grading.md

IISERM Grading System

Do all instructors grade in the same way?
How do I calculate my grade in a course?
How do I calculate my SPI in a semester?
How do I calculate my CPI over all the semesters?
How important are my grades for my career?

This article answers each one of the questions above.

For the most part, grades are relative

In a class of $N$ students, the mean (average) score and the standard deviation are respectively

$$\bar{x} = \frac{\sum x_i}{N} \text{ and } d = \frac{\sum {x_i}^2}{N} - \bar{x}^2,$$

where $x_i$ are the scores of each student.

Most (strict) instructors will assign your grade in the following way.

Your score	Your grade
More than $\bar{x}+2d $	A
Between $\bar{x}+d$ and $\bar{x}+2d$	B
Between $\bar{x}-d$ and $\bar{x}+d$	C
Between $\bar{x}-2d$ and $\bar{x}-d$	D
Less than $\bar{x}-2d$	F

In a nutshell, your grades depend on how well your peers are doing. Of course, you fail a course if you get an F in which case you will have to repeat it until you pass it.

Some instructors grade differently

Some instructors are more generous and might give you a B if you score above average or even slightly below average. That's cool, right?

Some instructors walk on an entirely different route. They give you absolute grades by declaring cutoffs for each grade. For example, you get an A if your score is 75 or higher in a course.

Ok I know my grades in all courses, what is my SPI?

If you know your grades in all the courses you signed up in one semester, then your SPI in that semester is simply the mean (average) of all your grades weighted by their credits. Grades are converted into numbers in the following way.

Your grade	Number equivalent
A	10
B	8
C	6
D	4
F	0

Let $x_i$ be the grade (in number) in the course $i$ worth $c_i$ credits. Let $C = \sum c_i$ be the total number of credits you signed up in the semester. Then your SPI is:

$$ S = \frac{\sum c_i x_i}{C} $$

Ok so my CPI is simply the average of SPI weighted by credits?

Yes, you hit the jackpot. Suppose your SPI was $S_i$ in semester $i$ which was worth $C_i$ total credits. Then your CPI is

$$ Z = \frac{\sum S_i C_i}{\sum C_i} $$

At least, this is how CPI is defined and supposed to work.

Finally I am done calculating my horrible CPI. How impactful is it in my career?

Well, it depends on which career path you are taking. If you plan to leave academia, your CPI doesn't have much value and you will probably forget it in a couple of years. If you plan to stay in academia, it helps to have a good CPI. But CPI might not be as important as you think it is. I have known people who had a hard time getting into nice places even with a near perfect CPI and some others get into some of the best universities in the world with barely 8/10. It matters more what cool things you did during your five years in IISERM.