JEE MAIN - Mathematics (2024 - 9th April Morning Shift - No. 9)
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 :
43
46
44
47
Explanation
| Age | No. of Students | CF |
|---|---|---|
| 15 | 5 | 5 |
| 16 | 8 | 13 |
| 17 | 5 | 18 |
| 18 | 12 | 30 |
| 19 | $$x$$ | $$30+x$$ |
| 20 | $$y$$ | $$30+x+y$$ |
$$\begin{aligned} & 30+x+y=40 \\ & x+y=10 \end{aligned}$$
Median $$=\left(\frac{n+1}{2}\right)^{\text {th }}$$ observation
$$=\frac{40+1}{2}=\frac{41}{2}$$
Median $$=18$$
Mean deviation about median
$$\begin{aligned} & 5.3+8.2+5.1+12.0+x \cdot 1+y \cdot 2=1.25 \times 40 \\ & 15+16+5+x+2 y=50 \\ & x+2 y=14 \\ & \quad x+y=10 \\ & \Rightarrow \quad x=4 \\ & \Rightarrow \quad y=6 \\ & \begin{aligned} 4 x+5 y & =24+20 \\ & =44 \end{aligned} \end{aligned}$$
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