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

**Contents**:

## What is the Coefficient of Variation?

The coefficient of variation (CV) 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.

### Formula

The **formula for the coefficient of variation **is:

Coefficient of Variation = (Standard Deviation / Mean) * 100.

In symbols: CV = (SD/) * 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.

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!

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Thank you so much for this. i’ve been looking everywhere and all the answers were too vague.

Thank you ☺️

how to tell which one is more consistent between two data sets by CV ?

I’m not sure what you mean by more consistent. Compared to what?

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.

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.

Excellent review for CV, Thanks

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.

How calcute CV of if two data sets are mixed

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?

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

I think something is getting lost in translation. What is “€”?

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

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 ??

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.

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”?

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?

Standardize the scores.

What exactly does “multiply by 100%” mean?

How does it differ from “multiply by 100”?

I deleted the % sign — it didn’t make much sense. Thanks for pointing it out :)

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

Thanks for that correction, Brad.

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

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?

This is so much helpful!