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 :

Solution

Maths sir · 3 steps

Everything in the grouped median formula is given except N, so put the numbers in and solve for N.

1. Read off the data. The median class is 12 to 18, so the lower limit is l = 12 and the width is h = 6. Its frequency is f = 12. The 18 students below 12 marks are the cumulative frequency before the median class, so cf = 18.

   Median = l + (N/2 - cf)/f × h

2. Put in numbers. 14 = 12 + (N/2 - 18)/12 × 6. This gives 2 = (N/2 - 18)/2, so N/2 - 18 = 4.
3. So. N/2 = 22, so N = 44. The total number of students is 44, option (b).

The idea to keep. In a grouped median question, list l, h, f and cf first. Then the one unknown, whether it is N, f or cf, comes out of a single linear equation.

Answer from the NTA final answer key. Solution by PrepWiser.