Formula to calculate coefficient of variation from mean and standard deviation is
= (σ/x̄) ⋅ 100%
Here σ is the standard deviation and x̄ is the mean.
Formula to find standard deviation σ is
Formula to find arithmetic mean x̄ is
x̄ = ∑x / n
Example 1 :
The standard deviation and mean of a data are 6.5 and 12.5 respectively. Find the coefficient of variation.
Solution :
Standard deviation = 6.5
Mean = 12.5
Coefficient of variation (C.V) = (σ/x̄) ⋅ 100%
= (6.5/12.5) ⋅ 100%
= (65/125) ⋅ 100%
= (13/25) ⋅ 100%
= 52%
So, the coefficient of variation is 52%.
Example 2 :
The standard deviation and coefficient of variation of a data are 1.2 and 25.6 respectively. Find the value of mean.
Solution :
Standard deviation = 1.2
Coefficient of variation = 25.6
mean = ?
Coefficient of variation (C.V) = (σ/x̄) ⋅ 100%
25.6 = (1.2/x̄) ⋅ 100%
x̄ = (1.2/25.6) / 100%
= 4.687
x̄ = 4.69
So, the required mean is 4.69
Example 3 :
If the mean and coefficient of variation of a data are 15 and 48 respectively, then find the value of standard deviation.
Solution :
Mean (x̄) = 15
Coefficient of variation (C.V) = 48
Standard deviation (σ) = ?
Coefficient of variation (C.V) = (σ/x̄) ⋅ 100%
48 = (σ/15) ⋅ 100%
σ = (48 ⋅ 15) /100
= 720/100
x̄ = 7.2
Example 4 :
If n = 5, x̄ = 6 , Σx2 = 765 , then calculate the coefficient of variation.
Solution :
In order to find coefficient of variation, we must know standard deviation (σ)
Σx2/n = 765/5 = 153
(Σx/n)2 = (x̄)2 = 62 = 36
σ = √(153 - 36)
= √117
σ = 3√13
Coefficient of variation (C.V) = (σ/x̄) ⋅ 100%
C.V = (3√13)/6) ⋅ 100%
C.V = (3.60/2) ⋅ 100%
C.V = 180.28%
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