CHAPTER 5
MEASURES OF LOCATION AND
VARIABILITY
In this chapter we present the commonly used numbers that help describe a population
or a sample of observations. Such numbers are called parameters if they describe
populations; they are called statistics if they describe a sample. The most useful
single number or statistic for describing a set of observations is one that describes the
center or the location of the distribution of the observations. Section 5.1 presents the
most commonly used measures of location-the mean, median, and the mode-and
describes how to obtain them.
The second most useful number or statistic for describing a set of observations is
one that gives the variability or dispersion of the distribution of observations. Several
measures of variability are defined in Section 5.2 and formulas are given for their
computation.
We discuss the relationship between the results from the sample and those for the
population for the mean and variance in Section 5.3. In Section 5.4 we discuss the
reasoning behind the choice of the statistic to use to describe the center and variability
of the distribution, depending on what statements the investigator wishes to make and
the characteristics of the variables in the data set. The Stevens classification system
for variables is given. Section 5.5 presents one method for displaying sample statistics
graphically.Basic Statistics: A Primer for the Biomedical Sciences, Fourth Edition.
By Olive Jean Dunn and Virginia A. Clark
Copyright @ 2009 John Wiley & Sons, Inc.49