**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.

Reading Assignment

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.