If the median of the given 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 given 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 is as follows:

Class Boundary	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+\(x+y=n\)

Here, \(n=60\) (given).
According to the condition, \(45+x+y=60\)
or, \(x+y=15----(i)\)
Also, ∵Median = 28.5
So, the median class is (20-30).
∴ The median is determined using the formula:
\[ = l + \left[\cfrac{\cfrac{n}{2}-cf}{f}\right]×h \]
[Here, \(l=20, n=60, \)
\(cf=5+x, f=20, h=10\)]
\[ = 20 + \left[\cfrac{30-(5+x)}{20}\right]×10 \]
\[ = 20 + \cfrac{25-x}{20}×10 \]
\[ = 20 + \cfrac{25-x}{2} \]

According to the 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 the value of \(x\) in equation \((i)\),
\[ 8+y=15 \]
or, \(y=7\)

∴ The required values are \(x=8, y=7\).

30–40	40–50	50–60
15	y	5

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

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

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

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

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

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

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

Weight (kg)	Less than 38	Less than 40	Less than 42
Number of Students	0	4	6

Less than 44	Less than 46	Less than 48	Less than 50	Less than 52
9	12	28	32	35

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	65–85	85–105	105–125
Frequency	4	15	3

125–145	145–165	165–185	185–205
20	14	7	14