The children a board pass rate cannot see

If nine out of ten candidates pass a school-leaving examination, how much of the journey through school has that number described?

It sounds as though only the last tenth needs explaining. But the examination's denominator begins after another selection has already happened: who reached the examination and appeared for it.

Take a concrete, dated example. CBSE's Class XII results released on 13 May 2025 reported 16,92,794 candidates appearing and 14,96,307 passing in its full-subject results. Dividing the second number by the first produces 88.39%, after rounding.^[1]

That is a valid account of those examination candidates. It is not a claim that 88.39% of an Indian age cohort completed Class XII. The board's calculation does not contain that age cohort as its denominator.

I want to stay with what happens before the denominator starts. Because that is where the same percentage can acquire very different meanings.

Imagine a starting group of 100 young people. By a specified cutoff, 60 have taken a final examination and 54 have passed. For this illustration, assume passing completes the qualification and nobody has completed through another route. These are deliberately hypothetical numbers, not estimates for India.

The examination pass rate is 54 divided by 60: 90%. But the share of the starting group obtaining the qualification is 54 divided by 100: 54%.

Nothing is wrong with either calculation. What changes is the question each answers.

The 90% describes performance among those who appeared. It says nothing about why 40 members of the original group did not reach that examination by the cutoff.

The rate can fall while more people finish

Now consider an alternative outcome for that same starting group and the same cutoff. Eighty appear and 64 pass.

The examination pass rate is now 80%: 64 divided by 80. It is lower than the earlier 90%. Yet ten more young people have obtained the qualification, and the completed share of the starting group has risen from 54% to 64%.

This is not evidence that a falling pass rate is desirable. It is a demonstration that the direction of a pass-rate change cannot, by itself, tell us the direction of a completion change.

The extra candidates might have had less preparation. Or support before the examination might have changed. We would need evidence to distinguish those explanations in a real system. The arithmetic alone does not tell us what caused either result.

There is an equally important reverse possibility. Suppose fewer learners with a high risk of failing reach the examination. The pass rate among those who remain could rise without any improvement in what those candidates learned.

That possibility is not an allegation about a school or board. It is a property of the measure: changing the people included can change the percentage.

This is why I would hesitate before reading a school’s advertised pass rate as the probability that a child entering several years earlier will eventually obtain the qualification. The first is conditional on appearing; the second concerns the full journey from entry. They are not interchangeable promises.

But the apparent answer—follow every entrant—has its own complication. A learner leaving one school may finish in another. Someone absent from one board's results may qualify through a different board. A slower learner may complete after the chosen cutoff.

Counting every disappearance from one institution as educational failure would merely replace one misleading denominator with another. Our hypothetical closed group made the arithmetic simple; real educational pathways are not closed in that way.

Population-based completion indicators address a different part of the problem. The SDG methodology published by UNICEF uses people three to five years above the official age of entry into the final grade and asks what proportion have completed that education level. The age window allows for some delayed progression.^[2]

That approach brings people outside the current examination hall into view. It does not make the answer timeless or perfect: the same methodology notes that very late completion may still be missed and that household-survey data can be delayed.^[2]

So I do not think the answer is to abandon board results. A pupil passing is a meaningful achievement, and a board should report what happened among its candidates. The error begins when that answer is asked to stand in for a different one.

For India’s Class XII discussion, the distinction is substantive. Improving the chance of passing among those who appear and increasing the share of young people who obtain the qualification can overlap. Neither measure guarantees the other.

My conclusion is that a pass rate describes the final examination, not the probability of completing the whole journey through school. The starting population and the time allowed belong in any claim about that journey.

The children who never reached the examination hall cannot appear in its pass percentage. They have not, for that reason, ceased to be part of the school-education story.