Question

Consider the following frequency distribution.

Class	0-10	10-20	20-30	30-40	40-50
Frequency	5	x	10	y	15

If the sum of the frequencies is $50$ , and the median is $29$, then evaluate $|x-y|$.

Answer 1

Class	Frequency	c.f
0-10	5	5
10-20	x	5+x
20-30	10	15+x
30-40	y	15+x+y
40-50	15	30+x+y
Total	N=30+x+y

Sum of frequency $=50$
$\Rightarrow 30+x+y=50$
$\Leftrightarrow x+y=20\,\,\,...(i)$
Median $=29$
$\Rightarrow$ Median lies in the interval $20-30$
$\Rightarrow$ Median $=l_{1}+\frac{\left(\frac{ N }{2}- c . f \right)}{f} \times h$
$\Rightarrow$ Here $l_{1}=20, f=10$,
$ c.f =5+x, h=10$
$N =50$
$\Rightarrow 29=20+\frac{(25-(5+x))}{10} \times 10$
$\Rightarrow 9=20-x$
$\Rightarrow x=11\,\,\,...(ii)$
$y=9\,\ldots$ [From (i) and (ii)]
$\Rightarrow|x-y|=|11-9|=2$