Question

If the median of the distribution given below is $27$, find the value of the $x$ and $y$

C.I.	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	Total
f	$5$	$x$	$20$	$14$	$y$	$8$	$68$

Answer 1

C.I	f	c.f
0 - 10	5	5
10 - 20	x	5+x
20 - 30	20	25+x
30 - 40	14	39+x
40 - 50	y	39+x+y
50 - 60	8	47+x+y.
Total	68.

here, 47+x+y =68 _____ (1)

Given that, median = 27.

Hence the median class is 20 - 30.

$\therefore l=20,\frac{m}{2}=\frac{68}{2}=34,c.f=5+x,h=10,f=20.$

we know, median =$l+\frac{\frac{m}{2}-c.f}{f}\times h$

$27=20+\frac{34-(5+x)}{20}\times 10$

$27=20+\frac{34-5-x}{2}$

$\Rightarrow 54=40+34-5-x.$

$\Rightarrow =69-x.$

$\Rightarrow x=69-54$

$\Rightarrow x=15$

from (1), y = 68-47-15 = 6

Hence x = 15, y = 6