Coefficient of Variation Example
This worksheet may help you how to calculate coefficient of variation for the given data. The coefficient of variance is a dimensionless number.
Content DefinitionCoefficient 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 VarianceCoefficient 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 nonzero mean. You can know more about Standard deviation from this Standard Deviation Worksheet Coefficient of Variance Example1. 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/(N1)*((x_{1}x_{m})^{2}+(x_{2}x_{m})^{2}+..+(x_{n}x_{m})^{2})) =&radic(1/(51)((1343.2)^{2}+(3543.2)^{2}+(5643.2)^{2}+(3543.2)^{2}+(7743.2)^{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
The above example is a walk through to understand the concept of coefficient of variance when it comes to online calculation this online Coefficient of Variation Calculator is an essential tool to make the calculation easy. 
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