Jee Main 2024 30 01 2024 Shift1 - Question18
Question 18
For the following data table
| $x _i$ | $f _i$ |
|---|---|
| $0-4$ | 2 |
| $4-8$ | 4 |
| $8-12$ | 7 |
| $12-16$ | 8 |
| $16-20$ | 6 |
Find the value of $20 M$ (where $M$ is median of the data)
Show Answer
Answer: (245)
Solution:
| $x _i$ | $f _i$ | c.f. |
|---|---|---|
| $0-4$ | 2 | 2 |
| $4-8$ | 4 | 6 |
| $8-12$ | 7 | 13 |
| $12-16$ | 8 | 21 |
| $16-20$ | 6 | 27 |
$$ \begin{array}{r} N=\sum f=27 \\ \left(\frac{N}{2}\right)=\frac{27}{2}=13.5 \end{array} $$
So, we have median lies in the class $12-16$
$l _1=12, f=8, h=4$, c.f. $=13$
So, here we apply formula
$$ \begin{aligned} M & =I _1+\frac{\frac{N}{2}-c . f .}{f} \times h=12+\frac{13.5-13}{8} \times 4 \\ & =12+\frac{.5}{2} \end{aligned} $$
$M=\frac{24.5}{2}=12.25$
$$ 20 M=20 \times 12.25 $$
$$ =245 $$
BETA
