# WHAT IS THE COEFFICIENT OF VARIATION?

The coefficient of variation refers to the statistical measure of the dispersion of data points around the mean. The coefficient of variation represents the ratio of the standard deviation to the mean. Also, to compare the degree deviation between different data series, the coefficient variation is a standard metric. It is a very efficient measure to compare the statistics of distinct data series.

## COEFFICIENT OF VARIATION FORMULA:

In the domain of finance, the coefficient variation assists the investors to analyze the volatility and risks involved in comparison to the expected return on investment (ROI). It allows them to assess the risk-to-reward ratio before investing the money. Most of the time, investors look for security with a lower coefficient, as it provides the optimum risk-to-reward ratio with high returns and lower risks.

**Mathematical Formula Of Coefficient Of Variation**

Coefficient of Variation = (Standard Deviation/Mean)*100.

**EXAMPLE OF COEFFICIENT OF VARIATION FOR SELECTING INVESTMENTS**

There are many real-world examples of this. For example, someone is willing to invest and is considering different investment options for it. Let us discuss three different kinds of stocks

- Stock-1: Volatility of the shares is 20%, and ROI is 30%.
- Stock-2: Volatility of the stocks is 10%, and ROI is 22%.
- Stock-3: Volatility of the stocks is 40%, and ROI is 50%.

To find the best probable investment plan. The person did the following calculation

Coefficient Variation (Stock-1) = 20% ÷ 30% X 100% = 66.7%

Coefficient Variation (Stock-2) = 10% ÷ 22% X 100% = 45.4%

Coefficient Variation (Stock-3) = 40% ÷ 50% X 100% = 80.0%

Based on the calculation, the best option would be Stock-2, as it has the lowest coefficient of variation and optimum risk-to-reward ratio.

**WHAT IS VARIANCE AND IT’S FORMULA**

In statistics, Variance refers to the measurement of the extension between numbers in a data set. This means that it measures how far each number in a particular set is from the average

The mathematical representation of variance is:

*xi*=Value of the *ith* point in the data set

*x*=The average value of the data set

*n*=The total number of data points in the data set.

## WHAT IS STANDARD DEVIATION AND ITS FORMULA

Standard deviation calculates or measures the dispersion of data set relative to the mean.

It is calculated as the square root of the variance; more the dataset spread out, the higher the standard deviation.

Standard deviation is essential in the finance domain. It shows the past volatility of an investment when applied to the rate of return of investment. The higher the standard deviation of security is, the variance equally becomes higher between each price and the mean.

The mathematical representation of the standard deviation is this:

**where:**

*xi*=Value of the *ith* point in the data set

*x*=The average value of the data set

*n*=The total number of data points in the data set.