How to Calculate Coefficient of Variation (With Example)
By Indeed Editorial Team
Published June 25, 2022
The Indeed Editorial Team comprises a diverse and talented team of writers, researchers and subject matter experts equipped with Indeed's data and insights to deliver useful tips to help guide your career journey.
Coefficients of variation (CV) is the value that affects the measurement of data point dispersion relative to an average, or mean. Understanding how to calculate coefficient of variation enables you to analyze large sets of data. If you plan to pursue a career in statistics, analytics, finance, or business, learning how to calculate this coefficient is a valuable skill. In this article, we detail how to calculate the variation coefficient by providing a step-by-step guide to the calculation, both manually and using software, detail the importance of this value, and offer an in-depth example you can use as a reference.
How to calculate coefficient of variation manually
The process of how to calculate coefficient of variation is fairly straightforward. You can use the following steps as an outline to calculate your variation coefficient:
1. Define the formula
The formula for coefficient of variation (CV) divides the standard deviation by the sample mean value of a data set. It applies to data sets that rely on common distribution, thus falling into a bell curve structure. The formula in its simplest form is:
CV = Standard deviation / Mean value x 100
If you plan to use the formula in a business setting, such as for financial analysis, many professionals rephrase the equation to apply it directly to their situation. The CV formula applies to potential returns on investment, risk, and gains. Many analysts rephrase the expression as follows:
CV = Volatility / Expected return x 100
2. Define volatility
To identify the standard deviation or the volatility, first identify the mean value. This is the average of all the values in the data set. Next, subtract the mean value from each data point. To convert this into variance, first square the value by multiplying it by itself for each data point. Add together the result and calculate the average. Finally, take the square root of that value. This converts it into a usable percentage to represent volatility or standard deviation.
3. Define the expected return
The projected return on investment is a way to estimate the return figures based on the chance of recurrence. To determine this number, multiply all the data points by their likelihood of recurrence. The mode refers to the most prevalent value in a series. This has the highest recurrence likelihood, while numbers further from the mean are less likely to repeat. After you multiply the value by its return likelihood, total the answers. The result is the expected return value.
4. Execute the formula by dividing
To perform the formula, divide the volatility by the expected return figure. Ensure that both values follow the same units. If your volatility value is a decimal, you require an expected return in the same formula. The quotient is your coefficient of variance as a decimal value.
5. Convert to a percentage
For ease of reference and reporting purposes, most professionals prefer to convert the coefficient into a percentage. Using the decimal result, multiply the value by 100. Finally, express the coefficient as a percentage by adding a % after the value.
How to calculate coefficient of variation using software
Most accounting and spreadsheet technology uses an intuitive approach to executing this equation. The following steps outline how you can use a standard spreadsheet software to determine the coefficient function.
1. Enter the data
When you go to calculate the coefficient of variation, you either have an existing data set or import one from a different software. The alternative is manually inputting the data for the period in question. Before you proceed to the next step in the calculation, check the data to ensure its accuracy. Cross-reference random cells against your records to make a good faith effort to ensure the input is accurate before proceeding.
2. Apply the standard deviation function
Spreadsheets include features that allow you to input data then perform pre-set calculations. As it was one of the first-to-market solutions, most software companies use Microsoft as the standard of practice. In most of these applications, the command to assess standard deviation is =STDEVP, where the equals sign denotes a formula, and the following text references the dictionary of commands. Enter the formula into a cell proximal to your data set. Depending on the software, you can manually input or simply highlight the cells for your calculation.
3. Determine the mean value
The next step in the calculation is assessing the mean value, also through a formula. The command for mean is =AVERAGE, because it simply totals the values then divides by the number of data points. As with the standard deviation, you enter the formula into a cell proximal to the data set for ease of reference. Most software lets you either input the parameters manually or highlight them.
4. Solve for the coefficient
The final step requires the operator to divide the function-holding cells. For this reason, it's important to use the actual formula in a separate cell, rather than manually entering the value. This way, if you change a value within the data set range, it automatically adjusts the calculation. An example is if you place the standard deviation formula in B2 and the mean formula in C2, then the third new cell formula is =B2/C2. The result is the coefficient of variation.
5. Identify technical shortcuts
Especially if you are likely to repeat the process of calculating the coefficient of variation, it can help to use shorthand. The fewer steps you take to execute a calculation, the fewer opportunities for human error. Advanced command dictionaries often have formulas that allow you to complete the process in one step. For example, Excel features the command =STDEV.P, where you simply set the parameters and it provides you with the coefficient of variation.
6. Check the coefficient logically
When you rely on technology to complete your calculation, it's important to review the results. Because you know that a high coefficient means far-spread data and a low coefficient means a cluster, you can assess whether the result is reasonably accurate. For instance, if you perform an experiment where most participants answered similarly and you identify a high coefficient, it can signify a mishap during the calculation. Conversely, if the result is a low coefficient, you can feel confident in the results.
Importance of coefficient of variation
Coefficients of variation have significant importance in anything that involves data analysis. The CV can help assess the risk versus return ratio in an investment setting. Because it measures dispersion of a data set, it provides a relative metric that applies to multiple fields. Anything that relies on a bell curve to perform an analysis can benefit from understanding how far apart data points spread relative to the central value.
Some industries that rely on the variation coefficient include biology, where it helps scientists test for repeatability. The coefficient of variation can help school boards choose proper curriculums based on the testing scores of students. As the coefficient has roots in data spreads rather than clusters, it isn't 100-percent accurate, rather it works together with other metrics to draw conclusions regarding data sets.
Kareem is developing an investment portfolio and wants to assess the risk-to-return value for his options, stocks or bonds. To make this decision, Kareem applies the coefficient of variation formula. He knows that the volatility for stocks is 6% and for bonds is 2.5%. Kareem also knows that the projected return is 17% for stocks and 8% for bonds. Using this information, he first calculates the stock options:
CV = standard deviation / mean value x 100
CV = volatility / projected return x 100
CV = (0.06) / (0.17) x 100 = 0.35 x 100 = 35%
Kareem now knows that the coefficient of variation for stocks is 35%. His next step is performing the same calculation for bonds:
CV = standard deviation / mean value x 100
CV = volatility / projected return x 100
CV = (0.025) / (0.08) x 100 = 0.2 = 31%
Kareem compares the two investments and sees that the risk to reward ratio for bonds is 31%, which is less than for stocks. Using this information, and his comfortable risk level, he can decide where to invest his money.
Please note that none of the companies, institutions, or organizations mentioned in this article are affiliated with Indeed.
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