A Flat University Pass Rate That Hides Three Different Stories
A state university's examination branch compiles pass data for four affiliated colleges in the Commerce stream. The Vice-Chancellor's office must decide where to send a three-member academic audit team next month, and there is budget for only two colleges. In 2024, College C opened two new sections and absorbed students who would earlier have joined College A. A newspaper reports that 'the university's pass percentage has not moved in two years, showing that teaching quality is unchanged', and the Registrar wants the audit team sent to the colleges with the lowest pass percentage.
| College | 2023 appeared | 2023 passed | 2024 appeared | 2024 passed |
|---|---|---|---|---|
| A | 400 | 260 | 500 | 340 |
| B | 200 | 150 | 250 | 180 |
| C | 100 | 70 | 400 | 260 |
| D | 300 | 210 | 300 | 222 |
1. Compute the pass percentage for each college in both years and for the university as a whole. Then explain, with numbers, why the newspaper's inference is unsafe.
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| College | 2023 | 2024 |
|---|---|---|
| A | 260/400 = 65.0% | 340/500 = 68.0% |
| B | 150/200 = 75.0% | 180/250 = 72.0% |
| C | 70/100 = 70.0% | 260/400 = 65.0% |
| D | 210/300 = 70.0% | 222/300 = 74.0% |
| University | 690/1000 = 69.0% | 1002/1450 = 69.1% |
The aggregate is almost exactly flat, but three of the four colleges moved. The reason is composition: candidates appearing rose 45%, from 1,000 to 1,450, and almost all of that growth is College C, whose share went from 10% to about 27.6%. C's rate fell five points, so the mass of candidates shifted towards the weakest-performing college. A counterfactual makes it concrete: had C held its 2023 rate of 70% in 2024, it would have passed 280 rather than 260, and the university rate would have been 1,022/1,450 = 70.5%, not 69.1%.
The newspaper's inference is therefore unsafe twice over. First, a stable weighted average is compatible with large offsetting movements, so it cannot establish that nothing changed. Second, and more basic, the pass percentage is not a measure of teaching quality; it responds to intake composition, question-paper difficulty, moderation, internal assessment practice and student preparation. The data support a statement about outcomes, not about causes.
2. Recommend which two colleges the audit team should visit, with a rationale and, if needed, a different audit focus for each. Address the Registrar's proposal to rank by lowest pass percentage.
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Ranking by the 2024 pass percentage alone is the weakest available rule. It selects C, at 65%, but C is the college whose scale quadrupled in one year - a level statistic cannot distinguish a teaching failure from a capacity failure. It would also send the team past B, which fell three points on only 25% growth, and past A and D, which improved and serve as useful comparators.
Recommendation: visit B and C, with different mandates.
B - teaching and assessment audit. B has the best absolute rate but the only decline not explained by expansion. Ask for subject-wise pass rates, gaps between internal and external marks, question-paper difficulty and moderation records, faculty deployment, and the pattern of repeaters. A three-point fall on 250 candidates is about seven or eight students in absolute terms, so first confirm that it exceeds normal year-to-year variation; if it does not, a lighter enquiry is enough.
C - expansion and capacity audit. Four times the candidates in one year implies new sections, new teachers and probably new laboratory arrangements. Examine the faculty–student ratio, whether the new sections are staffed by permanent or guest teachers, library and laboratory provision, and whether the 2024 entrants' prior attainment differs from 2023. The five-point fall is expected under expansion; the question is whether minimum conditions were maintained.
Tell the Registrar plainly that level, trend and scale answer different questions, and the audit should be designed around the question being asked.
3. State two additional data items you would request before finalising the recommendation, and explain how each could change it.
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1. Subject-wise and programme-wise pass rates, with repeaters separated from first-attempt candidates. If B's decline is concentrated in one or two subjects, the visit becomes a narrow question-paper and moderation enquiry and may not need a full team. If it is spread across subjects, the teaching hypothesis strengthens. If C's fall is concentrated among 2024 entrants in particular sections, the capacity audit can focus on those sections instead of the whole college.
2. Intake profile - prior board examination results or cut-off marks for the 2023 and 2024 cohorts, plus the share of first-generation learners and repeaters. A college can improve its teaching and still show a falling pass rate if its intake weakened. If C's 2024 cohort had markedly lower prior attainment, the five-point fall becomes largely a composition effect and the audit priority shifts to bridge courses, language support and student services rather than teacher accountability.
Worth adding if available: the gap between internal and external marks, which can indicate marking practice; malpractice cases; and attendance records. But the two above are the ones capable of reversing the B-and-C recommendation, which is why they should be requested before the team is dispatched rather than after.