Statistics
Median of Grouped Data
nta_pyq_2025_apr
Grade 11
Question:
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
Step-by-Step Solution
Key Concept: Use the grouped median formula: $\text{Median} = l + \left(\frac{N/2 - F}{f}\right) \times h$, where $l$ = lower boundary, $F$ = cumulative frequency before the class, $f$ = class frequency, $h$ = class width.
$14 = 12 + \left(\frac{N/2 - 18}{12}\right) \times 6 \Rightarrow 2 = \left(\frac{N/2 - 18}{12}\right) \times 6 \Rightarrow N/2 - 18 = 4 \Rightarrow N = 44$.
Correct Answer: 44