## What is the Coefficient of Variation?

Coefficient of Variation refers to the statistical measure which helps in measuring the dispersion of the various data points in the data series around mean and is calculated by dividing the standard deviation by mean and multiplying the resultant with 100.

### Coefficient of Variation Formula

The term “coefficient of variation” refers to the statistical metric that is used to measure the relative variability in a data series around the mean or to compare the relative variability of one data set to that of other data sets, even if their absolute metric may be drastically different. Mathematically, the coefficient of variation formula is represented as,

**Coefficient of Variation Formula = Standard deviation / Mean**

It can be further expressed as below,

**Coefficient of Variation = √∑**

^{N}_{i}(Xi – X)^{2}/ X** **where

- X
_{i}= i^{th}random variable - X= Mean of the data series
- N = number of variables in the data series

### Step by Step Calculation

The calculation of the coefficient of variation equation can be done by using the following steps:

**Step 1:**Firstly, figure out the random variables that form part of a large data series. These variables are denoted by X_{i}.**Step 2:**Next, determine the number of variables in the data series, denoted by N.**Step 3:**Next, determine the mean of the data series by initially summing up all the random variables of the data series and then dividing the result by the number of variables in the series. The sample mean is denoted by X.**Step 4:**Next, compute the standard deviation of the data series based on the deviations of each variable from the mean and the number of variables in the data series.**Step 5:**Finally, the equation for the coefficient of variation is calculated by dividing the standard deviation of the data series by the mean of the series.

### Example

**Let us take the example of Apple Inc.’s stock price movement from January 14, 2019, to February 13, 2019. Calculate the coefficient of variation for Apple Inc.’s stock price for the given period.**

Below is data for calculation of the coefficient of variation of Apple Inc’s

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**Calculation of Mean**

On the based of the stock prices mentioned above, we can calculate the mean stock price for the period can be calculated as,

Mean stock price = Sum of stock prices / Number of days (add up all the stock prices and divide by the number of days. The detailed calculation is mentioned in the last section of the article)

= 3569.08 / 22

**Mean = $162.23**

**Calculation of Standard Deviation**

Next, determine the deviation of each stock price from the mean stock price. It is shown in the third column, while the square of the deviation is calculated in the fourth column.

Now, the standard deviation is calculated based on the sum of the squared deviations and the number of days as,

Standard deviation = (Sum of squared deviations / Number of days)^{1/2}

= (1454.7040 / 22)^{1/2}

**Standard Deviation = $8.13**

**Coefficient Calculation**

= $8.13 / $162.23

The coefficient will be –

Therefore, the coefficient for Apple Inc.’s stock price for the given period is 0.0501, which can also be expressed as the standard deviation is 5.01% of the mean.

### Relevance and Use

It is important to understand the concept of coefficient of variation formula because it allows an investor to assess the risk or volatility in comparison to the amount of expected return from the investment. Please keep in mind that the lower the coefficient, the better is the risk-return trade-off. However, there is one limitation of this ratio that if the mean or expected return is negative or zero, then the coefficient could be misleading (since mean is the denominator in this ratio).

### Recommended Articles

This article has been a guide to the Coefficient of Variation Formula. Here we discuss the calculation of the coefficient of variation with practical example and downloadable excel sheet. You can learn more about excel modeling from the following articles –

- Adjusted R Squared
- Formula of Covariance
- Formula of Portfolio Variance
- Correlation vs. Covariance
- Ordinary Annuity Formula

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