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

56 CHAPTER 2 | Frequency Distributions
3. Following are three rows from a frequency distribution table. Using interpolation,
what is the percentile rank for X = 18?
a. 52.5%
b. 30%
c. 29%
d. 25%
X c%
20–24 60%
15–19 35%
10–14 15%
ANSWERS
1. B, 2. D, 3. C
2.5 Stem and Leaf Displays
LEARNING OBJECTIVE
11. Describe the basic elements of a stem and leaf display and explain how the display
shows the entire distribution of scores.
In 1977, J.W. Tukey presented a technique for organizing data that provides a simple
alternative to a grouped frequency distribution table or graph (Tukey, 1977). This technique,
called a stem and leaf display, requires that each score be separated into two
parts: The first digit (or digits) is called the stem, and the last digit is called the leaf.
For example, X = 85 would be separated into a stem of 8 and a leaf of 5. Similarly,
X = 42 would have a stem of 4 and a leaf of 2. To construct a stem and leaf display for a
set of data, the first step is to list all the stems in a column. For the data in Table 2.3, for
example, the lowest scores are in the 30s and the highest scores are in the 90s, so the list
of stems would be
Stems
The next step is to go through the data, one score at a time, and write the leaf for each
score beside its stem. For the data in Table 2.3, the first score is X = 83, so you would
write 3 (the leaf) beside the 8 in the column of stems. This process is continued for the
entire set of scores. The complete stem and leaf display is shown with the original data in
Table 2.3.
■ Comparing Stem and Leaf Displays with Frequency Distributions
Notice that the stem and leaf display is very similar to a grouped frequency distribution.
Each of the stem values corresponds to a class interval. For example, the stem 3 represents
3
4
5
6
7
8
9