Determine the combined mean using the step deviation method from the following data: <br/> <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><td>30 - 40</td><td>40 - 50</td><td>50 - 60</td> </tr><tr> <td>Frequency</td><td>7</td><td>5</td><td>6</td><td>12</td><td>8</td><td>2</td> </tr></table>

Q.Determine the combined mean using the step deviation method from the following data:

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

Taking \(a = 25\) and \(h = 10\), we obtain:

Class Interval	Frequency \((f_i )\)	Class Midpoint \((x_i)\)	\(u_i = \cfrac{x_i - a}{10}\)	\(f_i u_i\)
0-10	7	5	-2	-14
10-20	5	15	-1	-5
20-30	6	25	0	0
30-40	12	35	1	12
40-50	8	45	2	16
50-60	2	55	3	6
Total	\(Σf_i = 40 \)			\(Σf_i u_i = 15\)

Using the step deviation method, the required mean is:
\(= a + h \times \cfrac{Σf_i u_i}{Σf_i} \)
\(= 25 + 10 \times \cfrac{15}{40}\)
\(= 25 + 3.75 = 28.75\) (Answer).
(Proved).

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	50–60
Frequency	7	10	23	50	6	4

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

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

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

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

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

Class Interval	5-14	15-24	25-34
Frequency	3	6	18

35-44	45-54	55-64
Frequency	20	10	3

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