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Let me remind you an incidence from movie ‘3 Idiot’.

It was examination night and everyone was busy in its preparation. Suddenly an adult magazine slide in into rooms of students. That guy was Chatur and he wanted student to prepare less for exam.”

As a researcher a question came in my mind: Why Chatur behaved in such a way? He can always read and become knowledgeable if he wants to be. His behaviour has strong connection with ‘Gaussian Distribution’ or ‘Normal Distribution (ND)’. Before answering to it let me brief you about ND.

snd

Normal Distribution

(If you already know ND then you may skip this section.)

Average of any data is given by (considering Discrete Random Variable and Probability Mass Function)

AVG=x1+x2+….+xn/n

Standard Deviation (SD) is given by

SD=SquareRoot[{(x1-AVG)2+(x2-AVG)2+…+(xn-AVG)2}/(n-1)]

In Standardised Normal Distribution (SND) these quantities can be defined by Standardised Normal Random Variable (SNRV) denoted by Z

Z=(x-AVG)/SD

How Students Are Evaluated in Exams?

Institutes like IISc, IITs, NITs and other universities in the world evaluate students based on relative grading while in schools we were being evaluated in absolute grading system.

Absolute Grading (AG)

It is simple average of your marks given as percentage. For example 70 out of 100 marks means 70% and this roughly translates to student knows 70% of the subject.

Relative Grading(RG)

Concept of ND will help here in understanding this evaluation system. Student in IISc is given grade on the scale of 1 to 8 (or 1 to 10 in some institutes). Ideally this grading should come from SND. Value of Z between -3 to 3 covers almost 99.99% area of SND curve. Value of Z will correspond to specific area under the curve. Grades will be given as explained below

Average of marks will be calculated followed by SD. Standardised Normal Random Variable Z will be obtained after knowing values of average and SD. Area corresponding to the value of Z will be recorded from SND tables. Table 1 below explains how grades are given.

In AG if student obtains marks around 60 and he is highest in class then according to AG his percentage will be around 60%. While for same situation in RG student will get AA (correspond to more than 90% of area under curve) grade despite of how much percentage of subject he knows. That is why it is difficult to say student knows subject thoroughly if he scored AA grade in subject. This is why the agency converting your grades to percentage (or vice versa) is bogus. Both can’t be converted to each other.

Table 1: Area under the curve for Z Value

Area under Curve for Z

IISc

Other institutes

0.9<Z<1.00

S

AA

0.8<Z<0.9

A

AB

0.7<Z<0.8

B

BB

0.6<Z<0.7

C

BC

0.5<Z<0.6

D

CC

0.4<Z<0.5

Failed below D

CD

0.3<Z<0.4

DD (Failed)

History of RG Implementation

It was the time when market was open and countries were busy in expanding business opportunities. Companies in USA wanted to penetrate their products deep inside society and best place is schools because it is one of the place where larger number of citizen gather. Companies started to fund inter school sports tournaments, getting publicity through advertisement and business in return. Selling products, advertising business, sponsoring best sportsman had become pride for every corporate. Due to such a huge business driven motivation students are focusing more on tournaments and it affected their education and academic reputation of schools. Apart from this institutional level problem, students are also facing own problems. To overcome this, colleges decided to adopt following strategy.

  1. Restrict sports training in summer

  2. Adopt relative grading as evaluation system

How RG Will Help?

Strategy 1 is understandable but main beauty is in #2. For example a student B studying in college A gets highest marks 80/100 in subject C will be reference and will be given grade AA because it is RG. Similarly a student X studying in college Y gets highest marks of 40/100 in same subject C will also be given grade AA because he is reference in that college. Now both the colleges can boast of good result because students are getting good grades.

Consider an example of two colleges. College 1 has D, E, F, G, and H students and College 2 has P, Q, R, S, and T students. Their marks and gradings are given below to explain how one single student’s performance will affect others’ grading.

Table 2: Grades of students from two different colleges

Stud

Marks

AVG

SD

Z

Area

Stud

Marks

AVG

SD

Z

Area

D

90

50

22.36

1.79

0.96

P

45

41

2.24

1.79

0.96

E

40

50

22.36

-0.55

0.29

Q

40

41

2.24

-0.45

0.32

F

40

50

22.36

-0.55

0.29

R

40

41

2.24

-0.45

0.32

G

40

50

22.36

-0.55

0.29

S

40

41

2.24

-0.45

0.32

H

40

50

22.36

-0.55

0.29

T

40

41

2.24

-0.45

0.32

Grades of toppers D and P are unaffected but D is nightmare for students because he does exceptionally well. He brings grades of others low and some students may fail due to his performance. Students can overcome this by studying hard. So, institute put sword on students’ head “If you won’t study and focus on sports then bookworms will fail you. Please do hard work”.

Coming to Chatur’s Behaviour

Chatur had personal grudge against students and RG gave him opportunity to take vengeance just like how student D took with other class members via scoring high. It can be concluded that Chatur studied in RG evaluation system.

Conclusions

RG adopted from USA universities and it is slowly gaining popularity in world. Definition of competition has changed as time passed. If there are two equals length line; one your and one for other, then there are three possible way you can make your longer

  1. In old days: Extend your line by half of length leading you by half length.

  2. Later time: Erase other line by half of length leading you by half length.

  3. Modern days: Extend your line by half and erase other line by half leading you by full length.

Chatur is from modern day and he opted option 3. Policy makers have made the game “System versus others” through RG in which others will fight against each other to be on top because one’s relative standing in the class matters more than the absolute level of one’s knowledge. It matters not how much you know, only that others know less than you. When one participant improves his own ranking, he necessarily worsens everyone else’s ranking. System will always remain successful and receiving most competitive students. I think this is one of the reason why communists hate capitalist America because it creates such a competitive situation that weaker have to struggle to survive!

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