# CALCULATING COEFFICIENT OF VARIATION FROM MEAN AND STANDARD DEVIATION

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  is

x̄  =  ∑x / n

## Examples

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/⋅ 100%

=  (1.2/25.6) / 100%

=  4.687

=  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

=  7.2

Example 4 :

If n = 5,  = 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% Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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