Question ID: #248
Marks obtained 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
- (1) 48
- (2) 44
- (3) 40
- (4) 52
Solution:
Median formula for grouped data:
$$\text{Median} = l + \frac{\left(\frac{N}{2} – cf\right)}{f} \times h$$
Here,
$l = 12,\; h = 6,\; f = 12,\; cf = 18,\; \text{Median} = 14$
Substitute values:
$$14 = 12 + \frac{\left(\frac{N}{2} – 18\right)}{12} \times 6$$
$$2 = \frac{\frac{N}{2} – 18}{2}$$
$$\frac{N}{2} – 18 = 4$$
$$\frac{N}{2} = 22$$
$$N = 44$$
Ans. (2)
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