CAT marks vs percentile: How scoring, scaling, and normalisation work

With the release of the final answer keys, candidates now have a clearer picture of their actual performance and scores. As expected, both sectional and overall scores have seen a sharp decline compared to previous years, and cut-offs in some sections are likely to touch record lows.

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With the absolute (raw) scores now available — and notably lower — one question gains importance:

How will scores across multiple slots and sections be equated and normalised?

The standard argument that a tough paper affects everyone equally does not fully apply to CAT, given that the exam is administered across multiple slots with different question papers taken by other groups of candidates.

With the CAT 2025 raw scores now available, it is clear that there was a slight but noticeable difference in the difficulty level of the paper both across slots and sections. But this variation in difficulty across slots and sections, though modest, is still meaningful and cannot be ignored from a candidate-impact perspective. The important point to remember is that such a difference is not unusual, and the CAT and other major entrance exams have a few standardised, scientific and well-accepted approaches which they employ post-exam to equate and normalise the scores.

Also Read | Where are IIM CAT toppers from the past five years today?

The most logical and impactful step towards such an attempt at equating and normalising the test scores is to try and minimise the very need for such an effort in the first place. In short, for any given section, the very design and development of the question paper for each slot is done in a manner so as to replicate the look, feel and difficulty level across slots as closely as possible.

And in case of the CAT, it has been historically observed that the CAT authorities make a conscious and significant effort on this front and manage to do a commendable job, most of the time! They manage to ensure a significant degree of uniformity, or at least similarity, of models, topics and difficulty levels across slots for a section. However, such an effort can only yield a certain limited level of results and can also easily become difficult to implement and replicate year after year, and inevitably, things go out of alignment. And this is where the more rigorous and scientific approach comes in and takes care of the job in a more professional, but not always foolproof, manner.

How IIMs use normalisation of scores?

Now, coming to the exact methodology that the IIMs use for such normalisation of scores across slots in a given section, an official process document has been shared on the CAT website.

The process has remained the same for several years now, and so has the document. The details of the process given in the document are slightly technical-sounding and are based on intimidating-looking formulas and expressions and can flummox a casual reader and the average CAT aspirant. But to help you make proper sense of all that the document says, we have simplified the content and made it intuitive and relatable. So read on to get a good understanding of what all the CAT does to equate and normalise your scores.

Firstly, the precise and concise statement that is shared in the document reads as follows: “The Normalisation process shall adjust for location and scale differences of score distributions across different forms.” Now, many so called experts have interpreted the terms ‘location’ and ‘scale’ in this cryptic-sounding statement to literally mean the different cities and the actual number of test-takers in different slots. However, such an interpretation is far removed from the intended meaning.

To grasp the correct meaning of these terms, one first needs to imagine a simple visual chart representing the scores of all the candidates in any section from any slot. Here, all possible marks (say, 0 to 100) are plotted along the horizontal axis and the number of students who scored each possible mark level are plotted along the vertical axis. This plot (for large enough populations) usually looks like what is called a bell curve – due to its similarity to a bell shape – or, mathematically, a normal curve.

To know more about CAT 2025 result, cut-off and IIM selection process, candidates can check the IE Education portal

Now, the simple average of all the candidate scores can be represented with a vertical line, and this line, or mark, is the mean of the distribution of scores plotted on such a chart. This mean itself is the location – as mentioned in the official document – of the distribution. Also, such a distribution can be flatly spread along the horizontal axis – like a short but wide hill – or it can be narrow and high – like a tall and steep mountain. This ‘spread’ of the distribution is what is also known as scale – as mentioned in the official document.

Now, the average of scores, that is the location, indicates the difficulty level of the section in that slot, and is also mathematically speaking, the mean of the distribution. And the scale is the spread of the scores, or the flat/steep -ness of the distribution, which indicates the relative score-ability of that section, and is represented by another mathematical parameter known as the standard deviation of the distribution.

Therefore, when the IIMs say their normalisation process will adjust for differences in location and scale, we can understand that they are referring to the ‘difficulty level’ and the relative ‘score-ability’ of the section in each slot.

Now that we have a better understanding of what the broad process means, we can look at a rather intuitive application of the same. Think of it like running a race: some runners may be given a flat track, while others get a hilly track. Simply comparing finishing times for a given distance (or maybe the distance run in a given time) would be unfair to the contestants. This is intuitively obvious because the effort required is not the same.

Normalisation is the adjustment that makes performances from different tracks comparable

Normalisation is the adjustment that makes performances from different tracks comparable. The approach used by the IIMs is also known as the z-score method. Under this system, each candidate’s performance is first compared to the average score in his or her slot, and then expressed in terms of number of steps above or below that average.

These “steps” are technically called standard deviations. As mentioned above, they measure how scattered or spread out the scores are in that slot. For example, being one step above average means your score was higher than the average score by the size of one standard deviation.

If two candidates, from different slots, are the same number of steps above their respective slot’s average, they are considered to have performed equally well and are eventually awarded the same scaled score, in principle ensuring fairness and equity.

The scaled scores such obtained are then considered to rank all students across slots in each section in the descending order, and the sectional percentiles are awarded based on their rank in each section. The process of percentile calculation is fairly straightforward, and we do not need to cover that here, except for the mention that it is simply the percentage of candidates who have scored below one’s score.

The overall percentiles are then calculated based on the total scaled scores, which are simply the sums of the individual sectional scaled scores.

Further, as mentioned earlier, after equating the scores in any given section across multiple slots, there are also differences present in the very ‘score-ability’ and difficulty-level of each section, which may or may not be eventually addressed fully in the process followed.

The CAT authorities have regularly mentioned this aspect of normalising the scores across sections also using what is termed as the percentile equivalence approach. In the percentile equivalence approach, instead of only asking how many steps above or below the average a candidate is, one looks directly at the candidate’s position among peers.

Despite the IIMs’ claim of normalising across sections, it has been historically observed that the raw scores and even the scaled scores in one or more sections may be, in general, higher or more scoring than those in the other sections.

This slight, yet important, difference tends to skew the composition of the toppers when considering the overall score across sections – because those who perform relatively strongly in the more score-able section get a slight edge over those who might instead have performed strongly in another section which happened to be not as score-able as the former. However, it remains to be seen how effectively they will do this for CAT2025.

(The author is the Senior Vice President, R&D, T.I.M.E.)