11-7
MAIN IDEA
Display data in stem-andleaf plots. Interpret data
in stem-and-leaf plots.
Stem-and-Leaf Plots
An elector is a voter that represents his or her state in a presidential
election. The number of electors for each state, including the
District of Columbia, is shown in the table below.
Number of Electors
New Vocabulary
stem-and-leaf plot
stems
leaves
back-to-back
stem-and-leaf plot
AL: 9
AK: 3
AZ: 10
AR: 6
CA: 55
CO: 9
CT: 7
DE: 3
DC: 3
FL: 27
GA: 15
HI: 4
ID:
IL:
IN:
IA:
KS:
KY:
4
21
11
7
6
8
LA: 9
ME: 4
MD: 10
MA: 12
MI: 17
MN: 10
MS: 6
MO:11
MT: 3
NE: 5
NV: 5
NH: 4
NJ: 15
NM: 5
NY: 31
NC: 15
ND: 3
OH: 20
OK: 7
OR: 7
PA: 21
RI: 4
SC: 8
SD: 3
TN: 11
TX: 34
UT: 5
VT: 3
VA: 13
WA: 11
WV: 5
WI: 10
WY: 3
Math Online
Source: The World Almanac
glencoe.com
Write each number on a self-stick note. Then group the numbers:
0–9, 10–19, 20–29, 30–39, 40–49, 50–59.
• Extra Examples
• Personal Tutor
• Self-Check Quiz
1. Is there an equal number of electors in each group? Explain.
2. Name an advantage of displaying the data in groups.
In a stem-and-leaf plot, numerical data are listed in ascending or
descending order. The digits in the greatest place value of the data are used
for the stems. The digits in the next greatest place value form the leaves.
Draw a Stem-and-Leaf Plot
1 OLYMPICS The table shows the total
points scored in the first beach
volleyball match played by each
team in the 2004 Olympics. Display
the data for the men’s teams in a
stem-and-leaf plot.
Step 1
Find the least and the
greatest number. Then
identify the greatest place
value digit in each number.
• The least number, 42, has
4 in the tens place.
Beach Volleyball Scores
Country
Men
Women
Greece
United States
Brazil
Canada
South Africa
Cuba
Germany
Australia
Switzerland
Norway
52
61
42
44
60
50
55
42
49
46
47
42
42
42
17
54
52
42
29
37
Source: Athens 2004
• The greatest number, 61, has 6 in the tens place.
Step 2
612
Chapter 11 Statistics
Draw a vertical line and write the stems
from 4 to 6 to the left of the line.
Stem Leaf
4
5
6
Step 3
Write the leaves to the right of the
the corresponding stem on the other
side of the line. For example, for 42,
write 2 to the right of 4.
Stem
4
5
6
Step 4
Rearrange the leaves so they are
ordered from least to greatest.
Repeat a leaf as often as it
occurs. Then include a key to
explain how to interpret the data.
Beach Volleyball Scores
Stem Leaf
4 2 2 4 6 9
C11-04A-877850.ai
5 0 2 5
6 0 1
5 |2 = 52 points
Leaf
2 4 2 9 6
2 0 5
1 0
C11-05A-877850.ai
a. Display the data for the women’s teams in a stem-and-leaf plot.
Interpret Data
2 PRESIDENTS The stem-and-leaf plot lists the ages of the U.S.
Presidents at the time of their first inauguration.
Age at Inauguration
Stem Leaf
4 23667899
5 0011112244444555566677778
5 |0 = 50 years 6 0111244689
Source: The World Almanac
Based on the data, what inferences can be made about the ages of
the U.S. Presidents at their first inauguration?
• Most of the data occur in the 50–59 interval.
• The youngest C11-06A-877850.ai
age is 42. The oldest age is 69. The range is 27.
• The median age is 55.
Refer to the stem-and-leaf plot in Example 1.
b. In which interval(s) do most of the scores occur?
c. What is the range of the data?
d. What is the median score?
Two sets of data can be compared using a back-to-back stem-andleaf plot. The back-to-back stem-and-leaf plot below shows the scores
of two basketball teams for the games in one season.
The leaves for
one set of data
are on one side
of the stem.
Points Scored
Falcons Stem Cardinals
76554222
6
42
88854
022579
7
100
1346899
8
1 |8 = 81 points
8 |6 = 86 points
The leaves for the
other set of data
are on the other
side of the stem.
Compare Data
3 WEATHER The average monthly
temperatures for Helena, Montana, and
Seattle, Washington, are shown. Which city
has more varied temperatures? Explain.
The data for Helena are spread out, while
the data for Seattle are clustered. So,
Helena has the more varied temperatures.
Average Monthly Temperatures
Seattle, WA Stem Helena, MT
2
016
3
24
76421
4
35
640
5
35
6511
6
279
1 |6 = 61°
4 |5 = 45°
Use the test score data below.
e. Which class had higher test scores?
3rd Period Stem 7th Period
88322
7
3
763100
12566899
8
32110
022333356
9
7 |3 = 73%
8 |7 = 78%
Explain.
f. Which class had more varied test
scores? Explain.
Example 1
(pp. 612–613)
Display each set of data in a stem-and-leaf plot.
1.
Average Life Span
Animal
Years
Animal
Years
Asian Elephant
40
African Elephant
35
Horse
20
Red Fox
Moose
12
Cow
Animal
Years
Lion
7
15
Chipmunk
15
6
Hippopotamus
41
Source: The World Almanac
2.
Summer Paralympic Games Participating Countries
Year
‘60
‘64
‘68
‘72
‘76
‘80
‘84
‘88
‘92
‘96
‘00
‘04
Countries
23
22
29
44
42
42
42
61
82
103
128
136
Source: International Paralympic Committee
Example 2
(p. 613)
SCHOOL For Exercises 3–5, use the test score data
shown at the right.
3. Find the lowest and highest scores.
4. What is the median score?
5. Write a statement that describes the data.
Example 3
(p. 614)
FOOD For Exercises 6 and 7, use the food data
shown in the back-to-back stem-and-leaf plot.
6. What is the greatest number of fat grams in
each sandwich?
7. In general, which type of sandwich has a lower
amount of fat? Explain.
614
Chapter 11 Statistics
Stem
5
6
7
8
9
Test Scores
Leaf
09
4578
044556788
233578
01559
5 |9 = 59%
Fat (g) of Various Burgers
and Chicken Sandwiches
Chicken
8
985533
0
8 |0 = 8 g
Burgers
0
1
2
3
059
06
036
2 |6 = 26 g
HOMEWORK
HELP
Display each set of data in a stem-and-leaf plot.
8.
For
Exercises
See
Examples
8–9
1
State
Number
10–15
16–19
2
3
California
Florida
Illinois
Michigan
New York
Ohio
Pennsylvania
Texas
53
25
19
15
29
18
19
32
State Representatives
Largest States
9.
2005–2006 Big 12
Women’s Softball
University
Baylor
Iowa State
Kansas
Missouri
Nebraska
Oklahoma
Oklahoma State
Texas
Texas A&M
Source: The World Almanac
Wins
38
23
36
26
44
40
21
55
34
Texas Tech
19
Source: Big 12 Sports
ANALYZE TABLES For Exercises 10–15,
use the table shown.
10. What is the mean number of home
runs hit by a single season home
run leader?
11. Display the number of home runs
in a stem-and-leaf plot.
12. What is the most home runs hit
between 1994 and 2005?
13. How many of the season leaders hit
fewer than 50 home runs?
14. What is the median number of home
runs hit by a single season home
run leader?
Real-World Link
The Louisiana Tech
women’s basketball
team has the bestwinning percentage
in Division I. Over a
31-year period, the
team has 873 wins
and 149 losses.
Source: NCAA
15. Write a sentence that describes
National League Single Season
Home Run Leaders, 1994–2005
Year
Player
Home Runs
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
Matt Williams
Dante Bichette
Andres Galarraga
Larry Walker
Mark McGwire
Mark McGwire
Sammy Sosa
Barry Bonds
Sammy Sosa
Jim Thome
Adrian Beltre
Andruw Jones
Ryan Howard
43
40
47
49
70
65
50
73
49
47
48
51
58
Source: Major League Baseball
the data.
ANALYZE TABLES For Exercises 16–19,
use the information shown in the
back-to-back stem-and-leaf plot.
16. What is the greatest number of games
won by a Big Ten Conference team?
NCAA Women’s Basketball Statistics
Overall Games Won, 2006–2007 Big Ten Conference Stem Big East Conference
87776632
0
233346899
543
1
0001226
3 |1 = 13
1 |0 = 10
17. What is the least number of games
won by a Big East Conference team?
EXTRA PRACTICE
See pages 698, 710.
18. How many teams are in the Big
East Conference?
19. Compare the median number of games won by each conference.
Lesson 11-7 Stem-and-Leaf Plots
615
H.O.T. Problems
20. COLLECT THE DATA Display the foot lengths, in inches, of the students in your
class in a stem-and-leaf plot. Then write a few sentences that analyze the data.
21. CHALLENGE Create a stem-and-leaf plot of at least 10 pieces of data in which
the maximum value is 70, the range is 50, and the median is 25.
WR ITING IN MATH Data about the ages of U.S. Presidents on their
22.
inauguration can be displayed in both a histogram and in a stem-and-leaf
plot. Discuss the advantages and disadvantages of using each display.
23. The back-to-back stem-and-leaf plot shows the amount of protein in certain foods.
Amount of Protein (g)
Dairy Products Stem Legumes, Nuts, Seeds
98877622
0
569
0
458
1
6
2
3
9
6 |2 = 26 grams
3 |9 = 39 grams
Which of the following is a true statement?
A The median amount of protein in
dairy products is 9 grams.
B The difference between the greatest
and least amount of protein in dairy
products is 28 grams.
C The average amount of protein in
legumes, nuts, and seeds is more than
the average amount in dairy products.
D The greatest amount of protein in
legumes, nuts, and seeds is 93 grams.
Draw a box-and-whisker plot for each set of data.
24. 22, 25, 36, 42, 33, 76, 45, 53, 44, 36, 37, 29
(Lesson 11-6)
25. 61, 67, 76, 72, 56, 53, 61, 24, 58, 74, 61, 68
RIVERS For Exercises 26–28, use the table at the right.
26. Determine the measures of variation for the data.
(Lesson 11-5)
Major U.S. Rivers
River
Length (mi)
27. Find any outliers of the data.
Arkansas
1,459
28. Use the measures of variation to describe the data.
Colorado
1,450
Columbia
1,243
Mississippi
2,348
Ohio
Rio Grande
981
1,900
Source: The World Almanac
PREREQUISITE SKILL Find the mean and median for each set of data.
29. 75, 66, 67, 85, 86, 74, 74, 62, 72
30. 20, 28, 21, 16, 16, 15, 20, 21, 56, 17, 16, 18
616
Chapter 11 Statistics
(Lesson 11-4)