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Departments: SPC Guide

Photo: Michael J. Cleary, Ph.D.


Beyond Deviation

Dr. Noah Tahl on the coefficient of variation



r. Noah Tahl learned about using control charts, standard deviation and histograms in a two-hour workshop he attended during a national health care conference. He’s seen for himself how these concepts help hospitals and other health care institutions organize and analyze their data, and he’s determined to use statistical process control to improve quality measures at St. Maybe Hospital. In this effort, he trains his staff to ensure that all department personnel understand the basics of statistics and can use them accordingly.

He’s determined to keep at least a page ahead of the group he’s training. So while everyone else is on the same page, Tahl stays up late to assure himself that he knows more than his trainees. It’s a never-ending struggle to stay ahead.

After he’s demonstrated the formula for calculating standard deviation and shown his trainees how control charts and histograms will help them understand processes, he introduces a software program that creates charts from data in established spreadsheets such as Excel. “This will make your life easier,” he promises, but as it turns out, it could very well make his own harder.

Alec Smart, one of his department managers, comes across the concept of the coefficient of variation as he explores the printout of his charted data. “What does it mean when the coefficient of variation is 11.92?” he asks.

Although the chapter on coefficient of variation isn’t one that Tahl has studied yet, he feels compelled to respond, especially because the entire class is looking expectantly at him. “That’s really the sum of the log of the standard deviation,” he mumbles. Although no one understands what he means, the trainees nod their heads and take notes.

Did Tahl provide the correct definition? And if so, is it important in health care? From the following, select the best description of the coefficient of variation:

A. The capability of a process

B. Whether a process is in or out of control

C. The peak level of a distribution

D. The ratio of the standard deviation to the mean

D is correct.

Coefficient of variation is a measure of how much variation exists in relation to the mean. Dr. Tahl’s guess was a meaningless collection of jargon. By obfuscating this simple technique, he was in fact robbing his trainees of the opportunity to gain another tool for data analysis.

Standard deviation alone isn’t particularly useful without a context. For example, knowing a standard deviation is 1.76 has no meaning, but understanding that a standard deviation of 2 had been anticipated provides a context that recognizes the variability is less than expected. Knowing the standard deviation has historically been 0.5 or less for a particular dimension, on the other hand, would suggest that 1.76 is considered high.

In examining the ratio of a standard deviation to a mean, the coefficient of variation provides a reference.

If the number is large, the data have much variability with respect to the mean.

A smaller number reflects a small amount of variation relative to the mean:


About the author

Michael J. Cleary, Ph.D., founder and president of PQ Systems Inc., is a noted authority in the field of quality management and a professor emeritus of management science at Wright State University in Dayton, Ohio. A 29-year professorship in management science has enabled Cleary to conduct extensive research and garner valuable experience in expanding quality management methods. He’s published articles on quality management and statistical process control in a variety of academic and professional journals.