**Coefficient of Variation Formula (Table of Contents)**

## What is the Coefficient of Variation Formula?

In statistics, the coefficient of variation also termed as CV is a tool which helps us to determine how data points in a data set are distributed around the mean. Basically, all the data points are plotted first and then the coefficient of variation is used to measure the dispersion of those points from each other and the mean. So it helps us in understanding the data and also to see the pattern it forms. It is calculated as a ratio of the standard deviation of the data set to mean value. Higher the coefficient of variation means that there is a greater level of dispersion of data around mean. Similarly, lower the value of the coefficient of variation, lesser is the dispersion and more precise will be the results. Even if the mean of two data series is considerably different, the coefficient of variation is very useful to compare the degree of variation from one data series to the other.

Formula For the Coefficient of Variation is given by:

**Coefficient of Variation = Standard Deviation / Mean**

Steps to Calculate the Coefficient of Variation:

**Step 1:** Calculate the mean of the data set. Mean is the average of all the values and can be calculated by taking the sum of all the values and then dividing it by a number of data points.

**Step 2: **Then compute the standard deviation of the data set. That is a little time-consuming process. Standards deviation can be calculated as: **√ [Σ(X _{i} – X_{m})^{2} / (n – 1)]**. X

_{i}is the ith data point and X

_{m }is the mean of the data set. Alternatively, we can also find the standard deviation in excel by using STDEV.S() function.

**Step 3: **Divide standard deviation by mean to get the coefficient of variation.

**Examples of Coefficient of Variation Formula (With Excel Template)**

Let’s take an example to understand the calculation of the Coefficient of Variation in a better manner.

#### Coefficient of Variation Formula – Example #1

**Let’s say we have two data sets A & B and each contains 20 random data points. Calculate the Coefficient of Variation for the data set X & Y.**

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**Solution:**

Mean is calculated as:

- Mean of Data Set A =
**61.2** - Mean of Data Set B =
**51.8**

Now, we need to calculate the difference between the data points and the mean value.

Similarly, calculate for all values of the data set A.

Similarly, calculate for all values of the data set B.

Calculate the square of the difference for both the data sets A and B.

Standard Deviation is calculated using the formula given below

**Standard Deviation = √ [Σ (X _{i} – X_{m})^{2} / (n – 1)]**

Coefficient of Variation is calculated using the formula given below

**Coefficient of Variation = Standard Deviation / Mean**

- Coefficient of Variation A = 22.982 / 61.2 =
**0.38** - Coefficient of Variation B = 30.574 / 51.8 =
**0.59**

So if you see here, B has a higher coefficient of variation than A, which means that data points of B are more dispersed than A.

#### Coefficient of Variation Formula – Example #2

**Let say you are a very risk-averse investor and you looking to invest money in the stock market. Since your risk appetite is low, you want to invest in safe stocks which have lower standard deviation and coefficient of variation. You have shortlisted 3 shares based on their fundamental and technical information and want to choose 2 stocks. You have also collected information about their historical returns for the last 15 years. **

**Solution:**

Mean is calculated as:

Standard Deviation is calculated using excel formula

Coefficient of Variation is calculated using the formula given below

**Coefficient of Variation = Standard Deviation / Mean**

- Coefficient of Variation ABC = 7.98% / 14% =
**0.57** - Coefficient of Variation XYZ = 6.28% / 9.1% =
**0.69** - Coefficient of Variation QWE = 6.92% / 8.9% =
**0.77**

Based on the information, you will choose stock ABC and XYZ to invest since they have the lowest coefficient of variation.

### Explanation

Since the coefficient of variation is a measure of risk, it helps in measuring the volatility in the prices of stocks and other financial instruments. It also helps investors and analysts to compare the risks associated with different potential investments.

Coefficient of variation is similar to standard deviation but a standard deviation of two variables cannot be compared in useful. But using standard deviation and the mean makes the relative comparison more meaningful. There is a limitation of the coefficient of variation also. Suppose that mean of a data set is zero. In that case, this tool will become ineffective. Not only this, if we have a data set which has many positive and negative values, Coefficient of variation become very problematic. So it is only more useful with data sets having the same plus-minus sign.

### Relevance and Uses of Coefficient of Variation Formula

Coefficient of variation has relevance in many other fields other than statistics. For example, in the field of finance, the coefficient of variation is a measure of risk. It is similar to standard deviation since that is also used as a measure of risk but the difference is that the coefficient of variation is a better indicator of relative risk. For example, let’s say A’s expected return of 15% and B’s expected return of 10% and A has a standard deviation of 10%, while B has a standard deviation of 5%. To choose a better investment, the coefficient of variation can be used. So coefficient of variation of A is 10 / 15 = 0.666 and coefficient of variation of B is 5 / 10= 0.5. So B is a better investment than A.

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