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

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Solution

Q.
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 [2025]

1 48

2 52

3 40

4 44

Ans.
(4)

In the given question, l = 12, cf = 18, median = 14, f = 12 and h = 6

$∴ Median = l + (\frac{\frac{N}{2} - c f}{f}) \times h$

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

$\Rightarrow 2 = \frac{\frac{N}{2} - 18}{2} \Rightarrow 4 = \frac{N}{2} - 18$

$\Rightarrow \frac{N}{2} = 22 \Rightarrow N = 44$

So, total number of students = 44.

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