This worksheet may help you **how to calculate coefficient of variation** for the given data. The coefficient of variance is a dimensionless number.

**Definition:**

Coefficient of Variation is the percentage variation in mean, standard deviation being considered as the total variation in the mean. If we wish to compare the variability of two or more series, we can use the coefficient of variation. The series of data for which the coefficient of variation is large indicates that the group is more variable and it is less stable or less uniform. If a coefficient of variation is small it indicates that the group is less variable and it is more stable or more uniform.
**Formula for Coefficient of Variance**

Coefficient of Variation CV = Standard Deviation / Mean

In other words coefficient of variation is defined ratio of the Standard Deviation to the Mean. The value of CV is calculated only for non-zero mean. You can know more about Standard deviation from this Standard Deviation Worksheet

**Coefficient of Variance Example:**

1. Find CV of {13,35,56,35,77}

Solution:

Number of terms (N) = 5

Mean:

Xbar = (13+35+56+35+77)/5

= 216/5 = 43.2

Standard Deviation (SD):

Formula to find SD is

σ=&radic(1/(N - 1)*((x_{1}-x_{m})^{2}+(x_{2}-x_{m})^{2}+..+(x_{n}-x_{m})^{2}))

=&radic(1/(5-1)((13-43.2)^{2}+(35-43.2)^{2}+(56-43.2)^{2}+(35-43.2)^{2}+(77-43.2)^{2}))

=&radic(1/4((-30.2)^{2}+(-8.2)^{2}+(12.9)^{2}+(-8.2)^{2}+(33.8)^{2}))

=&radic(1/4((912.04)+(67.24)+(163.84)+(67.24)+(1142.44)))

=&radic(588.2)

σ=24.2528

**Coefficient of variation (CV)**

CV = Standard Deviation / Mean

= 24.2528/43.2

= 0.5614

Hence the required Coefficient of Variation is 0.5614

2. A company has two sections with 40 and 65 employees respectively. Their average weekly wages are $450 and $350. The standard deviation are 7 and 9. (i) Which section has a larger wage bill?. (ii) Which section has larger variability in wages?

Solution:

(i) Wage bill for section A = 40 x 450 = 18000

Wage bill for section B = 65 x 350 = 22750

Section B is larger in wage bill.

(ii) Coefficient of variance for Section A = 7/450 x 100 =1.56 %

Coefficient of variance for Section B = 9/350 x 100 = 2.57%

Section B is more consistent so there is greater variability in the wages of section A.

__Practice Problems:__

1. Calculate the coefficient of variance of the marks secured by a student in the exam as given : 82, 95, 75, 78, 87

2. The standard deviation and the mean of 16 values are 15.6 and 20.5. Find the coefficient of variation

3. A group of 80 candidates have their average height is 145.8 cm with coefficient of variance 2.5%. What is the standard deviation of their height?

When you try this calculation on your own, use this *coefficient of variation Calculator* to verify your answers.

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