Question

The median of the distribution given below is $144$. Find the values of $x$ & $y$. If the sum frequency is $20$.

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

Answer 1

Median of the distribution is $14.4$ & sum of frequencies is $20$

Class interval $0-6$ $6-12$ $12-18$ $18-24$ $24-30$

Frequency $4$ x $5$ y $1$

Class interval frequency cumulative frequency

$0-6$ $4$ $4$

$6-12$ x $4+x$(c.f)

$12-18$(l) $5$(f) $9+x$

$18-24$ y $9+x+y$

$24-30$ $1$ $10+x+y$

$10+x+y$

$\Rightarrow 10+x+y=20$

$\Rightarrow x+y=10$.........$\left(1\right)$

Given $\sum f=N=20$

$\Rightarrow N/2=10$

Here given median is $14.4$

so median class is $12-18$

Median class

lower limit(l)$=12$

Class height(h)$=6$

Frequency $=5$

Prececidue cf of median class$=4+x$

Median$=l+\left(\frac{N/2-c.f}{f}\right)\times h$

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

$5\times 2.4=(10-4-x)\times 6=(6-x)\times 6$

$12=36-6x$

$\Rightarrow 6x=36-12$

$6x=24$

$\Rightarrow x=4$

$\therefore x=4,y=6$

$\left(1\right)$ $\Rightarrow x+y=10$

$\Rightarrow 4+y=10$

$y=6$.