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Chapter 18: A. Basic Statistics and Applications 205
Find the mode for the following data set:
EXAMPLE 18.6
3, 8, 5, 6, 10, 17, 19, 20, 3, 2, 11
Solution:
In the given data set each value occurs once except 3 which occurs twice.
Thus, the mode for this set is:
M 0 = 3
Find the mode for the following data set:
EXAMPLE 18.7
1, 7, 19, 23, 11, 12, 1, 12, 19, 7, 11, 23
Solution:
Note that in this data set, each value occurs the same number of times. Thus, in this data
set there is no mode.
EXAMPLE 18.8
Find modes for the following data set:
5, 7, 12, 13, 14, 21, 7, 21, 23, 26, 5
Solution:
In this data set 5, 7, and 21 occur twice and the rest of the values occur only once.
Thus, in this example there are three modes, that is,
Part IV.A.1
M 0 = 5, 7, and 21
Note that there is no mathematical relationship as such between the mean,
mode, and median. However, the values of mean, mode, and median do provide
us important information about the potential type or shape of the frequency distribution
of the data. Although the shape of the frequency distribution of a data
set could be of any type, most frequently we see the three types of frequency distributions
shown in Figure 18.1.
The location of the measures of centrality as shown in Figure 18.1 provide
the information about the type of data. A data set is symmetric when the values
in the data set that lie equidistant from the mean, on either side, occur with equal