Statistics How To

How to Find a Coefficient of Variation

Probability and Statistics > Basic Statistics > How to Find a Coefficient of Variation

Contents:

  1. What is the Coefficient of Variation?
  2. How to Find the Coefficient of Variation

What is the Coefficient of Variation?

coefficient of variation
The coefficient of variation (CV) is a measure of relative variability. It is the ratio of the standard deviation to the mean (average). For example, the expression “The standard deviation is 15% of the mean” is a CV.

The CV is particularly useful when you want to compare results from two different surveys or tests that have different measures or values. For example, if you are comparing the results from two tests that have different scoring mechanisms. If sample A has a CV of 12% and sample B has a CV of 25%, you would say that sample B has more variation, relative to its mean.

Formula

The formula for the coefficient of variation is:

Coefficient of Variation = (Standard Deviation / Mean) * 100.
In symbols: CV = (SD/xbar) * 100.

Multiplying the coefficient by 100 is an optional step to get a percentage, as opposed to a decimal.

Coefficient of Variation Example

A researcher is comparing two multiple-choice tests with different conditions. In the first test, a typical multiple-choice test is administered. In the second test, alternative choices (i.e. incorrect answers) are randomly assigned to test takers. The results from the two tests are:

Regular Test Randomized Answers
Mean 59.9 44.8
SD 10.2 12.7

Trying to compare the two test results is challenging. Comparing standard deviations doesn’t really work, because the means are also different. Calculation using the formula CV=(SD/Mean)*100 helps to make sense of the data:

Regular Test Randomized Answers
Mean 59.9 44.8
SD 10.2 12.7
CV 17.03 28.35

Looking at the standard deviations of 10.2 and 12.7, you might think that the tests have similar results. However, when you adjust for the difference in the means, the results have more significance:
Regular test: CV = 17.03
Randomized answers: CV = 28.35

The coefficient of variation can also be used to compare variability between different measures. For example, you can compare IQ scores to scores on the Woodcock-Johnson III Tests of Cognitive Abilities.

Note: The Coefficient of Variation should only be used to compare positive data on a ratio scale. The CV has little or no meaning for measurements on an interval scale. Examples of interval scales include temperatures in Celsius or Fahrenheit, while the Kelvin scale is a ratio scale that starts at zero and cannot, by definition, take on a negative value (0 degrees Kelvin is the absence of heat).

How to Find a Coefficient of Variation: Overview.

Watch the video, or read the article below:

Use the following formula to calculate the CV by hand for a population or a sample.

how to find a coefficient of variation
σ is the standard deviation for a population, which is the same as “s” for the sample.
μ is the mean for the population, which is the same as XBar in the sample.

In other words, to find the coefficient of variation, divide the standard deviation by the mean and multiply by 100.

How to find a coefficient of variation in Excel.

You can calculate the coefficient of variation in Excel using the formulas for standard deviation and mean. For a given column of data (i.e. A1:A10), you could enter: “=stdev(A1:A10)/average(A1:A10)) then multiply by 100.

How to Find a Coefficient of Variation by hand: Steps.

Sample question: Two versions of a test are given to students. One test has pre-set answers and a second test has randomized answers. Find the coefficient of variation.

Regular Test Randomized Answers
Mean 50.1 45.8
SD 11.2 12.9

Step 1: Divide the standard deviation by the mean for the first sample:
11.2 / 50.1 = 0.22355

Step 2: Multiply Step 1 by 100:
0.22355 * 100 = 22.355%

Step 3: Divide the standard deviation by the mean for the second sample:
12.9 / 45.8 = 0.28166

Step 4: Multiply Step 3 by 100:
0.28166 * 100 = 28.266%

That’s it! Now you can compare the two results directly.

Questions? Post a comment and I’ll do my best to help!

Check out our YouTube channel for more stats help and tips.

If you prefer an online interactive environment to learn R and statistics, this free R Tutorial by Datacamp is a great way to get started. If you’re are somewhat comfortable with R and are interested in going deeper into Statistics, try this Statistics with R track.

How to Find a Coefficient of Variation was last modified: August 15th, 2017 by Stephanie

34 thoughts on “How to Find a Coefficient of Variation

  1. Liam

    I have data sets from repeat examinations on 22 patients. I’m looking for some way to quantify the reliability of my measurements. Can i calculate an individual CV for each patient (based on just two values each time) and then compute “the average CV”? Or would the resulting number be meaningless? Thanks in advance for any help.

  2. Andale

    The result would probably be meaningless. First, you’re looking to quantify “reliability”, but the CV is a way to compare data sets that have different measurement criteria, like a different scale. Second, you need the SD, which would be impossible to calculate meaningfully from two data points. Why not calculate the CV for the entire group of 22 people? That gives you the “average” for the set.

  3. Ryan

    What a great article. It helped me so much in my job. Clear, concise, informative. And it applies the knowledge to MS Excel which is what I really needed.

  4. Andale

    Could you expand on what you mean by mixed sets? Is there no way to separate them? How about you find the CV for the mixed sample. Would that work for your purposes?

  5. Mohamed fikry

    How I solve this plz?

    Find out the coefficient of variation of a series for which the following results are given: N=50, €X=25, €X(square) = 500
    Where X = deviation from the assumed average 5

  6. george

    Am so happy with this please I need a private contact or someone should contact me on here +2348162055748 I really wanna learn more

  7. Mohannas

    Hi thank u
    Whats your comment if there is two disease
    Disease A: and disease B

    But disease A have more larger value of mean , vairance , sd , and cv than disease B
    What dose that mean ??

  8. Heather

    How do you find the coefficient of variation if you are given a set of data that includes the standard deviation and amount of sales but NO mean? So I have 30 lines that have their own standard deviation and other info….I’m looking for the item with the highest Cv.

  9. Andale

    If you don’t have the mean you can’t find the cov. Is there any way of figuring out the mean from the “other info”?

  10. Odoom Bryan Samuel

    Pls given 200 as sample packages,26kg as the average weight(mean), 3.9kg as standard deviation and 8.8 cubic feet as another mean, 2.2 cubic feet as the other standard deviation. How can you compare the variation of weight and the volume?

  11. C Joyce

    What exactly does “multiply by 100%” mean?
    How does it differ from “multiply by 100”?

  12. Brad

    The second “=” in the Excel formula should be deleted. Also, why do you not multiply the Excel formula by 100?

  13. Mark

    Please I want to know how to solve for the coefficient of variation when given just the mean. How will you solve it ?

  14. Andale

    You can’t. It’s like asking what’s the range of allowances for kids if you only know the average is $10. Are you given any other information?

  15. arnold komba

    if you are given a table with years and respective profit what do we take as classmark and frequence when computing mean standard deviation and coefficient of variation

  16. Andale

    It depends on what you mean by “better.” CV is a measure of variance, much like a standard deviation. A smaller standard deviation (or CV) doesn’t mean it’s better than a bigger one, just that it varies more. If you are looking for the smallest possible variation in your results then yes, the smaller CV would be better.

  17. Clancy

    This is very helpful. I want to clarify your response in #30 above. I believe you are saying that a smaller CV means there is less variation than a larger CV. Is that correct? For example, if Sample A has a CV of 12% and Sample B has a CV of 19% I would say that there is less variation in Sample A. Do I understand correctly?

    Thanks

  18. Andale

    I just added a little to the article to help clarify this point (I hope :) ).
    If sample A has a CoV of 12% and sample B has a CoV of 19%, you would say that sample B has more variation, relative to its mean (rather than just “more variation”).

Leave a Reply

Your email address will not be published. Required fields are marked *