The population of lions was noted in different regions across the world in the following table: If the median of the given data is 525, find the…

Number of lions	Number of regions	Cumulative frequency
$\displaystyle 0$-$\displaystyle 100$	$\displaystyle 2$	$\displaystyle 2$
$\displaystyle 100$-$\displaystyle 200$	$\displaystyle 5$	$\displaystyle 7$
$\displaystyle 200$-$\displaystyle 300$	$\displaystyle 9$	$\displaystyle 16$
$\displaystyle 300$-$\displaystyle 400$	$\displaystyle 12$	$\displaystyle 28$
$\displaystyle 400$-$\displaystyle 500$	\(\displaystyle x\)	\(\displaystyle 28+x\)
$\displaystyle 500$-$\displaystyle 600$	$\displaystyle 20$	\(\displaystyle 48+x\)
$\displaystyle 600$-$\displaystyle 700$	$\displaystyle 15$	\(\displaystyle 63+x\)
$\displaystyle 700$-$\displaystyle 800$	$\displaystyle 9$	\(\displaystyle 72+x\)
$\displaystyle 800$-$\displaystyle 900$	y	\(\displaystyle 72+x+y\)
$\displaystyle 900$-$\displaystyle 1000$	$\displaystyle 2$	\(\displaystyle 74+x+y\)
	$\displaystyle 100$

\[\begin{aligned} & 74+x+y=100 \\ & x+y=26 \end{aligned} \] Median class is $\displaystyle 500$-$\displaystyle 600$ \[525=500+\left[\frac{\dfrac{100}{2}-(28+x)}{20}\right] \times 100 \] On solving, we get \(\displaystyle x=17\) \[y=9 \]