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 Intervals	Frequency	Cumulative frequency(cf)
0-6	4	4
6-12	x	4+x
12-18	5	9+x
18-24	y	9+x+y
24-30	1	10+x+y
	$\sum f=10+x+y=20$

We have, Median=14.4
Clearly, it lies in the class interval 12-18.So, 12-18 is the median class.
∴ l=12, h=6, f=5 anf F=4+x and $\frac{N}{2}=10$
So,
$Median=l+\frac{\frac{N}{2}-F}{f}\times h$

$=>14.4=12+\frac{10-(4+x)}{5}\times 6$

$=>2.4\times \frac{5}{6}=10-(4+x)$

$2=6-x;x=4$

and also,
10+x+y=10
⇒10+4+y=20
⇒y=6
answer= x= 4 and y= 6