Coefficient of Variation Formula
In statistics and probability theory, coefficient of variation (CV) is a measure of scattering or dispersion of given data points around the mean value. It is also known as relative standard deviation. The coefficient of variation is defined as the ratio of standard deviation (σ) to the mean (μ). Sometimes it is expressed in percentage. The coefficient of variation formula is useful particularly in those cases where we need to compare results from two different surveys having different values. Let us learn the coefficient of variation formula along with a few solved examples.
What Is Coefficient of Variation Formula?
The coefficient of variation formula is useful particularly in those cases where we need to compare results from two different surveys having different values. coefficient of variation formula can be given as:
CV =\(\dfrac{σ}{μ}\) × 100, μ≠0
Where,
CV = coefficient of variation.
σ = standard deviation.
μ = mean.
Let us see how to use the coefficient of variation formula in the following solved examples section.
Solved Examples Using Coefficient of Variation Formulas

Example 1: Two plants C and D of a factory show the following results about the number of workers and the wages paid to them.
No. of workers 5000 6000 Average monthly wages Rs 2500 Rs 2500 Standard deviation 9 10 Using coefficient of variation formulas, find in which plant, C or D is there greater variability in individual wages.
Solution:
To Find: Which plant has greater variability.
For this, we need to find the coefficient of variation. The plant that has a higher coefficient of variation will have greater variability.
Coefficient of variation for plant C.Using coefficient of variation formula,
CV = (σ/μ) × 100, μ≠0
CV = (9/2500) × 100
CV = 0.36%
Now, CV for plant D
CV = (σ/μ) × 100
CV = (10/2500) × 100
CV = 0.4%
Plant C has CV = 0.36 and plant D has CV = 0.4
Answer: Hence plant D has greater variability in individual wages.

Example 2: Coefficient of variation of two distributions are 60 and 70, and their standard deviations are 25 and 16, respectively. What is their arithmetic means?
Solution:
To Find: Arithmetic means of given distributions.
Given: \(CV_1\) = 60, \(σ_1\) =25
\(CV_2\) = 70, \(σ_2\) = 16
Using coefficient of variation formula,
CV = (σ/μ) × 100, μ≠0
\(CV_1\) = \(\dfrac{σ_1}{μ_1}\) × 100
60 = \(\dfrac{25}{μ_1}\) × 100
\(μ_1\) = 41.66
Similarly,
\(CV_2\) =\(\dfrac{σ_2}{μ_2}\) × 100
70 = \(\dfrac{16}{μ_2}\)×100
\(μ_2\) = 22.87.
Answer: The value of \(μ_1\) = 41.66 and \(μ_2\) = 22.87.