Coefficient of Variation (CV) Calculator

Your Data
Select Population if the data contains all measurable values or all values you are interested in.
Select Sample if the data is a sample of a large or unlimited population and you wish to make a statement about the entire population.
Input the data separated by comma, space or enter. To calculate coefficient of variation, you need at least two values in your dataset.
Choose the number of decimal places.

How to Find the Coefficient of Variation of a Population: A Step-by-Step Guide

You can quickly calculate the CV of a population if you select Population in our Coefficient of Variation Calculator. Yet knowing how to do it by hand allows for a more in-depth understanding of the statistical method. To do so, follow these steps:

  1. Calculate the population mean of the dataset:

    μ=i=1nXin

  2. Subtract the mean from each value in the dataset:

    (Xiμ)

  3. Calculate each observation’s squared deviation from the population mean:

    (Xiμ)2

  4. Calculate the sum of all the squared differences to obtain the sum of squares (SS):

    SS=i=1n(Xiμ)2

  5. Divide the sum of squared differences by n to obtain the population variance (

    σ2
    ):

    σ2=i=1n(Xiμ)2n

  6. Take the square root of the sum of the squared deviations to calculate the population standard deviation:

    σ=i=1n(Xiμ)2n

  7. Calculate the coefficient of variation by dividing the population standard deviation by the sample mean:

    CV=sX¯

How to Find the Coefficient of Variation of a Sample: A Step-by-Step Guide

Statistical analysis software typically calculates the coefficient of variation automatically. You can also obtain it using our CV Calculator. But there are benefits to computing it manually as you get to know how the formula works:

Follow these steps when calculating the coefficient of variation of a sample:

  1. Calculate the sample mean of the dataset:

    X¯=i=1nXin

  2. Subtract the mean from each value in the dataset:

    (XiX¯)

  3. Calculate each observation’s squared deviation from the sample mean:

    (XiX¯)2

  4. Calculate the sum of all the squared differences to obtain the sum of squares (SS):

    SS=i=1n(XiX¯)2

  5. Divide the sum of squared differences by n – 1 to obtain the variance (

    s2
    ):

    s2=i=1n(XiX¯)2n1

  6. Take the square root of the sum of the squared deviations to calculate the sample standard deviation:

    s=i=1n(XiX¯)2n1

  7. Calculate the coefficient of variation by dividing the sample standard deviation by the sample mean:

    CV=σμ

Coefficient of Variation (CV) Calculator

What Is the Coefficient of Variation (CV)?

The coefficient of variation (CV) measures the amount of dispersion around the mean in a dataset. You’ll also find it referred to as relative standard deviation (RSD), which—in contrast to standard deviation—is unitless. What this means is that this statistical measure allows us to compare the dispersion across different datasets that have different units of measurement. The CV can be expressed as a percentage (e.g., 300%) or as a multiple (e.g., 3 times). We’ll touch more on this later in the article.

In addition to its primary application in statistics, the coefficient of variation is also used to evaluate the risk and volatility of investments in a finance setting and to audit the accuracy of a specific process in quality assurance.

You can obtain the CV in a few clicks with our Coefficient of Variation Calculator. But to interpret the results, you must fully grasp the definition

What Does Coefficient of Variation Mean?

The coefficient of variation is a relative measure of variability that indicates the size of a standard deviation as a percentage of its mean. It is a unitless measure that allows you to compare datasets with different means and scales. For example, you can compare the variability of a dataset measured in euros with another measured in percentages.

You can also compare datasets with different scales. Suppose that you’re observing two companies with varying annual figures:

  • Company A’s annual sales are $5 million, $8 million, $7 million, and $9 million.
  • Company B’s annual sales are $80 million, $83 million, $82 million, and $84 million.

Despite the difference in mean sales, both companies have a standard deviation of $1.71 million. But the largest observation in the first sample ($9 million) is nearly two times larger than the smallest observation ($5 million). In contrast, the largest observation in the second sample ($84 million) is only 5% larger than the smallest observation ($80 million). Therefore, a standard deviation of $1.71 million represents a high degree of variability relative to Company A’s mean of $7.25 million, but a small degree of variability relative to Company B’s mean of $82.25 million.

The coefficient of variation is a particularly useful measure in such situations when you need to compare datasets that use varied units of measurement.

How to Calculate the Coefficient of Variation

The calculations for population and sample CV slightly differ. You can obtain both with our Coefficient of Variation Calculator, but computing it manually will help you better understand how the formula works.

The coefficient of variation formula for population data is as follows:

CV=σμ

Here

μ
, denotes the population mean, while
σ
is the population standard deviation.

When analyzing data from a sample, on the other hand, we use the following coefficient of variation formula:

CV=sX¯

Where

X¯
is the sample mean and
s
is the sample standard deviation.

How to Interpret the Coefficient of Variation

The coefficient of variation represents the ratio between the standard deviation and the mean.

The higher the coefficient of variation, the higher the standard deviation; in such cases, data observations are widely spread out around the mean.

A low CV, on the other hand, means that the standard deviation is relatively small and the data points are clustered closely around the mean. In other words, this indicates low variability in the dataset.

When the coefficient of variation is equal to 1 or 100%, then the standard deviation is equal to the mean. Meanwhile, a CV less than 1 indicates that the standard deviation is smaller than the mean, which is the typical scenario. We observe a CV higher than 1 when the standard deviation is higher than the mean.

If we refer back to the example of the two companies’ annual sales, we would compute the coefficient of variation for Company A as:

CV=sX¯=$1.71$7.25=0.24

Analysts often express the CV as a percentage. Since the result is 0.24, we say that the standard deviation is 24% of the size of the mean.

We obtain the coefficient for Company B with the same formula:

CV=sX¯=$1.71$82.25=0.02

The results confirm that the first sample has significantly more variability in sales than the second.

Please also note that 0.24 and 0.02 are unitless, pure numbers. In other words, we can easily compare them to one another.

Applications of Coefficient Variation

The coefficient of variation is useful in a variety of fields. In this CV Calculator article, we’ll look at just some of its applications across different industries.

Finance

When used in finance, the coefficient of variation measures the amount of risk (standard deviation) per unit of mean return.

A high CV indicates relatively high level of risk. For example, you have two investment opportunities:

  • Investment A offers a mean return of 18% and a standard deviation of 23%.
  • Meanwhile, Investment B has a mean return of 10% and a standard deviation of 15%.

Which one is a better option, considering both CVs?

By calculating the coefficient of variation for each of the two investments, we obtain the following:

CVA=2318=1.28

CVB=1510=1.50

Since Investment A has a lower coefficient of variation, it offers a better mean return per unit of risk. Therefore, it’s the better opportunity.

Quality Control

We use the coefficient of variation to assess the consistency and reliability of the production process. In quality control, a low CV indicates a high degree of consistency, whereas a high CV indicates a lack thereof.

Consider a company that manufactures engine valves; each valve should be exactly 50mm, otherwise it won’t fit in the respective seat. The manufacturer assesses the consistency of dimensions for two different production batches:

  • Batch A with a standard deviation of 1mm
  • Batch B with a standard deviation of 0.5 mm

In this case, the second batch is more optimal since its coefficient is equal to 0.01 versus the second’s CV of 0.02.

Retail

A retail store can use the coefficient of variation to assess the sales variability for different product categories or individual items.

A particular product with a high CV can be an indicator of inconsistent demand. In such case, the store may need to adjust the inventory levels.

The measure is also useful to store owners who want to understand how their sales vary from one period to another to improve their sales forecasting and inventory planning.

Environmental Science

The coefficient of variation helps assess the variability of environmental parameters across different time periods and locations, such as:

  • Temperature
  • Humidity
  • Аir quality

What Are the Advantages and Disadvantages of the Coefficient of Variation?

The coefficient of variation is a useful measure that has both advantages and disadvantages. By understanding those, professionals can make more informed decisions about when and how to use the measure in their analyses.

Let’s take a look at the pros and cons of CV.

Advantages of Coefficient of Variation

Here are some of the ways that the CV makes for a useful statistical measure:

  • The coefficient of variation (CV) is unitless. In other word, you can use the measure to compare the variability of datasets measured in different units.
  • The CV can be used as a risk assessment tool in finance and other fields where risk is a concern. The measure can help in protecting investors from potentially volatile investments.
  • The coefficient of variation (CV) is a valuable tool for evaluating and confirming the consistency of data, which refers to the degree of uniformity in the values within a dataset. The CV measures how consistent the values are from the mean of the dataset, with a smaller CV indicating higher consistency in the data.

Disadvantages of Coefficient of Variation

As all methods and practices, the coefficient of variation also has some drawbacks, such as:

  • It’s dependent on the mean of the dataset, therefore it may not be a useful measurement when the mean is 0 or close to 0. In such cases, you’re unable to calculate the CV.
  • The coefficient of variation is sensitive to outliers since it is based on the sample mean and standard deviation. As a result, it may not be useful when dealing with extreme values in the dataset.
  • The measure does not provide information about the direction of the variability; only about its magnitude. For example, if a distribution has a high coefficient of variation, this means that the data is highly variable relative to the mean, but it doesn't indicate whether the variation is positive or negative. And the direction of variability can be an important indicator of underlying trends or patterns in the data.

Coefficient of Variation vs Standard Deviation

Standard deviation is a measure of absolute dispersion-the amount of variability without comparing it to any reference point or benchmark. It computes the amount of variation or dispersion in a dataset. More specifically, it shows us the average distance of each observation from the mean.

On the other hand, relative measures of dispersion, such as the coefficient of variation, are unitless. This makes them useful for making comparisons between data sets with different units of measurement.

In this article, we’ll look at some guidelines on when to use standard deviation and coefficient of variation.

When should you opt for standard deviation? It’s appropriate to use it to:

  • Determine the spread of values in a single data set;
  • Compare data measured in the same units;
  • Calculate confidence intervals for the mean.

And you should use the coefficient of variation to:

  • Compare the variability of two or more datasets;
  • Utilize a standardized measure of variability that is independent of the data’s scale;
  • Calculate the variability of datasets with different sample sizes.
How to find the coefficient of variation in Excel?

There is no built-in function in Excel that allows you to calculate the coefficient of variation directly. Instead, you have to use the formulas for standard deviation (STDEV.S or STDEV.P) and mean (AVERAGE).

For example, let’s calculate the coefficient of variation in Excel for the following dataset:

Dataset

First, we need to obtain the mean using the AVERAGE function:

Average function in Excel.

The next step is to estimate the standard deviation. Assuming that the dataset represents a sample, we will use the STDEV.S function:

Using STDEV.S function to find the standard deviation.

The last step is to divide the standard deviation by the mean:

Dividing standard deviation by the mean.
We obtain coefficient of variation of 0.48.

As a result, we obtain a coefficient of variation of 0.48.

You can double-check the results with the Coefficient of Variation Calculator above.


What is a good coefficient of variation?

Whether a particular coefficient of variation is considered good or bad depends on the situation. Generally, a lower coefficient indicates greater consistency and data precision, whereas a higher coefficient signals greater dispersion and variability. For example, in chemistry or physics, a CV of less than 5% may be considered a good value. But in other fields such as economics, an acceptable value would be considered 20% or less. It all depends on the industry and specific context, in which you’re applying the analysis. In other words, it’s important to remember that there is no hard and fast rule as to what a good or bad coefficient of variation is.