If the median of the distribution given below is $28.5,$ find the values of $x$ and $y$.

Class interval	Frequency
$0-10$	$5$
$10-20$	$x$
$20-30$	$20$
$30-40$	$15$
$40-50$	$y$
$50-60$	$5$
Total	$60$

(A) The cumulative frequency for the given data is calculated as follows:

Class interval	Frequency	Cumulative frequency
$0-10$	$5$	$5$
$10-20$	$x$	$5+x$
$20-30$	$20$	$25+x$
$30-40$	$15$	$40+x$
$40-50$	$y$	$40+x+y$
$50-60$	$5$	$45+x+y$

From the table,the total frequency $n = 60$.
Thus,$45+x+y = 60 \implies x+y = 15 \dots (1)$.
The median is $28.5$,which lies in the class interval $20-30$.
Therefore,the median class is $20-30$.
Lower limit $(l) = 20$,frequency $(f) = 20$,cumulative frequency $(cf) = 5+x$,and class size $(h) = 10$.
Using the median formula: $\text{Median} = l + \left( \frac{\frac{n}{2} - cf}{f} \right) \times h$.
$28.5 = 20 + \left( \frac{30 - (5+x)}{20} \right) \times 10$.
$8.5 = \frac{25-x}{2}$.
$17 = 25 - x \implies x = 8$.
Substituting $x=8$ into equation $(1)$: $8+y = 15 \implies y = 7$.
Thus,$x = 8$ and $y = 7$.