Question

If the median for the following frequency distribution is 28.5, find the values of x and y.

Class Intervals	frequency
0-10	5
10-20	x
20-30	20
30-40	15
40-50	y
50-60	5
Total	60

Answer 1

$Class-Interval$	$Frequency$ $f_i$	$c.f$
$0-10$	$5$	$5$
$10-20$	$x$	$5+x$
$20-30$	$20$	$25+x$
$30-40$	$15$	$40+x$
$40-50$	$y$	$40+x+y$
$50-60$	$5$	$45+x+y$
	$\sum f_i=45+x+y$

$N=60$ [ Given ]

Then, $\frac{N}{2}=\frac{60}{2}=30$

$\therefore$ Median class $=20-30$

Then, $l=20,c.f=5+x,f=20$ and $h=10$

$Median=l+\frac{\frac{N}{2}-c.f}{f}\times h$

$28.5=20+\frac{30-(5+x)}{20}\times 10$

$8.5=\frac{25-x}{2}$

$17=25-x$

$\therefore$ $x=8$

$\sum f_i=60$

$45+x+y=60$

$45+8+y=60$

$\therefore$ $y=7$

$\therefore$ $x=8$ and $y=7$