Given that the mean of the data is \( 20.6 \), determine the value of \( a \). <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>\( x_i \)</td><td>10</td><td>15</td><td>\( a \)</td><td>25</td><td>35</td> </tr> <tr> <td>\( f_i \)</td><td>3</td><td>10</td><td>25</td><td>7</td><td>5</td> </tr> </table>

Q.Given that the mean of the data is \( 20.6 \), determine the value of \( a \).

\( x_i \)	10	15	\( a \)	25	35
\( f_i \)	3	10	25	7	5

Variable \((x_i )\)	Frequency \((f_i )\)	\((x_i f_i)\)
10	3	30
15	10	150
\(a\)	25	\(25a\)
25	7	175
35	5	175
Total	\(\sum f_i=50\)	\(\sum x_i f_i=530+25a\)

\(\therefore\) According to the question, the mean is \( 20.6 \). \[ \cfrac{\sum x_i f_i}{\sum f_i} = 20.6 \] \[ \cfrac{530+25a}{50} = 20.6 \] \[ 530+25a = 1030 \] \[ 25a = 500 \] \[ a = 20 \]

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	0-10	10-20	20-30	30-40	40-50
Frequency	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

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

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

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

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	5-14	15-24	25-34	34-44	45-54	55-64
Frequency	3	6	18	20	10	3

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

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

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

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

Size (\(x\))	2	3	4	5	6	7	8	9
Frequency (\(f_i\))	3	4	5	3	5	4	3	2

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

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

Class	100–120	120–140	140–160	160–180	180–200
Frequency	12	14	8	6	10