Marks obtains by all the students of class 12 are presented in a freqency 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

We are given a grouped frequency distribution with median = 14, median class 12-18, median class frequency $$f = 12$$, and cumulative frequency below 12 is $$F = 18$$.

$$\text{Median} = L + \left(\frac{N/2 - F}{f}\right) \times h$$

where $$L = 12$$ (lower boundary), $$F = 18$$ (cumulative frequency before median class), $$f = 12$$ (median class frequency), $$h = 6$$ (class width).

$$14 = 12 + \left(\frac{N/2 - 18}{12}\right) \times 6$$

$$2 = \frac{N/2 - 18}{2}$$

$$4 = N/2 - 18$$

$$N/2 = 22$$

$$N = 44$$

The correct answer is Option 3: 44.