Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

86 CHAPTER 3 | Central Tendency
3.5 Selecting a Measure of Central Tendency
LEARNING OBJECTIVE
8. Explain when each of the three measures of central tendency—mean, median, and
mode—should be used, identify the advantages and disadvantages of each, and
describe how each is presented in a report of research results.
You usually can compute two or even three measures of central tendency for the same set
of data. Although the three measures often produce similar results, there are situations in
which they are predictably different (see Section 3.6). Deciding which measure of central
tendency is best to use depends on several factors. Before we discuss these factors, however,
note that whenever the scores are numerical values (interval or ratio scale) the mean
is usually the preferred measure of central tendency. Because the mean uses every score
in the distribution, it typically produces a good representative value. Remember that the
goal of central tendency is to find the single value that best represents the entire distribution.
Besides being a good representative, the mean has the added advantage of being
closely related to variance and standard deviation, the most common measures of variability
(Chapter 4). This relationship makes the mean a valuable measure for purposes of
inferential statistics. For these reasons, and others, the mean generally is considered to be
the best of the three measures of central tendency. However, there are specific situations in
which it is impossible to compute a mean or in which the mean is not particularly representative.
It is in these situations that the mode and the median are used.
■ When to Use the Median
We will consider four situations in which the median serves as a valuable alternative to the
mean. In the first three cases, the data consist of numerical values (interval or ratio scales)
for which you would normally compute the mean. However, each case also involves a
special problem so that it is either impossible to compute the mean, or the calculation of
the mean produces a value that is not central or not representative of the distribution. The
fourth situation involves measuring central tendency for ordinal data.
Extreme Scores or Skewed Distributions When a distribution has a few extreme
scores, scores that are very different in value from most of the others, then the mean may
not be a good representative of the majority of the distribution. The problem comes from
the fact that one or two extreme values can have a large influence and cause the mean to
be displaced. In this situation, the fact that the mean uses all of the scores equally can be
a disadvantage. Consider, for example, the distribution of n = 10 scores in Figure 3.8. For
this sample, the mean is
M 5 SX
n 5 203
10 5 20.3
Notice that the mean is not very representative of any score in this distribution. Although
most of the scores are clustered between 10 and 13, the extreme score of X = 100 inflates
the value of SX and distorts the mean.
The median, on the other hand, is not easily affected by extreme scores. For this sample,
n = 10, so there should be five scores on either side of the median. The median is
11.50. Notice that this is a very representative value. Also note that the median would be
unchanged even if the extreme score were 1000 instead of only 100. Because it is relatively
unaffected by extreme scores, the median commonly is used when reporting the average
value for a skewed distribution. For example, the distribution of personal incomes is very