Sample Problems on How to calculate Coefficient of Variation

Problem 1: The standard deviation and mean of the data are 9.7 and 17.8 respectively. Find the coefficient of variation.

Solution:

SD/σ = 9.7                  

mean/μ = 17.8          

Coefficient of variation = σ/μ × 100%

                                     = 9.7/17.8 × 100

Coefficient of variation =  54.4%

Problem 2: The standard deviation and coefficient of variation of data are 2.5 and 36.7 respectively. Find the value of the mean.

Solution:

C.V=36.7                 

SD/σ= 2.5

Mean/x̄=?

C.V =  σ/x̄ × 100

36.7 = 2.5 / x̄ ×100

x̄ = 2.5/36.7×100

x̄ = 6.81

Problem 3: If the mean and coefficient of variation of data are 24 and 56 respectively, then find the value of standard deviation?

Solution:

C.V=56                    

SD/σ=?

Mean/x̄= 24

C.V=  σ/x̄ × 100

56 =  σ/ 24 × 100

σ = 24×56/100

σ = 13.44

The standard deviation is 13.44

Problem 4: The mean and standard deviation of marks obtained by 40 students of a class in three subjects Mathematics, English and economics are given below.

Which of the three subjects shows the highest variation and which shows the lowest variation in marks?

Solution:

Coefficient of variation for maths =σ/x̄ × 100

σ=11 

x̄=56               

C.V = 11/56×100

Coefficient of variation for maths= 19.64%

Coefficient of variation for english= σ/x̄ × 100

σ=16                

x̄=78

C.V = 16/78×100

Coefficient of variation for english= 20.51%

Coefficient of variation for economics= σ/x̄ × 100

σ=13                

x̄=69

C.V = 13/69×100

Coefficient of variation for economics =18.84%

The highest variation is in english.

And the lowest variation is in economics.

Problem 5: The following table gives the values of mean and variance of heights and weights of the 10th standard students of a school.

Which is more varying than the other?

Solution:

Coefficient of variation for heights

Mean x̄1= 166cm, variance σ1² = 85.70 cm²

Therefore standard deviation σ1 = 9.25

Coefficient of variation

     C.V1=  σ/x̄ × 100

            = 9.25/166×100

    C.V1 = 5.57%    (For heights)

Coefficient of variation for weights

Mean x̄2= 65.60kg , variance σ2² = 39.9 kg²

Therefore standard deviation σ2 = 6.3kg

Coefficient of variation

     C.V1=  σ/x̄ × 100

            = 6.3 / 65.60×100

  C.V2=9.54% (For weight)

C.V1 = 5.57% and C.V2  = 9.54%

Since C .V2  > C .V1 , the weight of the students is more varying than the height.

Problem 6: If the mean and coefficient of variation of data are 16 and 40 respectively, then find the value of standard deviation?

Solution:

C.V=40      

SD/σ=?

Mean/x̄= 16

C.V=  σ/x̄ × 100

40 =  σ/ 16 × 100

σ= 16×40/100

σ= 6.4

Problem 7: The mean and standard deviation of marks obtained by 40 students of a class in three subjects Mathematics, English and economics are given below.

Which of the three subjects shows the highest variation and which shows the lowest variation in marks?

Solution:

Coefficient of variation for social studies = σ/x̄ × 100

 σ=10.                x̄=65

C.V = 10/65×100

Coefficient of variation for Social studies= 15.38%

Coefficient of variation for Science= σ/x̄ × 100

σ=12                x̄=60

C.V = 12/60×100

Coefficient of variation for science = 20%

Coefficient of variation for Hindi = σ/x̄ × 100

σ=14                x̄=57

C.V = 14/57×100

Coefficient of variation for Hindi = 24.56%

The highest variation is in economics.

And the lowest variation is in maths.

How to calculate the Coefficient of Variation? Statistics is the process by which the data is collected and analyzed. The coefficient of variation in statistics is explained as the ratio of the standard deviation to the arithmetic mean, for instance, the expression standard deviation is 15 % of the arithmetic mean is the coefficient variation.

This article provides the steps to calculate the coefficient of variation along with solved examples and practice problems.