What Do All of These Means Mean?
David J. Lilja, Ph.D., P.E.
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.
After completing this 3-hour course, you will be able to:
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.
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 , for instance, argue strongly for using the geometric mean since it has some interesting mathematical properties. Smith , 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!
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.
Once you finish studying the above course content, you need to take a quiz to obtain the PDH credits.