September 2003

Vol. 5, No. 9


Quality Quiz
from Professor Cleary

Congratulations! 
You're right!

Coefficient of variation is a measure of how much variation exists in relation to the mean, so it represents a highly useful—and easy—concept in data analysis. But Dr. Barbara SeVille's guess was a meaningless collection of jargon that she had picked up from a variety of sources. By obfuscating this simple technique, she was in fact robbing her trainees of the opportunity to gain another tool for data analysis.

Coefficient of variation  =

The standard deviation alone is sometimes not particularly useful, without a context within which one can determine meaning. For example, knowing that the standard deviation is 1.76 has no meaning; but understanding that a standard deviation of 20 had been anticipated gives a context that recognizes that variability is less than expected. Knowing that the standard deviation has historically been .5 or less for a particular dimension, on the other hand, 1.76 would be considered high. Without perspective, the figure for standard deviation has limited meaning.

The coefficient of variation provides a reference, by looking at the ratio of a standard deviation to a mean.

Coefficient of variation  =

If the number is large, the data has a great deal of variability with respect to the mean.

e.g., C.V. =

 = 

= .50

If the number is smaller, this reflects a small amount of variability relative to the mean.

e.g., C.V. =

 = 

= .05


 

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