UPSC NDA I 2025 Mathematics Paper

Calculate the cumulative frequency.
Cumulative frequency for the 160−162cm range: 12
Cumulative frequency for the 162−164cm range: 12+15=27
Cumulative frequency for the 164−166cm range: 27+24=51
Cumulative frequency for the 166−168cm range: 51+13=64
The total number of students is 64 , so the median class contains the 32 nd student. The cumulative frequency before 32 is 27 (for the 162-164 cm class), and after 32 is 51 (for the 164-166 cm class). Therefore, the median class is 164−166cm.
The formula for finding the median in a grouped frequency distribution is:
Median =L+(‌

‌ N 2 −F

f

)×h
L= lower boundary of the median class =164
N= total number of students =64
F= cumulative frequency before the median class =27
f= frequency of the median class =24
h= class width =2
Substituting the values:
‌ Median ‌=164+(‌

32−27

24

)×2=164+(‌

5

24

)×2=164+0.42=164.42