# 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. In statistics, the Coefficient of variation formula (CV), also known as relative standard deviation (RSD), is a standardized measure of the dispersion of a probability distribution or frequency distribution. The value of the coefficient of variation is lower, shows the data with less variability and high stability.

### Coefficient of Variation Formula

The 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.

## Applications of Coefficient of Variation

The coefficient of variation (CV) is a statistical formula to determine the relative dispersion of data points in a data set around the mean.It has major applications in finance as it allows investors to determine the risk in comparison to the expected amount of return.

Let us see how to use the coefficient of variation formula in the following solved examples section.

## Example Using Coefficient of Variation Formula

**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 | $2500 | $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:** If the coefficient of variation of two distributions are 60 and 70, and their standard deviations are 25 and 16, respectively, find 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.**

**Example 3: **Coefficient of variation of two distributions are 50 and 75, and their standard deviations are 30 and 15, respectively. What is their arithmetic means?

**Solution:**

To Find: Arithmetic means of given distributions.

Given: \(CV_1\) = 50, \(σ_1\) =30

\(CV_2\) = 75, \(σ_2\) = 15

Using coefficient of variation formula,

CV = (σ/μ) × 100, μ≠0

\(CV_1\) = \(\dfrac{σ_1}{μ_1}\) × 100

50 = \(\dfrac{30}{μ_1}\) × 100

\(μ_1\) = 60

Similarly,

\(CV_2\) =\(\dfrac{σ_2}{μ_2}\) × 100

75 = \(\dfrac{15}{μ_2}\)×100

\(μ_2\) = 20.

**Answer: The value of \(μ_1\) = 60 and \(μ_2\) = 20.**

## FAQs on Coefficient of Variation

### What Is the Formula for Coefficient of Variation in Statistics?

In statistics, the Coefficient of variation formula refers to the formula to calculate the measure of the dispersion of a probability distribution or frequency distribution. The coefficient of variation formula is given as CV =\(\dfrac{σ}{μ}\) × 100, μ≠0, where CV = coefficient of variation., σ = standard deviation and μ = mean.

### How To Use Coefficient of Variation Formula?

The coefficient of variation formula gives the measure of the dispersion of a probability distribution or frequency distribution.

- Step 1: Check for the sample set.
- Step 2: Calculate standard deviation and mean.
- Step 3: Put the values in the coefficient of variation formula, CV =\(\dfrac{σ}{μ}\) × 100, μ≠0,

### What Is the Coefficient of Variation Formula in Words?

The coefficient of variation equals the standard deviation divided by the mean and then multiplied by a hundred to be expressed in percentage.

### What Are the Components of the Coefficient of Variation Formula?

The coefficient of variation formula can be given as CV =\(\dfrac{σ}{μ}\) × 100, μ≠0. Thus, the components of the coefficient of variation formula are

- CV = coefficient of variation.
- σ = standard deviation.
- μ = mean.