What is a percentile?

The Hindu

5 days ago

On June 14, the results of the NEET-UG, India's most competitive medical entrance examination, were declared. Among over 22 lakh candidates, Mahesh Kumar, a student from Rajasthan, stood out with a score of 686 out of 720. Yet, his percentile was reported not as 100 but as 99.9999547. This number may seem puzzling. Why is the national topper in the country not awarded a 100th percentile? What does percentile mean anyway? As lakhs of students await their ranks and counselling, it becomes important to decode the mathematics behind this misunderstood metric.
Percentage vs percentile
A percentage is a straightforward measure of how much a student scores out of the total possible marks. For example, Mahesh's 686 out of 720 translates to roughly 95.27%. Based on the questions answered, it is an absolute measure, showing how much a student knew. A percentile, on the other hand, is a relative measure. It tells us how a student performed compared to others. A 99 percentile means the student did better than 99% of the test-takers. It doesn't say how much the student scored, but where they stand in the crowd. This distinction becomes crucial in exams where lakhs of candidates participate. In competitive exams, especially those with a vast number of candidates, a small difference in marks can translate into thousands of ranks. The use of percentiles helps standardise the evaluation. A mark of 640 might land in a higher percentile one year and a lower percentile the next year simply because the overall performance of the cohort changes. Percentiles help admission authorities compare students by relative performance.
How percentiles are calculated
The basic formula used to calculate percentile is: Percentile = {Number of candidates scoring less than you} divided by {Total number of candidates}*100.
This is why even the top ranker doesn't get a 100 percentile. For Mahesh, the number of candidates scoring less than him is 22,09,317 out of 22,09,318 (including himself). When multiplied by 100, that fraction gives a value that is very marginally below 100. This explains the seven-decimal-place result: 99.9999547. It also means that the 100 percentile is mathematically impossible under this formula. You can get very close, but never exactly 100.
Interestingly, while a 100 percentile is impossible, a zero percentile is theoretically allowed. The lowest scorer, who performs worse than everyone else, will have zero candidates below them. This gives: Percentile= {0} divided by {Total candidates}* 100 = 0
However, such a percentile is rarely displayed in public portals. Systems often show a minimum value or round it up to a small positive number.
One fascinating implication of the percentile system is that it reveals the scale of competition. If a student's percentile is 92.8571428, the number of digits after the decimal (in this case, seven) can hint at the total number of test-takers. This is because: Total number of candidates (approximately) = {1}divided by [{1 - ({Percentile}/{100}].
A high degree of decimal precision is used to differentiate between students who are extremely close in performance. For example, a difference of 0.00001 in percentile could separate thousands of candidates in a large exam like NEET.
Across the world, many tests adopt percentile scoring systems. The GMAT, used for MBA admissions, reports raw scores and percentiles. The SAT and GRE also use scaled scores derived from statistical normalisation, often converted to percentiles for easier interpretation. Even in countries like South Korea and China, high-stakes national exams incorporate relative grading systems to separate top scorers fairly and consistently.
Implications and clarity
The widespread use of percentiles recognises how much a student knows and how well they've performed against others. In tightly packed score ranges —especially at the top — even a half mark can create a significant shift in ranks. Percentiles, with their precision, reveal that shift clearly. For parents and students, understanding this system can prevent unnecessary confusion. A score of 95% may be in the 98th percentile, and 85% may be in the 70th percentile, depending upon the clustering of candidates. Percentiles, though abstract, paint the most accurate picture of where you stand, not just what you scored.
In a country where aspirations often run higher than available seats, one's percentile shows the narrative of competition, effort, and performance relative to lakhs of others. It offers a clearer understanding that victory lies not in perfection in competitive exams but in being ahead of the rest.
Dr. C. Aravinda is an academic and public health physician.