The Indian Institute of Technology Madras is one among the foremost institutes of national importance in higher technological education, basic and applied research.

This IIT Chennai is providing grading system for student’s marks:

Letter Grades:

Based on the academic performance, each student is awarded a final letter grade at the end of the semester, in each subject.

The letter grades and the corresponding grade points are as follows:

Grade Grade points Remarks
S 10
A 9
B 8
C 7
D 6
E 4
U 0
P - Pass
F 0 Fail
W 0 Failure due to insufficient attendance in course
I 0 Incomplete (Subsequently to bechanged into pass (E to S) or U grade in the same semester)
X 0 Completed NSO/NCC/NSS requirements
Y 0 Incomplete (in NSO/NCC/NSS)

It is assumed that the marks follow a Normal Distribution (The bell curve).
First the mean (μμ) and standard deviation (σσ)of the marks obtained is computed.

If XX is the marks obtained by the student, then
X≥μ+1.65σX≥μ+1.65σ would result in an S grade

μ+0.85σ≤X<μ+1.65σμ+0.85σ≤X<μ+1.65σ would result in an A grade.

μ+0.12σ≤X<μ+0.85σμ+0.12σ≤X<μ+0.85σ would result in a B grade.
μ−0.65σ≤X<μ+0.12σμ−0.65σ≤X<μ+0.12σ would result in a C grade.
μ−1.3σ≤X<μ−0.65σμ−1.3σ≤X<μ−0.65σ would result in a D grade.

Some threshold θ≤X<μ−1.3σθ≤X<μ−1.3σ would result in an E grade.
X<θX<θ would result in a U grade.