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

The given series is in inclusive form. Converting it to exclusive form and preparing the cumulative frequency table, we have

Class interval	Frequency(fi )	Cumulative Frequency(c.f.)
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
	10 + x + y = 20

Median = 14.4
It lies in the interval 12–18, so the median class is 12–18.
Now, we have
$l=12,h=6,f=5,F=4+x,N=20$
We know that

$$\begin{gathered} 14.4=12+\frac{6\times \left(10-4-x\right)}{5} \\ \Rightarrow 12=36-6x \\ \Rightarrow 6x=24 \\ \Rightarrow x=4 \end{gathered}$$
Now,
10 + x + y = 20
$$\begin{gathered} \Rightarrow x+y=10 \\ \Rightarrow y=10-4=6 \end{gathered}$$