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QJEEM24Ma1304: JEE Main 2024 Mathematics - Class 11 JEEM24Ma1304 Solution: The frequency distribution of the age of students in a class of …

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 xx yy

If the mean deviation about the median is 1.25, then 4x+5y4x+5y is equal to :

Multiple Choice Options

  • A 43
  • B 46
  • C 44
  • D 47

Step-by-Step Verified Solution

Age No. of Students CF
15 5 5
16 8 13
17 5 18
18 12 30
19 xx 30+x30+x
20 yy 30+x+y30+x+y

amp;30+x+y=40amp;x+y=10\begin{aligned}& 30+x+y=40 \\& x+y=10\end{aligned}

Median =(n+12)th =\left(\frac{n+1}{2}\right)^{\text {th }} observation

=40+12=412=\frac{40+1}{2}=\frac{41}{2}

Median =18=18

Mean deviation about median

amp;5.3+8.2+5.1+12.0+x⋅1+y⋅2=1.25×40amp;15+16+5+x+2y=50amp;x+2y=14amp;x+y=10amp;⇒x=4amp;⇒y=6amp;4x+5yamp;=24+20amp;=44\begin{aligned}& 5.3+8.2+5.1+12.0+x \cdot 1+y \cdot 2=1.25 \times 40 \\& 15+16+5+x+2 y=50 \\& x+2 y=14 \\& \quad x+y=10 \\& \Rightarrow \quad x=4 \\& \Rightarrow \quad y=6 \\& \begin{aligned}4 x+5 y & =24+20 \\& =44\end{aligned}\end{aligned}

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