Chapter 2: Graphs, Charts, and Tables--Describing Your Data

CHAPTER 2 • GRAPHS, CHARTS, AND TABLES—DESCRIBING YOUR DATA 39
TABLE 2.6 DVD Movies Owned: Blockbuster Survey
9 4 13 10 5 10 13 14 10 19
0 10 16 9 11 14 8 15 7 15
10 11 9 7 6 12 12 14 15 16
15 14 10 13 9 12 12 10 10 11
15 14 9 19 3 9 16 19 15 9
4 2 4 5 6 2 3 4 7 5
6 2 2 0 0 8 3 4 3 2
2 5 2 5 2 2 6 2 5 6
5 2 7 3 5 1 6 4 3 6
3 7 7 1 6 2 7 1 3 2
4 0 2 2 4 6 2 5 3 7
4 16 9 10 11 7 10 9 10 11
11 12 9 8 9 7 9 17 8 13
14 13 10 6 12 5 14 7 13 12
9 6 10 15 7 7 9 9 13 10
9 3 17 5 11 9 6 9 15 8
11 13 4 16 13 9 11 5 12 13
0 3 3 3 2 1 4 0 2 0
3 7 1 5 2 2 3 2 1 3
2 3 3 3 0 3 3 3 1 1
13 24 24 17 17 15 25 20 15 20
21 23 25 17 13 22 18 17 30 21
18 21 17 16 25 14 15 24 21 15
Mutually Exclusive Classes
Classes that do not overlap so that
a data value can be placed in only
one class.
All-Inclusive Classes
A set of classes that contains all
the possible data values.
Equal-Width Classes
The distance between the lowest
possible value and the highest
possible value in each class is equal
for all classes.
for the variable of interest. Care needs to be taken when constructing these classes to
ensure each data point is put into one, and only one, possible class. Therefore, the classes
should meet four criteria.
First, they must be mutually exclusive.
Second, they must be all-inclusive.
Third, if at all possible, they should be of equal width.
Equal-width classes make analyzing and interpreting the frequency distribution easier.
However, there are some instances in which the presence of extreme high or low values
makes it necessary to have an open-ended class. For example, annual family incomes
in the United States are mostly between $15,000 and $200,000. However, there are some
families with much higher family incomes. In order to best accommodate these high
incomes, you might consider having the highest income class be “over $200,000” or
“$200,000 and over” as a catchall for the high-income families.
Fourth, avoid empty classes if possible.
Empty classes are those for which there are no data values. If this occurs, it may be
because you have set up classes that are too narrow.
Steps for Grouping Data into Classes There are four steps for grouping data, such
as that found in Table 2.6, into classes.
Step 1 Determine the number of groups or classes to use. Although there is
no absolute right or wrong number of classes, the rule of thumb is to have
between 5 and 20 classes. Another guideline for helping you determine
how many classes to use is the 2 k n rule, where k the number of
classes and n the number of data values. For example, for n 230, the
2 k n rule would suggest k 8 classes (2 8 256 230).