# Understanding Measurement and Coefficient of Variation

By Finn Orfano

## Coefficient of Variation

If you like probability and statistics, then coefficient of variation is something you can figure out. What is coefficient of variation? What does coefficient of variation measure? Even though calculating it might be a little difficult, the concept isn’t that difficulty.

Coefficient of variation is a measure of the ratio of the standard deviation to the mean. In statistics it is abbreviated as CV. To calculate CV you take the standard deviation of the data and divide it by the mean of the data. Mean is another word for average. To calculate the average of a set of data, you add all the numbers and then divide by how many numbers you added. Standard deviation simply put is the mean of the mean. Let’s take a better look at standard deviation.

Standard deviation is a way of stating how far away or close the results are to mean of the data. So, how do you calculate it? Let’s look at an example of data. Here is a list of numbers, let’s say they are test scores: 65, 89, 77, 98, 66, 100, 95, 81, 83, 65. The mean of these numbers is 81.9. Next, subtract the mean from every score (you may get negative numbers.) In our set of data, the standard deviations would be: -16.9, 7.1, -4.9, 16.1, -15.9, 18.1, 13.1, -0.9, 1.1, and -16.9. The next thing to do is square all of the deviations, our results would be: 285.61, 50.41, 24.01, 259.21, 252.81, 327.61, 171.61, 0.81, 1.21, and 285.61. After you have squared all of the deviations, you need to add them all together, in which we would get 1658.9. Divide that number by one less than the number of numbers in the set of data, so we would divide by 9 since there were 10 numbers and we would get 184.32. To find the standard deviation, you then take the square root, if we round we would get about 13.58.

Now that we have the mean and the standard deviation calculate we can calculate the coefficient of variation, simply by dividing the standard deviation by the mean. For our example of test scores we would take 13.58 and divide it by 81.9 and get approximately 0.17. Since coefficient of variation is typically represented by a percent we will say the CV is 17%. So, now that all of the math has been calculated what does it really mean?

By calculating the coefficient of variation you are seeing what percent of your results are equal to the mean of the data. In our example 17% of our results were equal to the mean.

If you are really into analyzing the data, then calculating the coefficient of variation is for you. It can be a little complicated to understand, but if you follow the steps it is not that difficult to calculate.