JEE Main 2024 (Online) 9th April Morning ShiftQuestion 1
The frequency distribution of the age of students in a class of $40$ students is given below.
Age : $15,16,17,18,19,20$
No of Students : $5,8,5,12,x,y$
If the mean deviation about the median is $1.25$, then $4x+5y$ is equal to :
Statistics
Solution
$5+8+5+12+x+y=40\Rightarrow x+y=10$. Cumulative: 5,13,18,30 so the 20th and 21st values both equal $18$; median $=18$. $\sum f|d|=5\cdot3+8\cdot2+5\cdot1+0+x\cdot1+y\cdot2=36+x+2y=40\cdot1.25=50\Rightarrow x+2y=14$. With $x+y=10$: $y=4,x=6$. $4x+5y=24+20=44$. Option B.