Results of Mathematics in CUET PG 2025

Introduction

This document presents an introductory analysis of the result of CUET PG 2025 in Mathematics subject.

We load the dataset:

msc <- read.csv("data/msc.csv", header=T)
head(msc, 8)

##   Rank      App.No.    Roll.No.      Candidate.Name            Father.Name
## 1    1 253510253188 UP180606597 RITIK ROSHAN SHARMA           UMESH SHARMA
## 2    2 253510121892 DL011001236     DIVYANSH MITTAL         TIRUPATI GUPTA
## 3    3 253510307212 KL130101356            ADARSH V        VINOD KUMAR P N
## 4    4 253510113180 WB130200647       PURABI MAHATA BHABESH CHANDRA MAHATA
## 5    5 253510100600 WB100207644   ISHAN CHAKRABORTY       MONI CHAKRABORTY
## 6    6 253510169307 UP160100626       SANYAM TANEJA         NARENDER KUMAR
## 7    7 253510156977 DL010803377  DEEPAK KUMAR SINGH            KAMAL SINGH
## 8    8 253510245743 DL011213624         MAAHIR SADH             KAPIL SADH
##   Gender Marks
## 1   Male   239
## 2   Male   229
## 3   Male   227
## 4 Female   222
## 5   Male   216
## 6   Male   210
## 7   Male   208
## 8   Male   208

Congratulations to my batch-mate Maahir Sadh on securing AIR 8. On that note, we list the top ranks from each state. For this, we slice the first two characters of roll numbers (they correspond to the state that the candidate belongs to):

msc <- msc %>%
  mutate(State = substr(msc$Roll.No., 1, 2))

and thus:

msc %>%
  group_by(State) %>%
  slice_max(Marks, n = 1, with_ties = FALSE) %>%
  select(State, Rank, Candidate.Name, Marks) %>%
  arrange(Rank)

## # A tibble: 34 × 4
## # Groups:   State [34]
##    State  Rank Candidate.Name           Marks
##    <chr> <int> <chr>                    <int>
##  1 UP        1 RITIK ROSHAN SHARMA        239
##  2 DL        2 DIVYANSH MITTAL            229
##  3 KL        3 ADARSH V                   227
##  4 WB        4 PURABI MAHATA              222
##  5 OR       15 CHANDRA SEKHAR MAHAPATRO   201
##  6 MP       16 ADARSH TIWARI              199
##  7 UK       17 ANSH GUPTA                 198
##  8 BR       19 SHABD PRAKASH              194
##  9 MR       28 DHRUV SANTOSH SHAH         190
## 10 CG       29 PANKAJ KUMAR VERMA         190
## # ℹ 24 more rows

Number of candidates from each state:

table(msc$State)

## 
##   AL   AM   AN   AP   BR   CG   CH   DL   GJ   GO   HP   HR   JH   JK   KK   KL 
##   48  549    8  123  431  270   25 1383   56   12  386  433  205  294  197  609 
##   LK   LL   MG   MN   MP   MR   MZ   NL   OR   PB   RJ   SM   TA   TL   TN   UK 
##    2    6  253  173  234  123   43   23  719   74  680   46  162  350  342  254 
##   UP   WB 
## 2733  650

Number of male and female candidates:

table(msc$Gender)

## 
## Female   Male 
##   6408   5488

On that note:

msc %>%
  group_by(Gender) %>% 
  summarise(
    Count = n(),
    Min = min(Marks),
    Average = mean(Marks),
    Median = median(Marks),
    Max = max(Marks)
  )

## # A tibble: 2 × 6
##   Gender Count   Min Average Median   Max
##   <chr>  <int> <int>   <dbl>  <dbl> <int>
## 1 Female  6408   -31    46.9     40   222
## 2 Male    5488   -21    55.0     45   239

On General Trends

We see that the scatter plot of marks vs. rank follows something around a sigmoid curve:

ggplot(msc, aes(x=Marks,
                y=Rank,
                col=Gender)) +
  geom_point()

Further and subsequently that marks of all candidates follow the Gaussian distribution, in this case one that is skewed to the right, given that the exam was moderate in terms of difficulty level.

ggplot(msc, aes(x=Marks,
                color=Gender,
                fill=Gender)) +
  geom_density(alpha=0.05,
               linewidth=1)

We find the general performance of students State-vise:

ggplot(msc, aes(y=Marks,
                color=Gender)) +
  geom_boxplot() +
  facet_wrap(~State)