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

84 CHAPTER 3 | Central Tendency
TABLE 3.4
Favorite restaurants named by a sample of n = 100 students.
Caution: The mode is a score or category, not a frequency. For this example, the mode is Luigi’s,
not f = 42.
Restaurant
College Grill 5
George & Harry’s 16
Luigi’s 42
Oasis Diner 18
Roxbury Inn 7
Sutter’s Mill 12
f
you cannot add restaurants to obtain SX and you cannot list the scores (named restaurants)
in order.
The mode also can be useful because it is the only measure of central tendency that corresponds
to an actual score in the data; by definition, the mode is the most frequently occurring
score. The mean and the median, on the other hand, are both calculated values and often produce
an answer that does not equal any score in the distribution. For example, in Figure 3.6
(page 84) we presented a distribution with a mean of 4 and a median of 2.5. Note that none
of the scores is equal to 4 and none of the scores is equal to 2.5. However, the mode for this
distribution is X = 2 and there are three individuals who actually have scores of X = 2.
In a frequency distribution graph, the greatest frequency will appear as the tallest part
of the figure. To find the mode, you simply identify the score located directly beneath the
highest point in the distribution.
Although a distribution will have only one mean and only one median, it is possible
to have more than one mode. Specifically, it is possible to have two or more scores that
have the same highest frequency. In a frequency distribution graph, the different modes
will correspond to distinct, equally high peaks. A distribution with two modes is said to be
bimodal, and a distribution with more than two modes is called multimodal. Occasionally,
a distribution with several equally high points is said to have no mode.
Incidentally, a bimodal distribution is often an indication that two separate and distinct
groups of individuals exist within the same population (or sample). For example, if you
measured height for each person in a set of 100 college students, the resulting distribution
would probably have two modes, one corresponding primarily to the males in the group
and one corresponding primarily to the females.
Technically, the mode is the score with the absolute highest frequency. However, the
term mode is often used more casually to refer to scores with relatively high frequencies—
that is, scores that correspond to peaks in a distribution even though the peaks are not the
absolute highest points. For example, Athos et al. (2007) asked people to identify the
pitch for both pure tones and piano tones. Participants were presented with a series of
tones and had to name the note corresponding to each tone. Nearly half the participants
(44%) had extraordinary pitch-naming ability (absolute pitch), and were able to identify
most of the tones correctly. Most of the other participants performed around chance
level, apparently guessing the pitch names randomly. Figure 3.7 shows a distribution of
scores that is consistent with the results of the study. There are two distinct peaks in the
distribution, one located at X = 2 (chance performance) and the other located at X = 10
(perfect performance). Each of these values is a mode in the distribution. Note, however,
that the two modes do not have identical frequencies. Eight people scored at X = 2 and
only seven had scores of X = 10. Nonetheless, both of these points are called modes.
When two modes have unequal frequencies, researchers occasionally differentiate the
two values by calling the taller peak the major mode, and the shorter one the minor mode.