JEE Main · 2025 · 23 Jan 2025 · Shift 1 · Statistics

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Marks obtains by all the students of class 12 are presented in a frequency distribution with classes of equal width. Let the median of this grouped data be 14 with median class interval 12-18 and median class frequency 12. If the number of students whose marks are less than 12 is 18, then the total number of students is

(A)48
(B)44✓ Correct
(C)40
(D)52

Answer: (B)

Solution

Using the median formula for grouped data,

Median = ℓ + (\frac{\frac{N}{2} - F}{f}) h

with

ℓ = 12

F = 18

f = 12

h = 6

, Median

= 14

14 = 12 + (\frac{\frac{N}{2} - 18}{12}) 6 ⟹ 2 = \frac{\frac{N}{2} - 18}{2} ⟹ \frac{N}{2} - 18 = 4 ⟹ \frac{N}{2} = 22 ⟹ N = 44

JEE Main · 2025 · 23 Jan 2025 · Shift 1 · Single correct option

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