Stem-and-Leaf Plots
Objectives

Display and interpet data on a stem-andleaf plot
Application

Mr Servello wants to study the distribution of the
scores for a 100-point unit exam given in his first
period chemistry class. The scores of the 35
students in the class are listed below.
82
71
89
77
76
64
49
65
88
84
89
54
44
95
87
98
78
91
93
69
80
44
90
85
86
93
75
89
74
55
99
62
62
79
96
Organizing Data

He can organize and display the scores in
a compact way by using a stem-and-leaf
plot. In a stem-and-leaf plot, the greatest
common place value of the data is used to
form the stems. The numbers in the next
greatest common place-value position are
then used to form the leaves. In the list
previously given, the greatest place value
is tens. Thus, the number 82 would have
stem 8 and leaf 2.
To make a stem-and-leaf plot

First, make a vertical list of
the stems. Since the test
scores range from 44 to
99, the stems range from
4 to 9. Then, plot each
number by placing the
units digit (leaf) to the
right of its correct stem.
Thus, the scores 82 is
plotted by placing leaf 2 to
the right of the stem 8.
The complete stem-andleaf plot is shown at the
right.
Note: a stem may have one or
more digits. A leaf always has
just one digit.
Stem
Leaf
4
944
5
45
6
59422
7
7168954
8
2499870596
9
83562309
8|2 represents a score of 82.
To make a stem-and-leaf plot

A second stem-andleaf plot can be made
to arrange the leaves
in numerical order
from least to greatest
as shown at the right.
This will make it
easier for Mr. Juarez
to analyze the data.
Stem
Leaf
4
449
5
45
6
22459
7
1456789
8
0245678999
9
02335689
Ex. 1: Use the information in the stem-andleaf plots above to answer each question.
1.
2.
3.
What were the
Stem
highest and the
lowest scores? 99 and 44 4
5
Which test score
occurred most
6
frequently? 89 (3 times)
In which 10-point
interval did the most
students score? 80-89(10
students)
4.
Leaf
449
45
22459
7
1456789
8
0245678999
9
02335689
How many students
received a score of 70 25 students
or better?
More than 2 digits


Sometimes the data for a stem-and-leaf plot are
numbers that have more than two digits. Before
plotting the numbers, they may need to be
rounded or truncated to determine each stem
and leaf. Suppose you want to plot 356 using
the hundreds digit for the stem.
Rounded: Round 356 to 360. Thus you would
plot 356 using stem 3 and leaf 6. What would be
the stem-and-leaf of 499?
5 and 0
More than 2 digits

Truncated—To truncate means to cut off, so
truncate 356 as 350. Thus you would plot 356
using stem 3 and leaf 5. What would be the
stem and leaf of 499?
4 and 9
Back-to-back stem-and-leaf

A back-to-back stem-and-leaf plot is
sometimes used to compare two data or
rounded and truncated values of the same
data set. In a back-to-back plot, the
same stem is used for the leaves of both
plots.
Ex. 2: The average annual pay for workers in selected states are listed below.
Make a back-to-back stem-and-leaf plot of the average annual pay comparing
rounded values and truncated values. Then answer each question.
State
Avg. Annual
Pay
State
Avg. Annual
Pay
Alaska
$28,033
Michigan
$24,193
California
$24,126
Minnesota
$21,481
Colorado
$21,472
New Jersey
$25,748
Connecticut
$26,234
New York
$26,347
Delaware
$21,977
Ohio
$21,501
Illinois
$23,608
Pennsylvania
$21,485
Maryland
$22,515
Texas
$21,130
Massachusetts
$24,143
Virginia
$21,053
Ex. 2: Since the data range from $21,053 to $28,033, the stems
range from 21 to 28 for both plots.
State
Avg.
Annual
Pay
State
Avg.
Annual Pay
Rounded
Stem
Truncated
Alaska
$28,033
Michigan
$24,193
555511
21
0144459
California
$24,126
Minnesota
$21,481
50
22
5
Colorado
$21,472
New Jersey
$25,748
6
23
6
Connecticut
$26,234
New York
$26,347
211
24
111
Delaware
$21,977
Ohio
$21,501
7
25
7
Illinois
$23,608
Pennsylvania
$21,485
32
26
23
Maryland
$22,515
Texas
$21,130
Massachusett
s
$24,143
Virginia
$21,053
27
0
28
0
Ex. 2: Since the data range from $21,053 to $28,033, the stems
range from 21 to 28 for both plots.
a.
What does 21|5
represent in each
plot?
Answer: It represents
$21,450 to $21,549
for rounded data and
$21,500 to $21,599
for truncated data.
Rounded
Stem
Truncated
555511
21
0144459
50
22
5
6
23
6
211
24
111
7
25
7
32
26
23
27
0
28
0
Ex. 2: Since the data range from $21,053 to $28,033, the stems
range from 21 to 28 for both plots.
b.
What is the difference
between the highest
lowest average
annual pay?
Answer: About $6,900
for rounded data and
$7,000 for truncated
data.
Rounded
Stem
Truncated
555511
21
0144459
50
22
5
6
23
6
211
24
111
7
25
7
32
26
23
27
0
28
0
Ex. 2: Since the data range from $21,053 to $28,033, the stems
range from 21 to 28 for both plots.
c.
Did more of the
states have average
annual pay above or
below $25,000?
Answer: Below $25,000
Rounded
Stem
Truncated
555511
21
0144459
50
22
5
6
23
6
211
24
111
7
25
7
32
26
23
27
0
28
0
Ex. 2: Since the data range from $21,053 to $28,033, the stems
range from 21 to 28 for both plots.
d.
Does there appear to
be any significant
difference between
the two stem-andleaf plots?
Answer: NO
Rounded
Stem
Truncated
555511
21
0144459
50
22
5
6
23
6
211
24
111
7
25
7
32
26
23
27
0
28
0
Ex. 3: Set up the problem

The enrollment of several small colleges in the
Center City area are listed below. Make a backto-back stem-and-leaf plot of enrollments
comparing rounded values and truncated values.
Then answer each question.
College
Enrollment Figure
Miller Business School
1342
Capital College
1685
Para-Professional Institute
1013
Parke College
2350
State Community
3781
Fashion Institute
1096
College of Art and Design
1960
Franklin Community College
3243
Ex. 3: Since the data range from 1013 to 3781, we an use stems
that represent 1,000 each.
a.
What range of
student enrollment is
represented on the
rounded side by 2|4?
Answer: 2350-2449
Rounded
Stem
Truncated
7310
1
00369
40
2
3
82
3
27
Ex. 3: Since the data range from 1013 to 3781, we an use stems
that represent 1,000 each.
b.
What range of
student enrollment is
represented on the
truncated side by
1|9?
Rounded
Stem
Truncated
7310
1
00369
40
2
3
82
3
27
Answer: 1900-1999
Since each stem represents 1,000; for example
3|8 represents 3,000-3,999