"Application of coefficient of variance"

The coefficient of variation is the measure of the dispersion of data points in a data series around the mean.

The coefficient of variation represents the ratio of the standard deviation to the mean.

Advantages of Coefficient of Variation:-

• It is independent of unit, so you can compare coefficient of variation of ph value v/s calcium deposition. Since it is ratio of Standard deviation by mean, the units cancel each other and what is left is a percentage (unit independent \ unitless).
• In special cases when the difference in Mean is too large, it come handy.

Disadvantages of Coefficient of Variation:-

• If the value of mean approaches 0, the coefficient of variation approaches infinity. So the minute changes in the mean will make major changes. Even if the mean of a variable is not zero, but the variable contains both positive and negative values and the mean is close to zero, then the "Coefficient of Variation" can be misleading.
• The "Coefficient of Variation" of a variable or the "Coefficient of Variation" of a prediction model for a variable can be considered as a reasonable measure if the variable contains only positive values.
• A major drawback is that there is no sense to calculate the coefficient of variation of any variable expressed in logarithm. This is because the log of 1 is equal to 0, so by changing units, we are only redefining zero to redefine the value of CV. The value of coefficient of variation of logarithm is absolutely meaningless.

Application:-

• In Finance it is known as Risk to Reward Ratio.

e.g.:- Aditya is looking for a safe investment that provides stable returns. He considers the following options for investment:

1) Stocks: Aditya was offered stock of AAA Corporation, It is a mature company with strong operational and financial performance. The volatility of the stock is 10% and the expected return is 14%.

2) ETFs: Exchange-Traded Fund (ETF) which tracks the performance of the S&P 500 index. The ETF offers an expected return of 13% with a volatility of 7%.

Since the Coefficient of Variation for ETF's is smaller as compared to stocks, this is optimal risk to reward ratio, and Aditya would go for ETF investment over stocks.

• If we have data for 2 variables Age and salary for top 50 companies as shown below.

As seen above in example the unit of measure for age is "years" and for salary is "dollars", and the question we have is what has less variability (age or salary), this cannot be answered by the conventional standard deviation method as the unit are different, but coefficient of variation cancels the units and we can conclude that age has less variability as compared to salary.

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