If the combined mean of the following frequency distribution table is 54, determine the value of \(K\): <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>0-20</td><td>20-40</td><td>40-60</td><td>60-80</td><td>80-100</td> </tr> <tr> <td>Frequency</td><td>7</td><td>11</td><td>K</td><td>9</td><td>13</td> </tr> </table>

Q.If the combined mean of the following frequency distribution table is 54, determine the value of \(K\):

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

Class Interval	Frequency (\(f_i\))	Class Midpoint (\(x_i\))	\(f_ix_i\)
0-20	7	10	70
20-40	11	30	330
40-60	\(k\)	50	\(50k\)
60-80	9	70	630
80-100	13	90	1170
Total	\(\sum f_i=\) \(40+k\)		\(\sum f_ix_i=\) \(2200+50k\)

\(\therefore\) According to the given condition, the combined mean is \(54\).
Thus, \(\cfrac{\sum x_i f_i}{\sum f_i}=54\)
or, \(\cfrac{2200+50k}{40+k}=54\)
or, \(2160+54k=2200+50k\)
or, \(54k-50k=2200-2160\)
or, \(4k=40\)
or, \(k=10\)

\(\therefore\) The required value of \(k=10\).

Class Interval	0–20	20–40	40–60	60–80	80–100
Frequency	7	11	k	9	13

Class Interval	0-10	10-20	20-30	30-40	40-50
Frequency	15	20	35	p	10

Numbers	0-10	10-20	20-30	30-40	40-50
Number of students	15	20	35	p	10

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

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

Class Interval	0-5	5-10	10-15	15-20	20-25	25-30	30-35
Frequency	5	12	18	28	17	12	8

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

Size Number of Items	4–8	8–12	12–16	16–20	20–24	24–28	28–32
Frequency	9	10	18	14	10	6	3

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

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

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

Age (in years)	16–18	18–20	20–22	22–24	24–26
Number of Candidates	45	75	38	22	20

Class	0–5	5–10	10–15	15–20	20–25	25–30	30–35
Frequency	5	12	18	28	17	12	8

Variable	5	10	15	20	25
Frequency	6	p	6	10	5

Class Interval	3-6	6-9	9-12
Frequency	2	6	12

12-15	15-18	18-21	21-24
24	21	12	3