Coefficient of Variation Calculator

Use this calculator to quickly find the sample coefficient of variation or population coefficient of variation using either raw data values or the summary statistics. The tool also provides you with a clear, step-by-step explanation, showing you how the coefficient of variation (CV) was calculated.

How to Use the Coefficient of Variation Calculator?

Want to quickly find the sample or population coefficient of variation, either using raw data values or summary statistics? Our coefficient of variation calculator simplifies this for you. Just follow these simple steps to get instant results, with a clear, step-by-step explanation:

If you have raw data

1. Choose whether your data is a sample or a population.
2. Select the raw data input option.
3. Enter your values separated by commas, spaces, or tabs.
4. Click Calculate.

However, if you already have summary statistics data

1. Choose whether your data is a sample or a population.
2. Select the summary data input option.
3. Enter the mean and the standard deviation.
4. Click Calculate.

The calculator will return the coefficient of variation and show you exactly how the coefficient of variation was computed for your data values.

The calculator is useful when you want to compare the spread of two or more datasets, especially when the values are measured in different units or the averages are very different. This helps you determine how large the standard deviation is relative to the mean.

What is the Coefficient of Variation?

The coefficient of variation (CV), also known as the relative standard deviation, is a ratio of the standard deviation to the mean. It measures how much variability exists between two datasets compared to the mean of the dataset. In simple terms, it tells us how spread out the data is relative to its average value.

Instead of looking at the standard deviation alone, CV expresses dispersion relative to the mean. This makes it an ideal statistic when you want to compare consistency across datasets with different scales, units, or average values.

Looking for a quick explanation of how to interpret the coefficient of variation? Here is how to interpret the value.

A lower coefficient of variation means the data is more consistent relative to the mean. On the other hand, a higher coefficient of variation implies that the data is more dispersed relative to the mean.

Why Use the Coefficient of Variation?

The standard deviation alone does not always give a fair comparison between datasets because it is expressed in the same unit as the original data. To address this limitation, the coefficient of variation standardizes this variation relative to the mean.

You should use a CV when:

• Comparing variability between datasets with different units
• Comparing consistency between groups with different means
• analyzing financial, laboratory, production, or performance data
• deciding which dataset is more stable relative to its average

This makes the coefficient of variation especially useful in statistics, business, science, economics, and quality control.

Coefficient of Variation Formula

The coefficient of variation formula varies slightly depending on whether you’re working with a sample or a population.

If you’re working with sample data, the CV formula is $CV = \frac{s}{\bar{x}}$. However, if you’re working with population data, the formula becomes $CV = \frac{\sigma}{\mu}$.

Where:

• CV is the coefficient of variation
• S is the sample standard deviation
• x̄ is the sample mean
• σ is the population standard deviation
• μ is the population mean

Sometimes, CV is often expressed as a percentage. In this case, you only need to multiply the CV by 100. Thus, the general formula becomes:

This form is easier to interpret because it shows variation as a percent of the mean.

How to Calculate the Coefficient of Variation?

Calculating the coefficient of variation depends on whether you have summary statistics data or a raw dataset. If you’re working with raw data and want to compute the coefficient of variation manually, follow these steps:

1. Calculate the mean of the data
2. Compute the standard deviation of the data
3. Divide the standard deviation by the mean and multiply by 100

However, if you’re already provided with summary statistics values (mean and standard deviation), the process is more straightforward and is as follows:

1. Identify the parameters (mean and standard deviation)
2. Divide the standard deviation by the mean and multiply by 100

The best thing about our coefficient of variation calculator is that you don’t have to do all those steps manually. You can easily switch between sample and population data, or even between summary statistics and raw data

Example 1. Calculating Coefficient of Variation using Raw Data

Find the coefficient of variation for the following sample data: 10, 34, 23, 54, 9

Solution

From the question, we’re working with raw sample data. Thus, the coefficient of variation formula is $CV = \frac{s}{\bar{x}} \times 100$.

Now, let’s follow the steps

Step 1. Find the mean

By definition, the sample mean formula is $\bar{x} = \frac{\sum{x_i}}{n}$

Where:

• $\sum{x_i}$ is the sum of all values in the data
• n is the total number of observations in the data

Thus, the sample mean $\bar{x} =\frac{10 + 34 + 23 +54 + 9}{5}$

=$\frac{130}{5}$

= 26

Want to find the sample mean quickly using an online tool? Use our free sample mean calculator. However, if you’re working with population data instead, use the population mean calculator.

Step 2. Find the sample standard deviation

By definition, the sample standard deviation formula is $s = \sqrt{\frac{\sum_{i=1}^{n}(x_i – \bar{x})^2}{n-1}}$

To find the sample standard deviation for the data, follow these sub-steps:

i) Find the sum of squared deviations from the mean

The table below shows how to find the squared deviations

xi	(xi-x̄)	(xi-x̄)2
10	(10-26) = -16	(-16)2 = 256
34	(34-26) = 8	(8)2 = 64
23	(23-26) =-3	(-3)2 = 9
54	(54-26) = 28	(28)2 = 784
9	(9-26) = -17	(-17)2 = 289

To find the sum of all squared deviations, you sum all the values in the column, (xi-x̄)²

Thus, ${\sum_{i=1}^{n}(x_i – \bar{x})^2} = 256 + 64 + 9 + 784 + 289$

= 1402

ii) Find n – 1

There are 5 observations in the dataset. Thus, n = 5. This implies that n-1 = 4

iii) Compute the sample standard deviation

Applying the sample standard deviation formula and substituting the values, we have:

= 18.7216

Note. You can quickly find this value using our sample standard deviation calculator.

Step 3. Compute the coefficient of variation

Now that we have the sample mean, x̄ = 26, and the sample standard deviation, we can easily compute the CV.

Thus, $CV = \frac{18.7216}{26} \times 100$

= 72.01%

This means the spread of the data is about 72.01% of the mean.

Example 2. Calculating CV from Summary Data

Suppose a sample dataset has:

• Mean = 12
• Standard deviation = 18

Find the coefficient of variation.

Solution

Step 1. Identify the parameters

From the question, we know that:

• sample mean, x̄ =12
• Sample standard deviation, s = 18

Step 2. Apply the CV formula

By definition, $CV = \frac{s}{\bar{x}} \times 100$. Substituting the values in the formula gives:

= 66.67%

This shows that the standard deviation is 66.67% of the sample mean.

How to Interpret the Coefficient of Variation

Here’s how to interpret the coefficient of variation

• A Low CV implies that the data has less relative variability, hence more consistency
• A high CV indicates that the data has more relative variability, hence less consistency

Tip. There is no single cutoff that applies to every field. What counts as a “good” or “bad” CV depends on the subject area. For instance, in quality control, a lower CV often suggests better precision, whereas in finance or economics, a higher CV may signal more risk relative to average return.

Important Note About Zero or Negative Means

You should be careful when the mean is zero or very close to zero. Here are some key notes to keep in mind:

• If the mean is zero, the coefficient of variation is undefined
• If the mean is very close to zero, the CV can become extremely large and misleading
• If the mean is negative, the CV is meaningless

Therefore, the coefficient of variation is most meaningful when the mean is positive and not close to zero.

Frequently Asked Questions