Question

The median of the following data is $525$. Find the values of $x$ and $y$, if the total frequency is $100$

Class interval	Frequency
$0-100$	$2$
$100-200$	$5$
$200-300$	$x$
$300-400$	$12$
$400-500$	$17$
$500-600$	$20$
$600-700$	$y$
$700-800$	$9$
$800-900$	$7$
$900-1000$	$4$

• A. $x=15$ $y=9$
• B. $x=5$ $y=9$
• C. $x=15$ $y=18$
• D. $x=9$ $y=15$

Answer 1

The correct option is D $x=9$ $y=15$

Computation of Median

Class interval	Frequency (f)	Cumulative frequency (cf)
0-100	2	2
100-200	5	7
200-300	x	7+x
300-400	12	19+x
400-500	17	36+x
500-600	20	56+x
600-700	y	56+x+y
700-800	9	65+x+y
800-900	7	72+x + y
900-1000	4	76+x + y
		Total = 100

We have,
$N=\sum f_i=100$
$\Rightarrow 76+x+y=100\Rightarrow x+y=24$
It is given that the median is $525$. Clearly, it lies in the class $500-600$
$\therefore l=500,h=100,f=20,F=36+x$ and $N=100$
Now,
$Median=i+\frac{\frac{N}{2}-F}{f}\times h$
$\Rightarrow 525=500+\frac{50-(36+x)}{20}\times 100$
$\Rightarrow 525-500=(14-x)\times 5$
$\Rightarrow 25=70-5x\Rightarrow 5x=45\Rightarrow x=9$
Putting $x=9$ in$x+y=24$, we get $y=15.$
Hence, $x=9$and $y=15.$