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 4 x+5 y is equal to :

Mathematics · Statistics

JEE Main 2024 — 9 April, Shift 1 — Question 16

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 $4 x+5 y$ is equal to :

$x+y=10......(1)\\median=18=M \\M.D=\frac{{\displaystyle\sum_{}}f_1\left|x_1-M\right|}{\sum_{}f_1}$

$1.25=\frac{36+x+2y}{40}\\x+2y=14..............(2)\\by(1)\;\&(2)$

$x=6,y=4\\\Rightarrow4x+5y=24+20=44\\\\\\$

Age $\left(x_i\right)\\\\\\\\$	F	$\left\\|x_i-M\right\\|\\\\\\\\$	$F_i\left\\|x_i-M\right\\|\\\\\\\\$
15	5	3	15
16	8	2	16
17	5	1	5
18	12	0	0
19	X	1	X
20	Y	2	2y

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