Statistics
Statistics
nta_pyq_2025_jan
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: Median for grouped data: $L+\dfrac{N/2-F}{f}\cdot h$ where $L=$ lower bound of median class, $F=$ cumulative frequency before the median class, $f=$ median class frequency, $h=$ class width.
$14=12+\dfrac{N/2-18}{12}\cdot 6\ \Longrightarrow\ \dfrac{N/2-18}{12}\cdot 6=2\ \Longrightarrow\ \dfrac{N}{2}-18=4.$
Hence $N=44.$
Correct Answer: 3