reverse this in their heads.
  • Ignoring difficulty data when grading. The "everyone missed Q5" pattern usually means Q5 is broken, not that everyone failed to learn.
  • Treating low p as a teaching problem when it's a question problem. Verify the question is well-written before concluding students don't know the material.
  • Item difficulty across high-stakes exams

    For comparison, the average item difficulty on professional exams:

  • AP exams: target around p = 0.60 — calibrated to differentiate scores 1-5.
  • SAT: average p around 0.65; harder items in the back of each section.
  • MCAT, GRE: adaptive, so item difficulty is selected per student to maintain ~50% expected correct rate.
  • Bar exam, USMLE: average p around 0.55 — high-stakes filtering exams.
  • Classroom unit tests typically run easier (p around 0.75) because the goal is documenting that most students learned the material, not differentiating among them.

    A diagnostic protocol after a quiz

    After the first 10-20 students take a new quiz:

  • Sort items by p. Anything with p > 0.95 or p < 0.20 gets reviewed.
  • For high-p items: was this a freebie? If yes, fine. If you intended it to be hard, the wording probably gave it away.
  • For low-p items: read the question aloud, work it yourself. If you struggle or notice ambiguity, the item is broken. If it's truly hard and well-written, keep it but note the difficulty.
  • Check the discrimination index on borderline-difficulty items (p around 0.40-0.60). High discrimination = useful item; low or negative = revise.
  • After 5-10 administrations, you have a refined item bank with known difficulty. AP/MCAT/NCLEX item banks went through this process for years before reaching production.

    Why item difficulty matters less than discrimination

    Two questions with the same difficulty (p = 0.60) can have very different value:

  • One is a "good 60%" — top students mostly right, bottom students mostly wrong (high discrimination)
  • One is a "noise 60%" — random students right (low or zero discrimination)
  • The first is a productive item; the second is a coin flip dressed up as a quiz question. Always check both metrics; never use difficulty alone.

  • What Is Item Discrimination?
  • How to Write Good Quiz Questions
  • How to Write Hard Quiz Questions
  • Quiz Analytics — Teacher Guide
  • What Is a Distractor (in Quiz Design)?
  • Generate a quiz and see per-question difficulty after the first 5 submissions.

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    Sarah Mitchell

    Curriculum Designer & Former High School Teacher

    More articles by Sarah

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