If the median of the following data is 28.5 and the total frequency is 60, determine the values of x and y. <style> table{width:100%;margin-bottom:5px; margin-top:5px;} table, th, td { border: 1px solid black; border-collapse: collapse; text-align: center;} </style> <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 for the class is:

Class Boundaries	Frequency	Cumulative Frequency (less than type)
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+\(x+y=n\)

Given \( n = 60 \), By condition, \( 45 + x + y = 60 \) or, \( x + y = 15 ----(i) \) Also, since the median is \( 28.5 \), The median class is \( (20-30) \). The median formula: \[ = l + \left[\cfrac{\cfrac{n}{2}-cf}{f}\right]×h \] 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: \[ 20+ \cfrac{25-x}{2} = 28.5 \] \[ \cfrac{25-x}{2} = 8.5 \] \[ 25 - x = 17 \] \[ -x = -8 \] \[ x = 8 \] Substituting \( x \) in equation (i): \[ 8 + y = 15 \] \[ y = 7 \] Thus, the 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

Class Interval	51-60	61-70	71-80	81-90	91-100	101-110
Frequency	4	10	15	20	15	4

Class Interval	20-29	30-39	40-49	50-59	60-69	70-79
Frequency	12	20	14	6	5	3

Marks \((x_i)\)	0–4	5–9	10–14	15–19	20–24	25–29	30–34	35–39
Frequency \((f_i)\)	4	5	7	8	7	5	6	3

Marks Obtained	0–10	10–30	30–60	60–70	70–90
Number of Students	15	25	30	4	10

Marks	0–5	5–10	10–15	15–20	20–25	25–30	30–35	35–40
Number of Students	2	6	10	16	22	11	8	5

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