IIT Roorkee: The Indian Institute of Technology (IIT), Roorkee, has responded to complaints about a large variation in student scores between Paper 1 and Paper 2 of the Joint Entrance Examination (JEE) Advanced 2026, saying the disparity can be explained using "Chebyshev's inequality" and "basic statistical principles" rather than any error in assessment.
A number of JEE candidates reportedly received different marks across the two papers. Students took to social media, flagging the discrepancy after results were released last week, sharing score comparisons that suggested unusually high swings for several candidates.
A user on X, Ananya Chopra, shared the huge difference between Paper 1 and Paper 2 marks, highlighting that a student scored -3 in Paper 1 and 104 in Paper 2.
JEE Advanced 2026 — a student scored -3 in Paper 1 and 104 in Paper 2. Same exam. Same day. Same syllabus.
— Ananya Chopra (@Ananya1669) June 7, 2026
Paper 2 was rated harder this year.
60,000 students. Dozens of 100+ mark swings between P1 and P2.
P1 ends 12 PM. P2 starts 2:30 PM. That's a 2.5hr window.#JEEAdvanced2026 pic.twitter.com/FZTCQNeUGw
Replying to Ananya, Manindra Agrawal, Professor and Director, IIT Kanpur, said that such claims show a lack of understanding of basic statistics. "When there are 60,000 students, some will have large gaps in marks for two papers," he asserted, supporting his claim using Chebyshev's inequality.
Claims like below show a lack of understanding of basic statistics. When there are 60,000 students, some will have large gaps in marks for two papers. Chebychev's inequality quantifies it. It has been the case in JEE Advanced since two papers were introduced. 😊 https://t.co/tbtjzh4lPH
— Manindra Agrawal (@agrawalmanindra) June 7, 2026
A student Nikunj Gupta shared IIT Roorkee's reply that he received on his mail ID. Calling it a "misunderstanding of basic statistical principles", the institute stated: "In an examination involving nearly 60,000 candidates, it is entirely expected that some students will exhibit large differences in scores between the two papers".
"This phenomenon can be explained and quantified using established statistical results such as Chebyshev's inequality," it added.
What Is Chebyshev's Inequality?
The theorem is about the range of standard deviations around the mean, in statistics. The inequality can be applied to any probability distribution in which the mean and variance are defined.
According to a reading material from Stanford University, the goal of Chebyshev's inequality is to bound the probability that the variable is far from its mean (in either direction).
According to Stanford, this inequality is still far from the actual probability. This is because Chebyshev's inequality only takes the mean and variance into account. "There is so much more information about a variable than just these two quantities," the report added.
The organising institute of the JEE Advanced 2026 further stated that "such score variations have been observed consistently in JEE (Advanced) since the introduction of the two-paper format and arise naturally from differences in question types, difficulty levels, marking schemes, and individual candidate performance across papers."
The reply i got from IIT roorkee such a reply that -3 to 104 score is possible because of so called statistics and mathematics Its very tough to score 100+ in JEE advanced so the conditional probability(2k students have capability) is of 177/2000(impossible) not 177/60000 pic.twitter.com/qCCIi1k3L8
— Nikunj Gupta (@NikunjG55759310) June 8, 2026
"The existence of a large score gap between the two papers is not, by itself, evidence of any irregularity. There is no indication of cheating or malpractice at any stage of the examination process, the institute added.
