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

Median `= l + {(N/2 - F)/f} xx h `

\[14 . 4 = 12 + \frac{6 \times \left( 10 - 4 - x \right)}{5}\]

\[ \Rightarrow 12 = 36 - 6x\]

\[ \Rightarrow 6x = 24\]

\[ \Rightarrow x = 4\]

Now,
10 + x + y = 20

\[\Rightarrow x + y = 10\]

\[ \Rightarrow y = 10 - 4 = 6\]