Raw Score Calculation
Suppose now XYZ is a candidate who appeared in the morning session and her raw score in QA section is R. Then the scaled score of XYZ in QA, say ^R is given by:
M1^0.1 is the mean raw score in QA section of the top 0.1% candidates in the morning session and denote it by M1^0.1
Mean = M1 is the mean of raw scores in QA section for all candidates appearing in the morning session.
SD = S1 is the standard deviation (SD) of the raw scores in QA section for all candidates appearing in the morning session.
G1 = M1 + S1 Sum of the mean and the standard deviation (SD) of the raw scores in QA section for all candidates appearing in the morning session.
Similar Methodology is applied for computation of scaled scores for other sections.
Percentile Calculation
N = The total number of candidates who appeared for CAT
r = rank assigned based on the scaled scores obtained in a section
P = percentile score of a candidate
The steps described below are followed to calculate the CAT 2024 overall and sectional percentile scores obtained by a candidate. While illustrating the percentile score calculation process, QA section is chosen as an example. Similar process is followed for the overall percentile score calculation and for the other two sections, i.e. DILR and VARC in CAT 2024.
Step 1: Calculate the total number of candidates (N) who appeared for CAT (i.e. including morning, afternoon and evening sessions).
Step 2: Assign a rank (r), based on the scaled scores obtained in the QA section, to all candidates who appeared for CAT 2024. In the case of two or more candidates obtaining identical scaled scores in the QA section, assign identical ranks to all those candidates.
As an illustration suppose exactly two candidates obtain the highest scaled score in the QA section, then both of those candidates are assigned a rank of 1. Moreover, the candidate(s) obtaining the second highest scaled score in the QA section are assigned a rank of 3 and so on.
Step 3: Calculate the percentile score (P) of a candidate with rank (r) in the QA section as: P = (N-r)/N x 100
Step 4: Round off the calculated percentile score (P) of a candidate up to two decimal points. For example, all percentile scores greater than or equal to 99.995 are rounded off to 100, all
percentile scores greater than or equal to 99.985 but strictly less than 99.995 are rounded off to 99.99 and so on…
A methodology similar to the one described above is used for the computation of the overall CAT 2025 percentile scores and for the percentile scores of other sections.
Step-by-Step Breakdown:
The formula shown in the image and the details provided suggest that the scaled score R^\hat{R}R^ in the QA section of the CAT exam is calculated based on the performance of the candidate (raw score RRR) in comparison to the performance of the top 0.1% candidates (mean of top 0.1% candidates’ raw scores, denoted as M10.1M_1^{0.1}M10.1) and the average performance of all candidates (mean M1M_1M1 and standard deviation S1S_1S1) in the morning session.
Let’s break this down step-by-step and use an example of 10 students, similar to your earlier example.
Variables in the Formula:
- R^ = Scaled score of the candidate.
- R = Raw score of the candidate in QA section.
- G1=M1+S1 = Sum of the mean and standard deviation of the raw scores in QA section for all candidates.
- M10.1 = Mean raw score in QA section of the top 0.1% candidates in the morning session.
- M1 = Mean of raw scores in QA section for all candidates.
- S1 = Standard deviation of the raw scores in QA section for all candidates.
Example with 10 Students
Let’s assume the following raw scores for the 10 students in the QA section:
| Student ID | Raw Score (R) |
|---|---|
| Student A | 100 |
| Student B | 95 |
| Student C | 90 |
| Student D | 85 |
| Student E | 80 |
| Student F | 75 |
| Student G | 70 |
| Student H | 65 |
| Student I | 60 |
| Student J | 55 |
Step 1: Calculate M1 (Mean of All Raw Scores)
The mean M1M_1M1 is calculated as the average raw score of all 10 students.M1=100+95+90+85+80+75+70+65+60+55 /10=775/10=77.5
Step 2: Calculate S1 (Standard Deviation)
The standard deviation S1S_1S1 is calculated using the formula:S1=1N∑(Ri−M1)2
Where Ri are the raw scores of the students, M1M_1M1 is the mean, and N=10 is the total number of students. Let me calculate the standard deviation for these 10 students.
Step 3: Calculate M1^0.1 (Mean of Top 0.1% Candidates)
Since there are only 10 students, let’s assume that the top 0.1% candidates are the top performer(s). Here, we take the mean raw score of the top candidate, which is 100100100, so:M10.1=100
Step 4: Calculate G1=M1+S1
This step involves adding the mean M1M_1M1 to the standard deviation S1 to get G1
Now, I will compute the standard deviation S1S_1S1 and the final values for G1 and then apply the formula to calculate R^. I’ll do this calculation next.
The calculations are as follows:
- M1M_1M1 (Mean of all raw scores) = 77.5
- S1S_1S1 (Standard deviation of raw scores) = 14.36
- M10.1M_1^{0.1}M10.1 (Mean of the top 0.1% candidates) = 100
- G1=M1+S1=91.86G_1 = M_1 + S_1 = 91.86G1=M1+S1=91.86
Now, let’s calculate the scaled score R^\hat{R}R^ for one of the students (say, Student B with a raw score R=95R = 95R=95) using the formula
Where G=M1=77.5G = M_1 = 77.5G=M1=77.5.
I’ll perform the calculation for Student B.
The scaled score (R^\hat{R}R^) for Student B, who has a raw score of 95, is approximately 86.18.
This calculation demonstrates how the scaled score is derived using the raw score, mean, standard deviation, and the performance of the top candidates. Similar calculations can be done for the other students using the same formula.
| Student | Raw Score | Scaled Score |
| Student A | 100 | 100 |
| Student B | 95 | 86.2 |
| Student C | 90 | 72.4 |
| Student D | 85 | 58.5 |
| Student E | 80 | 44.7 |
| Student F | 75 | 30.9 |
| Student G | 70 | 17.1 |
| Student H | 65 | 3.2 |
| Student I | 60 | -10.6 |
| Student J | 55 | -24.4 |
