Example 1 :
The mean and standard deviation of marks obtained by 40 students of a class in three subjects Mathematics, Science and Social Science are given below
Which of the three subjects shows highest variation and which shows lowest variation in marks?
Solution :
Mathematics :
Coefficient of variation (C.V) = (σ/x̄) ⋅ 100%
x̄ = 56, σ = 12
C.V = (12/56) ⋅ 100%
C.V = 0.2142 ⋅ 100%
C.V = 21.42%
Science :
Coefficient of variation (C.V) = (σ/x̄) ⋅ 100%
x̄ = 65, σ = 14
C.V = (14/65) ⋅ 100%
C.V = 0.2153 ⋅ 100%
C.V = 21.53%
Social Science :
Coefficient of variation (C.V) = (σ/x̄) ⋅ 100%
x̄ = 60, σ = 10
C.V = (10/60) ⋅ 100%
C.V = 0.1666 ⋅ 100%
C.V = 16.66%
The highest variation is in the subject Science and lowest variation is in the subject Social science
Example 2 :
The temperature of two cities A and B in a winter season are given below.
Find which city is more consistent in temperature changes?
Solution :
x 18 20 22 24 26 |
d = x - A d=x-22 -4 -2 0 2 4 |
d2 16 4 0 4 16 |
Σd2/n = 40/5 = 8
(Σd/n)2 = (0)2 = 0
σ = √(8 - 0)
= √8
σ = 2.82
Mean (x̄) = (18 + 20 + 22 + 24 + 26)/ 5
= 110/5
x̄ = 22
Coefficient of variation (C.V) = (σ/x̄) ⋅ 100%
x̄ = 22, σ = 2.82
C.V = (2.82/22) ⋅ 100%
C.V = 0.1281⋅ 100%
C.V = 12.81%
x 11 14 15 17 18 |
d = x - A d=x-15 -4 -1 0 2 3 |
d2 16 1 0 4 9 |
Σd2/n = 30/5 = 6
(Σd/n)2 = 0
σ = √(6 - 0)
= √6
σ = 2.44
x̄ = Σx/n
= (11+14+15+17+18)/5
x̄ = 75/5
x̄ = 15
Coefficient of variation (C.V) = (σ/x̄) ⋅ 100%
C.V = (2.44/15) ⋅ 100%
C.V = (244/1500) ⋅ 100%
C.V = 0.1626 ⋅ 100%
C.V = 16.26%
So, city A is more consistent.
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