What is the Coefficient of Variation?

Coefficient of Variation Formula

The term “coefficient of variation” refers to the statistical metric 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 represents as

Coefficient of Variation Formula = Standard deviation / Mean

One can further express it as below:

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 where

  • Xi = ith random variableX= Mean of the data seriesN = number of variables in the data series

Step by Step Calculation

Example

  • Firstly, figure out the random variables forming a large data series. Xi denotes these variables. Next, determine the number of variables in the data series, denoted by N. 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. Next, compute the data series’s standard deviation based on each variable’s deviations from the mean and the number of variables in the data series. One may calculate the equation for the variation coefficient by dividing the data series’s standard deviation by the series’ mean.

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

Calculation of Mean

On the based of the stock prices mentioned above, we can calculate the meanCalculate The MeanMean refers to the mathematical average calculated for two or more values. There are primarily two ways: arithmetic mean, where all the numbers are added and divided by their weight, and in geometric mean, we multiply the numbers together, take the Nth root and subtract it with one.read more stock price for the period can be 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 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 in the fourth column.

Now, one can calculate the standard deviation 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 express the standard deviation of 5.01% of the mean.

Relevance and Use

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

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

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