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Coefficient of Variation


If there are two or more sets of distributions, in order to decide which of the two distributions has more variability, we compare their coefficients of variation(C.V.).

C. V = . The distribution with greater C.V is said to be more variable. A set of readings with less variability is said to be more stable or consistent
Group Mean S.D
I       
II      

. Compare these values. If two sets of readings have the same mean and different standard deviations, then the reading with smaller S.D is said to be more consistent or less variable.

 

Example 1:
The marks of two students A and B is 12 tests are given below Identity the better student and the more consistent student.

A

75

74

78

72

78

77

79

81

79

76

72

71

B

87

84

80

88

89

85

86

82

82

79

86

80


Solution:
Let x denote the marks of A and the assumed mean for x be 76.
Let y denote the marks of B and the assumed mean for y be 76.
N = 12.

75

74

78

72

78

77

79

81

79

76

72

71

1

2

2

4

2

1

3

5

3

0

4

5

1

4

4

16

4

1

9

25

9

0

16

25

87

84

80

88

89

85

86

82

82

79

86

80

3

0

4

4

5

1

2

2

2

5

2

4

9

0

16

16

25

1

4

4

4

25

4

16

912

0

114

1008

0

124





[Here assumed mean = actual mean. Hence Σ d = 0]

 (Assumed mean = actual mean)

   = 3.215

C.V. of A =
C.V. of B =

Conclusion:
B's average score is more than that of A. B is a better student.
C.V of B is smaller than that of A. B is a more consistent preformer than A.

Example 2: The runs scored by two batsmen in ten innings are as follows:

A

10

115

5

73

7

120

36

84

29

19

B

45

12

76

42

4

50

37

48

13

0

(1) Who is a better player? (2) Who is more consistent.

Solution: Let be scores of A; Assumed mean = 50
   be scores of B; Assumed mean = 50

10

115

5

73

7

120

36

84

29

19

40

65

45

23

43

70

14

34

21

31

1600

4225

2025

529

1849

4900

196

1156

441

961

45

12

76

42

4

50

37

48

13

0

5

38

26

8

46

0

13

2

37

50

25

1444

676

64

2116

0

169

4

1369

2500

498 2 17882 327 173 8367

 

      

A is a better player.

C.V of B < C.V of A

B is more consistent than A.


Note:

  1. Adding (or subtracting) the same positive number to each observation in a group does not affect the variance and hence S.D.
  2. If each observation is multiplied by a non - zero constant 'K' the variance of the resulting observations becomes K2 times the original variance. The new S.D become K times the original S.D.




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