What Do All of These Means Mean?

David J. Lilja, Ph.D., P.E.

Course Overview

There is a strong desire to reduce the performance of a computer system to a single number. Typically this is done using one of several different statistical means, such as the arithmetic, harmonic, or geometric means. In this course you will learn how to calculate the different types of means and how to quantify the variability in a group of measured values. More importantly, you will learn when each of the different types of mean values should be used.

This course includes a multiple-choice quiz at the end, which is designed to enhance the understanding of the course materials.

Learning Objective

After completing this 3-hour course, you will be able to:

• Calculate the different types of means;
• Calculate the variance of a collection of data values;
• Understand what makes a "good" mean value; and
• Select the appropriate mean to summarize your data correctly.

The reading assignment for this course is Chapter 3 of Measuring Computer Performance: A Practitioner's Guide, David J. Lilja, Cambridge University Press, 2000.

If you don't have this book, you can purchase Chapter 1 in PDF format online at eBooks.com for a modest cost. The price for this course listed on this website does not include the cost of purchasing the chapter through eBooks.com. However, the price has been reduced to compensate for the cost of purchasing the chapter required. If you plan to take all 6 courses (E132 to E137) based on this book, you may consider to purchase a hard copy of the book or the entire book in PDF format online through eBooks.com.

Key Terms

• Index of central tendency.
• Median.
• Mode.
• Arithmetic mean.
• Harmonic mean.
• Geometric mean.
• Variance.
• Coefficient of variation.

Study Notes

We all think we know how to compute a mean value of a collection of data values -- simply sum all of the values and divide by n, the number of values in the sample.

In fact, this computation produces a specific statistic called the arithmetic mean. However, there are several other types of mean values, including the geometric mean and the harmonic mean. Several authors and researchers have advocated using one of these means instead of the arithmetic mean when trying to summarize data from computer systems performance studies. Fleming and Wallace [1], for instance, argue strongly for using the geometric mean since it has some interesting mathematical properties. Smith [2], however, says that the properties of the geometric mean make it inappropriate for comparing computer systems. He instead advocates for the arithmetic and harmonic means, depending on the type of data for which the mean value is being computed.

After completing this course, you should be able to compute each of the different types of mean values. More importantly, you should be able to determine when each of the different types of means should be applied.

If you would like to learn more about the controversy surrounding the choice of mean values, you can read the papers listed below.

Good luck in successfully completing this course!

References

P. J. Fleming and J. J. Wallace, "How Not To Lie With Statistics: The Correct Way To Summarize Benchmark Results," Communications of the ACM, March 1986, pp. 218-221.

James E. Smith, "Characterizing Computer Performance with a Single Number," Communications of the ACM, October 1988, pp. 1202-1206.

Quiz

Once you finish studying the above course content, you need to take a quiz to obtain the PDH credits.

DISCLAIMER: The materials contained in the online course are not intended as a representation or warranty on the part of PDH Center or any other person/organization named herein. The materials are for general information only. They are not a substitute for competent professional advice. Application of this information to a specific project should be reviewed by a registered architect and/or professional engineer/surveyor. Anyone making use of the information set forth herein does so at their own risk and assumes any and all resulting liability arising therefrom.