Question

The median of the following data is 525. Find the values of x and y, if the total frequency is 100. Here, CI stands for class interval and Fr for frequency.

CI	0-100	100-200	200-300	300-400	400-500	500-600	600-700	700-800	800-900	900-1000
Fr	2	5	x	12	17	20	y	9	7	4

• A. $x=9$ $and$ $y=15$
• B. $x=9$ $and$ $y=25$
• C. $x=11$ $and$ $y=27$
• D. $x=7$ $and$ $y=18$

Answer 1

The correct option is A $x=9$ $and$ $y=15$

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

medium is $525$, Total frequency $=100$

So, total frequency, below $525=$ above $525=\frac{100}{2}=50$

As, we don't know how many /what is the frequency below or above $525$ in the class $500-600$ so, we have to find from the options

$2+5+x+12+17+20+y+9+7+4=100$

$\Rightarrow 76+x+y=100\Rightarrow x+y=100-76=24$

$\Rightarrow x=9$ and $y=15$ from options.