CHAPTER 4 - Averaging

Abstract

This chapter discusses Averaging. When studying the variability of a numerical property, one usually is interested first in some type of average that characterizes the property in the mean. The mode is easy to determine, easy to take in at a glance but somewhat unsatisfactory for bimodal and multimodal distributions, that is for distributions with several peaks. However, the main disadvantage is M is an isolated rather than a global property of a distribution; M refers only to one specific x-value. On the other hand, it might be important to know where the frequency accumulates. The median is easy to determine. It is rather insensitive in regard to the tails of the distribution. Circular distributions constitute an important class of distributions in the geological sciences. The shape of the histogram and the mean value of the corresponding frequency distribution depend in general on the selection of the histograms origin. The average of a circular distribution may be defined by using the vector mean. A vector is represented by an arrow; its direction is defined by the direction of its tip, and its magnitude is defined by the length of the arrow.