The frequency distribution of the age of students in a class of 40 students is given below…

Question

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 :

Accepted Answer

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

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

Solutions · 1