UPSC CDS I 2025 Mathematics Paper

Median for grouped data =L+[(N∕2−CF)∕f]×h
Where, L= lower boundary of median class, N= total observations, CF= cumulative frequency before median class, f= frequency of median class, h= class width
Calculations:
Cumulative frequencies:
3⟶50
5⟶50+52=102
6⟶102+47=149
7⟶149+56=205
N∕2=205∕2=102.5⟶ lies in class x=6( since CF before =102)
Assuming class width h=1,L=6
Median =6+[(102.5−102)∕47]×1
⇒ Median =6+[0.5∕47]
⇒ Median ≈6+0.0106≈6