TABLE OF CONTENTS As we know, the average height of a given population does not tell us a great deal. If the average is, say, 1.7 m, we know that there will be some people who are shorter, say under 1.5 m, and some who are taller, perhaps over 2 m. If you are a manufacturer of clothes, you would need to know the spread or distribution of the heights of the population in order to design a range of sizes that are suitable.
We use the average or mean as a measure to describe a set of values. The arithmetic average is the one most commonly used, since it is easy to compute. The term average may give the impression it is an expected value. In practice, these two values may be quite different from each other.
There is a similar situation when we deal with equipment failure rates. The majority of the failures may take place in the last few weeks of operation, thereby skewing the distribution. For example, if we recorded failures of 100 tires, and their combined operational life was three million km, what can we learn from the mean value of 30,000 km of average operational life? In practice, it is likely that there were very few failures within the first 5000 km or so, and that a significant number of tires failed after 30,000 km. Hence the actual distribution of failures is important if we are to use this information for predicting...
