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Currently I am preparing for Gujarat Public Service Commission (GPSC) exam for recruitment as a faculty in govt. engineering college in Gujarat. The exam has only one paper containing 200 Multiple Choice Question (MCQ) having five options and 30% negative marking. Suddenly a thought came in my mind why negative marking is there in many entrance exams? After reading this article you will come to know that system is made active via playing a game with students. Before proceeding further let us have some understanding of Random Variables (RV) and its Expectations. RV is a variable which can be correlate with any physical quantity. In statistical terms it can be approximated to data while Expectation is its mean. You may read about it more in any basic course books from B.Com., M.Com., M.Sc. (Stat), or probability and statistics books.

Note: I used Probability and RV in my PhD thesis.

HOW MUCH MAXIMUM MARKS A STUDENT CAN OBTAIN IN EXAM?

Let assume there is an exam having 100 MCQ with four options and carrying one mark each. The expected marks obtained by student is

E(Marks)=Σ Assigned Marks of a questions*P(options)

= 100*1*P(A)+ 100*1*P(B) + 100*1*P(C) + 100*1*P(D)

= 100*1/4 + 100*1/4 + 100*1/4 + 100*1/4

= 100

So, on an average a student may get maximum 100/100 marks. If you observe the state board results then you will observe getting 80-90% has become easier nowadays.

WITH NEGATIVE MARKING

Suppose in above example there is 25% negative marking for each wrong answer, then expected marks can be calculated as below

E(Marks)=Σ Assigned Marks of a questions*P(options)

= 100*1*P(A)+ 100*1*P(B) + 100*1*P(C) – 100*1/4*P(D)

= 100*1/4 + 100*1/4 + 100*1/4 – 100*1/4*1/4

= 68.75

What happened? Where 31.25 marks gone?

SOME CASE STUDIES

I have attempted GATE-04, 05, 06, 07, 09 exams. Let me explain you mathematics behind these exams.

GATE 2009 (IIT Roorkee)

Question Paper

Q. 1 to 20 total 20 questions carrying 1 mark each = 20 marks.

Q. 21 to 60, total 40 questions carrying 2 marks each = 80 marks.

Negative Marking

1/3 negative marking in Q. 1 to 20 total 20 questions carrying 1 mark each.

2/3 negative marking in Q. 21 to 56, 57, 59 total 38 questions carrying 2 marks each.

E(Marks)=Σ Assigned Marks of a questions*P(options)

= 20*1*1/4 + 20*1*1/4 + 20*1*1/4 – 20*1/3*1/4 + 38*2*1/4 + 38*2*1/4 + 38*2*1/4 – 38*2/3*1/4

= 64 marks out of 100 marks.

If I say about my score in this exam, I got 57 marks and secured All India Rank 175. My guess is there may be very less students who crossed 64 marks level and GATE committee might have predicted it via this stats.

GATE 2007 (IIT Kanpur)

Question Paper

Q. 1 to 20 total 20 questions carrying 1 mark each = 20 marks.

Q. 21 to 85, total 65 questions carrying 2 marks each = 130 marks.

Negative Marking

1/4 negative marking in Q. 1 to 20 total 20 questions carrying 1 mark each.

1/2 negative marking in Q. 21 to 76, 78, 80, 82, 84 total 60 questions carrying 2 marks each.

E(Marks)=Σ Assigned Marks of a questions*P(options)

= 20*1*1/4 + 20*1*1/4 + 20*1*1/4 – 20*1/4*1/4 + 60*2*1/4 + 60*2*1/4 + 60*2*1/4 – 60*1/2*1/4

= 96.25 marks out of 150 marks.

GATE 2006 (IIT Kharagpur)

Scheme was same as GATE 2007.

GATE 2005

Question Paper

Q. 1 to 30 total 30 questions carrying 1 mark each = 30 marks.

Q. 31 to 80, and 81 to 85 carrying a,b options total 60 questions carrying 2 marks each = 120 marks.

Negative Marking

1/4 negative marking in Q. 1 to 30 total 30 questions carrying 1 mark each.

1/2 negative marking in Q. 31 to 80 and 81a, 82a, 83a, 84a, 85a total 55 questions carrying 2 marks each.

E(Marks)=Σ Assigned Marks of a questions*P(options)

= 30*1*1/4 + 30*1*1/4 + 30*1*1/4 – 30*1/4*1/4 + 55*2*1/4 + 55*2*1/4 + 55*2*1/4 – 55*1/2*1/4

= 96.25 marks out of 150 marks.

GATE 2004 (IIT Delhi)

Question Paper

Q. 1 to 30 total 30 questions carrying 1 mark each = 30 marks.

Q. 31 to 90, total 60 questions carrying 2 marks each = 120 marks.

Negative Marking

1/4 negative marking in Q. 1 to 30 total 30 questions carrying 1 mark each.

1/2 negative marking in Q. 31 to 90 total 60 questions carrying 2 marks each.

E(Marks)=Σ Assigned Marks of a questions*P(options)

= 30*1*1/4 + 30*1*1/4 + 30*1*1/4 – 30*1/4*1/4 + 60*2*1/4 + 60*2*1/4 + 60*2*1/4 – 60*1/2*1/4

= 108.75 marks out of 150 marks.

Finally we can tabulate the statistics as below

GATE exam

1 mark questions (with negative marking)

2 mark questions (with negative marking)

Maximum Marks

Expected Marks

Expected marks as % of total marks

2004

30 (25%)

60/60 (25%)

150

108.75

72.5

2005

30 (25%)

55/60 (25%)

150

96.25

64.2

2006

20 (25%)

60/65 (25%)

150

96.25

64.2

2007

20 (25%)

60/65 (25%)

150

96.25

64.2

2009

20 (33.33%)

38/40 (33.33%)

100

64.00

64.0

Following things can be concluded from above table

  1. From column 6 it can be seen that share of expected marks is reducing.

  2. From column 5 it can be seen that expected marks have reduced though maximum mark is unchanged.

  3. Students appeared in GATE 2004 were luckier because GATE committee was liberal in giving lesser challenge via taking lesser marks. May be at that time GATE Committee did not realise it can toughen exam.

  4. Transition from 2005 to 2006 suggest that expected marks are same with reduction in 1 mark questions and rise in 2 mark questions, keeping number of 2 marks questions same.

  5. GATE 2009 stats suggest that raising negative marking keeps share of expected marks almost same despite of reduction in maximum marks and number of 2 marks questions.

It seems GATE committee is continuously trying to take away students’ marks and giving tougher challenges.

WHY GATE COMMITTEE IS DOING THIS?

 

Let us understand how GATE Score is given.

Performance Index (PI) of candidate is given by

(m-a)/s

Where

m= Marks obtained by candidate in subject.

a= Average of marks of all candiates who appeared in the paper mentioned on scorecard.

s= Standard deviation (SD) of marks of all candidate who appeared in the paper mentioned in this scorecard.

To facilitate performance comparison across GATE papers and over a block of years, this PI is scaled with respect to global average and global SD

(mg-ag)/sg=(m-a)/s

Where

mg= Rescaled marks defined with reference to global average and SD

ag= Global average of marks of all candidates who appeared across all papers and years

sg= Global SD of marks of all candidates who appeared across all papers in years.

Therefore candidate’s rescaled marks is

mg=ag+sg*PI

Considering 150 as maximum marks in GATE paper, rescaled marks mg is finally represented as GATE score on 0 to 1000 and is given by

GATE Score=1000*mg/150=1000*ag/150 + (1000/150)*sg*PI

You can observe from GATE score equation that lesser marks obtained by student (m), lesser his GATE Score. That is why GATE committee always try student get lesser marks and via offering negative marking committee is assuring average marks (expected marks) of student is always lesser.

 

GPSC Exam

Question Paper

Q. 1 to 100 total 100 questions carrying 1 mark each = 100 marks.

Q. 101 to 200, total 100 questions carrying 2 marks each = 200 marks.

Negative Marking

They have developed more dangerous scheme which becomes deadly with inclusion of negative marking. There are 5 options out of which fixed option (E) only will carry 0 mark. Even unattempted question will be considered for negative marking unless option (E) is selected. They have given following scheme for negative marking.

30% negative marking in Q. 1 to 100 total 100 questions carrying 1 mark each.

30% negative marking in Q. 101 to 200 total 100 questions carrying 2 marks each.

Without negative marking expected marks will be

E(Marks)=Σ Assigned Marks of a questions*P(options)

= 100*1*1/5 + 100*1*1/5 + 100*1*1/5 + 100*0*1/5 + 100*1*1/5 + 100*2*1/5 + 100*2*1/5 + 100*2*1/5 + 100*0*1/5 + 100*2*1/5

= 240 marks out of 300 marks (80% share of maximum marks).

This means this method of fifth option carrying zero mark is taking away students’ mark without even negative marking is implemented.

With negative marking, expected marks of student is,

E(Marks)=Σ Assigned Marks of a questions*P(options)

= 100*1*1/5 + 100*1*1/5 + 100*1*1/5 + 100*0*1/5100*0.3*1/5 + 100*2*1/5 + 100*2*1/5 + 100*2*1/5 + 100*0*1/5100*0.6*1/5

= 160 marks out of 300 marks (53.33% share of maximum marks).

I don’t know officers at GPSC are knowing what they have done but this exam scheme is deadly and will give them maximum number of disqualified students. They must set lower cut off marks otherwise hardly anyone will qualify.

HISTORY OF NEGATIVE MARKING

Well, there are two types of students; hard working and lazy. Hard working students anyway will prepare well while lazy student won’t. In normal exams, it is possible lazy student may guess and attempt the questions which he is not sure and may get same score compared to hard working student while in return he is not losing in guessing the answer. This is wrong because guesstimators may corrupt whole system, whose people are also part, via taking wrong decision through their little to zero knowledge of subject. Also, what is justification given to hard working student? Examiners thought of making self correcting system which may punish those lazy guessers via developing negative marking exams.

WHAT IS CONNECTION WITH RELIGION?

According to every religion in the world, you will be rewarded for your right things and punished for your wrong things. Guessing and scoring competitively is wrong and system act as god to punish for your wrong. Negative marking is derived based on the core religious principal of reward and punishment. God (system) is there to watch and punish (negative marks) you for your wrong doings (guesses). I don’t know why none of the communists are objecting it  .

CONCLUSIONS

The system is build lively/acting by snatching students’ marks for each of his sins. System is playing a game with you in which it has eaten away your marks at the moment you appear in exam. Message of the gamer is; don’t blabber in exams and attempt only those questions for which you are sure. Of course you may gamble and attempt the questions on which you are not sure. There is no harm in trying. If successful then full marks. If fail then you are losing a little (Isn’t it sounds like business?). Play on your own risk because it is risky game where you may lose something for your wrong. Via this philosophy, system is encouraging students parallely to take risk and avoid blabbering both.

 

ઝબકારો: Religion is created out of a need by human and rejecting it means rejecting ourself. Whether present or in coming future, we can’t abandon religion because it has significantly influenced our thinking pattern.

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