Question

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

Answer 1

Class Interval	Frequency	Combine Frequency
$0-100$	$3$	$3$
$100-200$	$4$	$3+4=7$
$200-300$	$X$	$x+7$
$300-400$	$12$	$x+7+12=x+19$
$400-500$	$17$	$x+19+17=[x+36]$
$500-600$	$20$	$x+36+20=x+56$
$600-700$	$9$	$x+56+9=x+65$
$700-800$	$Y$	$x+65+y=X+Y+65$
$800-900	$8$	$x+Y+65+8=X+Y+73$
$900-1000$	$3$	$x+y+73+3=X+Y+76$

Median $525$ (Median class $:500-600$)

$h=100$

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

$525=500+\frac{100/2-(x+36)}{20}\times 100$

$\frac{25}{100}\times 20=50-x-36$

$\therefore x=9$

$\sum fi\Rightarrow 76+Y+X=100$

$\Rightarrow 9+Y=100-76$

$Y=24-9$

$=15$

$X,Y\Rightarrow 9,15$