How is percentile and marks calculated in CAT?

Answer 1

MOST OF you who wrote CAT2004 would, by now, have checked your scores from the Internet. However, the score card gives you only percentage and percentile scores and you must be very eager to know how you can calculate the actual marks you scored in CAT2004.

Here is a method to calculate your marks based on your percentage scores. This method has been given by T.I.M.E., a reputed CAT training organisation. Go through each of the following items before you calculate your CAT scores.

Percentile score


What does the percentile score of a student mean? Simply put, it is the percentage of students below him in a test. Let us take an example.

Student X wrote an exam which was written by a total of 1000 students. Suppose X stood 10th in the test - that is, there were 990 students below him in that test. 990 as a percentage of 1000 is 99. So, 99 per cent of the students who wrote the test were below X.






What this means is that the percentile of X is 99. Suppose Student Y stood 95th in the same test, i.e., there were 905 students below him. So, Y's percentile score in this test will be 90.5.

Can there be a percentile score of 100? Logically speaking, NO. This is because even the top ranker does not have 100 per cent of the students below him (he himself is not below him). If there are N students writing the exam, the maximum number of students who can be below the top ranker is N-1. Hence, the percentile score can only be {lcub}(N-1)/N{rcub}*100 which is less than 100.

But, when you express the percentile score to a certain decimal place that you desire, rounding off the digits after the decimal point can lead to a score of 100. For example, as has happened in the case of CAT, if we decide to round off the figure to two decimal places, any student who gets a percentile score of 99.995 or more will be given 100 as the percentile figure after rounding off.

How many students will be there in the country with a score of 100 percentile?

There will be SEVEN students in the country who would have got a percentile score of 100 - as per the explanation given below.

As we discussed above, all the students with a percentile score of 99.995 or more will be given a score of 100, that is, the top 0.005 per cent of the students in the country will get a percentile of 100. Since about 1,40,000 students were supposed to have written CAT this year, 0.005 per cent of 140,000 will work out to seven.

Percentage score


What is percentage score given by the IIMs in the CAT Score Card? How is it different from percentage scores that students are used to in Board exams and University exams?






In Board exams and University exams, percentage marks scored by a student in a subject is his/her marks expressed as a percentage of the maximum POSSIBLE mark in that subject. For example, if the maximum possible marks in a subject is 200, and a student has scored 168 marks, his/her percentage in this subject is 84.

However, CAT Score Card uses the term "percentage score" in a different manner. In each of the individual sections, the marks scored by a student as a percentage of the highest mark SCORED in that section by any student is shown as the percentage mark of the student.

For example, let us take a section where the maximum possible mark is 50. Suppose the highest mark scored by anybody writing the exam this year is 40 in this section. If a student scored 35 marks in this section, then his "percentage score" for this section (as given in CAT score card) will be 35 divided by 40 x 100 = 87.5.

Is the percentage score given in CAT Score Card for TOTAL defined the same way in which it is defined for individual section?

No, it is not. The total score used for the percentage calculation is the SUM of the highest scores in all the sections. For example, in CAT2004, there were three sections. The highest scores in the First, Second and Third sections were 36, 43.67 and 43.67 respectively. The sum of these three figures is 123.33.

The percentage scores for the TOTAL are calculated with 123.33 as the base. That is, a student's percentage score for the TOTAL is his/her total score in the test paper expressed as a percentage of 123.33.

Will any student have this 123.33 as his/her total score in the paper? That is, will anybody have 100 as the percentage score for the TOTAL?

This is possible but improbable. It is possible if the SAME student topped in all the three sections. If this happens, then, in addition to the 100 score for the TOTAL, that same student will also get 100 in EACH of the three sections.

Negative marking


What is the level of negative marking in CAT? Have the IIMs indicated the negative marking along with the scores given in the score card?

The CAT paper does not specify the level of negative marking and the IIMs do not disclose the negative marking officially. They have not given any indications of the negative marking even in the score card.

However, we at T.I.M.E. have always asked students to take one-third mark as the negative mark for each wrong answer. We have been doing this since our inception in 1992. (There was also a possibility of progressive negative marking used by the IIMs for CAT paper). Our position was based on proper understanding of the paper and mathematical reasoning.

While a lot of other CAT training institutes have always used one-fourth negative mark for each wrong answer, we have always held that it was wrong. Unfortunately, till CAT2002, there was no way of proving or disproving either school of thought.

However, when CAT2003 scores came out, we calculated the highest scores in each section and indirectly proved that the IIMs used one-third negative mark for each wrong answer. This vindicated our long-held position on negative marks. Even after this, a few CAT training institutes have continued using one-fourth negative marking while one CAT training institute (based in Delhi) changed its negative marking to one-third after it saw the CAT2003 score calculations given out by us.

What about negative marking this year? In CAT2004, there were half-mark, one-mark and two-mark questions. Would all of them have one-third negative marking?

No. In our CAT2004 analysis (that we released on the day of CAT), we have asked students to calculate their scores as follows:

Giving one-sixth negative mark for each half-mark question.

Giving one-third negative mark for each one-mark question.

Giving two-third negative mark for each two-mark question.

Has this been validated, now that CAT score cards are available?

Yes. Using the highest marks in each section that we calculated and made available on our website, students found that their scores are matching perfectly if they use the above scheme of negative marking.

How was this negative marking known precisely even though the IIMs did not give any indication?

That is where understanding the paper and the correction process becomes important. Logic also plays an important role.

Cut-offs


What is the cut-off mark to get calls from the IIMs? Students getting above 98.6-98.7 percentile stand a good chance of getting a call from at least one IIM.

Why are you saying that 98.6-98.7 percentile will be required to get IIM calls?

Each IIM calls a certain number of students for Group Discussions/Interviews.

While, as the IIMs state in CAT bulletin, CAT score is just one of the parameters taken into account to call students for GDs/Interviews, CAT score plays a large role. Some students get multiple IIM calls.

If you take all that into account, around 2000 students (in General Category) get IIM calls. This works out to about 1.4 per cent of the roughly 140,000 students who were supposed to have written CAT. That means, a percentile of 98.6.

Now, go through the following to know your CAT2004 scores. The highest score in the CAT2004 for individual sections and the score used for working out the overall percentage are as follows (See Table 1).

You can now check your individual scores as follows: Let us say your score card is as given in Table 2.

Multiply the percentage figure in each section with the HIGHEST SCORES of the respective sections given in Table I. Similarly, multiply your percentage score for the Total with the HIGHEST SCORE for the TOTAL given above.

Then your scores in the three sections and the Total are as given in Table 3.

Incidentally, the figures taken are the actual scores of a (general category) student who wrote CAT2004. This student, with a total score of 51 marks, got a percentile of 98.65. This student got interview calls from IIM-A and IIM-B.

However, please note that there would be students who have got similar scores or even higher scores and yet not got the coveted calls.

The explanation for the above would be that the IIMs take the CAT score as one of the parameters for selection and other considerations such as academics, work experience, etc. also matter.

There is also a possibility that the IIMs could be giving some pre-decided weightages to these sectional scores before deciding on the interview call list. Now go ahead and calculate your CAT scores.

Answer 2

Cat Percentile Calculation