Calculation of Mean in Individual Series:

Calculation of Mean in Individual Series:
Direct Method

= =
Short cut Method
=A+
Question: - Marks of 10 students are as 15, 20, 30, 22, 25, 18, 40, 50, 55 and 65. Find out
the average marks.
Solution:
Question: - Marks of 10 students are as 15, 20, 30, 22, 25, 18, 40, 50, 55 and 65. Find out
the average marks.
Solution:
Marks
(X)
15
20
30
22
25
18
40
50
55
65
=340
= = = 34
Hence, Average marks of the 10 students = 34
Marks
(X)
15
20
30
22
25
18
40 (A)
50
55
65
N = 10
=A+
= 40 +
= 40 – 6
= 34
Arithmetic Mean = 34
d=X-A
-25
-20
-10
-18
-15
-22
0
10
15
25
=-110 + 50 = -60
Calculation of Mean in Discrete Series:

Calculation of Mean in Discrete Series:

Direct Method
Short cut Method
=
=A+
Question: - Following are the daily earnings of 19 workers. Calculate the mean wages.
Question: - Following are the daily earnings of 19 workers. Calculate the mean wages.
Wages (Rs)
Number of Workers
Wages (Rs)
Number of Workers
10
4
20
5
30
3
40
2
50
5
Solution:
10
4
20
5
30
3
40
2
Solution:
Wages (X)
10
20
30
40
50
Frequency (f)
4
5
3
2
5
= 19
(fX)
40
100
90
80
250
= 560
Wages (X)
10
20
30 (A)
40
50
= = = 29.47
=A+
Mean wages of 19 workers = 29.47
= 30 +
= 30 – 0.53 = 29.47
Arithmetic Mean = 29.47
Frequency (f)
4
5
3
2
5
= 19
d=X-A
-20
-10
0
10
20
(Fd)
-80
-50
0
20
100
= -130 +120 = -10
50
5
Calculation of Mean in continuous Series:

Calculation of Mean in Continuous Series:

Direct Method
Short cut Method
=
=A+
Question: - The following table shows marks of students. Calculate mean marks of the
students.
Question: - The following table shows marks of students. Calculate mean marks of the
students.
Marks
Number of
students
Marks
Number of
students
0-10
20
10-20
24
20-30
40
30-40
36
40-50
20
Solution:
Marks
0-10
10-20
20-30
30-40
40-50
0-10
20
10-20
24
20-30
40
30-40
36
40-50
20
Solution:
Mid Value (m)
=5
=15
=25
=35
=45
Frequency (f)
20
24
40
36
20
=140
(fm)
100
360
1000
1260
900
=3620
Marks
0-10
10-20
20-30
Mid Value (m)
=5
=15
30-40
40-50
= =
=A+
= 25.86
= 25 +
Mean Marks = 25.86
= 25 + 0.86
=25 (A)
=35
=45
Frequency (f)
20
24
40
d=m-A
-20
-10
0
(fd)
-400
-240
0
36
20
=140
10
20
360
400
=120
= 25.86
Mean Marks = 25.86
Calculation of Weighted Mean
=
Question: Calculate the weighted mean of the following data:
Marks (X)
Weight (W)
81
2
76
3
74
6
58
7
70
3
73
7
Calculation of Combined Arithmetic Mean
=
Solution:
Marks (X)
81
76
74
58
70
73
=
=
= 70.04
Weighted Mean = 70.04 marks.
Weight (W)
2
3
6
7
3
7
=28
WX
162
228
444
406
210
511
=1961
Question: 60 students of batch A obtained 40 mean marks and 40 students of batch B
obtained 35 mean marks. Find out mean marks of batch as a whole.
Solution:
= 60, = 40, = 40, = 35
=
=
= = =38
Combined Mean Marks = 38