The process to obtain high percentile score at a moderate raw score of 100 which is scaled to 160 and then again converted to percentile score of 85 to 90+ in CAT exam passes through various stages. However, the key process is detailed as under:
- Your Raw sectional and overall score obtained in CAT exam.
- This raw score is converted to Scaled score
- The scaled score is converted to percentile score.
CAT scoring pattern
Chances to increase percentile in CAT have improved with introduction of 25%+ Non-MCQs. Following is the scoring pattern in CAT 2017:
- Maximum marks 300
- 3 marks awarded for each correct answer for MCQs & Non MCQs
- -1 mark for every wrong answer for MCQs
- No deduction for wrong answer to Non-MCQ
Score scaling and Score Normalization lead to percentile score
The process of converting the raw score to percentile score again depends upon many factors – number of candidates who have appeared in CAT exam, difficulty level of slot-1 and slot-2 question paper. Taking all this into account scaled scores are arrived at. This process goes on for score normalization and leads to percentile scores.
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Normalization depends on LoD in both sessions
The Scaling & Normalization process of CAT 2017 scores have also brought about certain changes as both the components take into account the level of difficulty in both the sessions in which CAT 2017 exam was conducted on November 26, 2017. While the Normalization process implemented for CAT 2017 scores has adjusted for location and scale differences of score distributions across different forms, the scaled scores obtained by this process have been converted into percentiles for purposes of shortlisting.
CAT 2017 website claims to have the most transparent process on score normalization and calculation of percentile. A bit of information on score normalization process in CAT 2017 is also available on CAT website. The process claims to focus on Fairness, Equity and comparison of performances across both the test sessions in CAT 2017.
Transparent Scoring pattern
CAT Centre 2017 has declared “In order to ensure fairness and equity in comparison of performances of the candidates across different test sessions, the scores of the candidates shall be subjected to a process of Normalization. The Normalization process to be implemented shall adjust for location and scale differences of score distributions across different forms and the scaled scores obtained by this process shall be converted into percentiles for purposes of shortlisting.”
IIMs follow GATE pattern to convert score to percentile
On the question of transparency of normalization process across the multiple sessions CAT Centre states “The process of Normalization is an established practice for comparing candidate scores across multiple Forms and is similar to those being adopted in other large educational selection tests conducted in India such as Graduate Aptitude Test in Engineering (GATE).”
To understand the conversion of raw score to percentile score and to know about the score normalization process in CAT 2017, understand first the GATE process which stands a bit changed.
Those appearing in GATE or have understood the process can understand it better but for those who are unaware about the process have to understand the GATE process first. In fact the commerce, science, medical, paramedical and graduates in Humanities who appeared in CAT 2017 still remain oblivious of the percentile calculation formula in CAT 2017.
GATE normalization process adopted in CAT
During 2017, the CE, CS, EC, EE and ME examinations are conducted in multiple sessions. Suitable normalization process is therefore applied to take into account any variation in the difficulty levels of the question sets across the different sessions. The normalization is done based on the fundamental assumption that "in all multi-session GATE papers, the distribution of abilities of candidates is the same across all the sessions".
According to the GATE committee, this assumption is justified since "the number of candidates appearing in multi-session subjects in GATE is large and the procedure of allocation of session to candidates is random. Further it is also ensured that for the same multi-session subject, the number of candidates allotted in each session is of the same order of magnitude."
GATE formula
Based on the above the committee arrived at the following formula for calculating the normalized marks, for CE, CS, EC, EE and ME subjects. From GATE 2014 onward (and year 2014-15 of the 2-year validity period of GATE 2013 score), a candidate's GATE score is computed by the following new formula.
where, S = Score (normalized) of a candidate; M = Marks obtained by a candidate ("normalized marks" in case of multiple-session subjects CE, CS, EC, EE and ME); M_{q} = Qualifying marks for general category candidates in that subject (usually 25 or μ + σ, whichever is higher); μ = Average (i.e. arithmetic mean) of marks of all candidates in that subject; σ = Standard deviation of marks of all candidates in that subject; M_{t} = Average marks of top 0.1 % candidates (for subjects with 10000 or more appeared candidates) or top 10 candidates (for subjects with less than 10000 appeared candidates); S_{t} = 900 = Score assigned to M_{t; } S_{q} = 350 = Score assigned to M_{q}.
Percentile
A candidate's percentile denotes the percentage of candidates scoring lower than that particular candidate. It is calculated as: Percentile = ( 1 - All India rank( No. of candidates in that subject) x 100%
Application of formula in CAT 2017
The formula to calculate the percentile in CAT 2017 can be devised. The score normalization process formula by CAT expert would be as follows-
Normalized mark (︿M_{ij}) of j^{th} candidate in i^{th} slot, is given by
︿M_{ij} = M^{g}_{t} - M^{g}_{q}M_{ti} - M_{iq} ( M_{ij} - M_{iq} ) + M^{g}_{q}
where,
M_{ij} is the actual marks obtained by the j^{th} candidate in the i^{th} slot,
M^{g}_{t} is the average marks of the top 0.1 % candidates in all slots,
M^{g}_{q} is the sum of mean and standard deviation of marks of all candidates in all slots,
M_{ti} is the average of marks of top 0.1 % candidates in the i^{th} slot,
M_{iq} is the sum of mean and standard deviation of marks of all candidates in the i^{th} slot.
Example of converting Score to Percentile
Total Test takers = 2,00,000
slots = 2
Test takers in each slot = 1,00,000 [ .1% of it = 100]
M_{ij} = 170 out of 300 ( is the actual marks obtained by the j^{th} candidate in
the 2nd slot)
M^{g}_{t} = [195 + 190 ]/2 = 192 ( is the average marks of the top 0.1 % candidates of
both the slots)
here, 195 and 190 are the average of the top .1% aspirants of all slots
M^{g}_{q} = 112 (is the sum of mean and standard deviation of marks
of all candidates in both the slots)
M_{ti } = 190 (is the average of marks of top 0.1 % candidates in
the 2nd slot)
M_{iq } = 110 (is the sum of mean and standard deviation of marks
of all candidates in the 2nd slot.)
So, according to the given formula, normalized score = (192-112)(170-110)/(190-110) + 112 = 172
165 core marks = Scaled score 195
Going by past trend and allowing for all the odds, if you have scored more than 200 marks with sectional score of 73 in VARC, 56 marks in DILR and 71 marks in Quant, it has fetched 99+ percentile in CAT 2017. Please note this is not your raw score out of 300, it is the scaled score which is reflected in your score card after IIMs complete the scaling process as detailed above. Your required raw score to get scaled score of 195 and achieve 99 percentile could be much less say, around 160 or 165 marks out of 300.
To a large extent it can be estimated that your total marks of 193 to 195 could award you a percentile of 98-99 in CAT. Besides a gap of 10 marks is expected to exist between the award of 99 and 100 percentile in CAT.