If the median of the following data is 28.5, and the total frequency is 60, determine the values of x and y. <table><tr> <td>Class Interval</td><td>0-10</td><td>10-20</td><td>20-30</td> </tr><tr> <td>Frequency</td><td>5</td><td>x</td><td>20</td> </tr></table> <table><tr> <td>30-40</td><td>40-50</td><td>50-60</td> </tr><tr> <td>15</td><td>y</td><td>5</td> </tr></table>

Q.If the median of the following data is 28.5, and the total frequency is 60, determine the values of x and y.

Class Interval	0-10	10-20	20-30
Frequency	5	x	20

30-40	40-50	50-60
15	y	5

The frequency distribution table:

Class Boundaries	Frequency	Cumulative Frequency (Less Than)
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+\(x+y=n\)

Here, \(n=60\) (Given). By condition, \(45+x+y=60\), or, \(x+y=15----(i)\). Since the median = 28.5, The median class is (20-30). Formula for median: \(=l+\left[\cfrac{\cfrac{n}{2}-cf}{f}\right]×h\) Where: \(l=20\), \(n=60\), \(cf=5+x\), \(f=20\), \(h=10\). \(=20+\left[\cfrac{30-(5+x)}{20}\right]×10\) \(=20+\cfrac{25-x}{20}×10\) \(=20+\cfrac{25-x}{2}\) By condition: \(20+ \cfrac{25-x}{2}=28.5\) or, \(\cfrac{25-x}{2}=8.5\) or, \(25-x=17\) or, \(-x=-8\) or, \(x=8\). Substituting \(x\) in equation (i): \(8+y=15\) or, \(y=7\). ∴ Required values: \(x=8, y=7\).

30–40	40–50	50–60
15	y	5

Marks	Less than 10	Less than 20	Less than 30	Less than 40	Less than 50	Less than 60	Less than 70	Less than 80
Number of students	4	16	40	76	96	112	120	125

Class Interval	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60
Frequency	7	5	6	12	8	2

Class Boundaries	Less than 10	Less than 20	Less than 30	Less than 40	Less than 50	Less than 60	Less than 70	Less than 80
Frequency	4	16	40	76	96	112	120	125

Class Interval	0-5	5-10	10-15
Frequency	5	12	18

Class interval	0–10	10–20	20–30	30–40	40–50	50–60
Frequency	10	\(x\)	25	30	\(y\)	10

Class Interval (Marks)	0-10	10-20	20-30	30-40	40-50
Number of Students	15	20	35	p	10

Age (in years)	10–20	20–30	30–40	40–50	50–60	60–70
Number of Patients	12	8	22	20	18	20

15-20	20-25	25-30	30-35
28	17	12	8

15-20	20-25	25-30	30-35
28	17	12	8

Class Interval	0-20	20-40	40-60	60-80	80-100
Frequency	7	11	K	9	13

15-20	20-25	25-30	30-35
28	17	12	8