Question

The median of the distribution given below is $14.4$. Find the values of x and y, if the total frequency is $20.$

Class interval	0-6	6-12	12-18	18-24	24-30
Frequency	4	x	5	y	1

Answer 1

Class Interval	Frequency	midpoint (x)	Comm frequecy
0-6	4	3	4
6-12	x	9	4+x
12-18	5	15	9+x
18-24	y	21	9+x+y
24-30	1	27	10+x+y
Total	20

$\sum f=20$
$x+y=10----------\left(1\right)$
Median is $14.4$
S0, Median class is $12-18$
Median $=L+\frac{\frac{n}{2}-C}{f}\times w$
So $14.4=12+\frac{\frac{20}{2}-(4+x)}{5}\times 6$
$14.4\times 5=60+(10-4-x)\times 6$
$72=60+60-24-6x$
$6x=120-24-72$
$6x=120-96$
$6x=24$
$x=4$
from eq (1)
$4+y=10\Rightarrow y=6$