Chapter 12
Resource Masters
Consumable Workbooks
Many of the worksheets contained in the Chapter Resource Masters booklets are
available as consumable workbooks in both English and Spanish.
Study Guide and Intervention Workbook
0-07-827794-9
Study Guide and Intervention Workbook (Spanish)
0-07-827795-7
Skills Practice Workbook
0-07-827788-4
Skills Practice Workbook (Spanish)
0-07-827790-6
Practice Workbook
0-07-827789-2
Practice Workbook (Spanish)
0-07-827791-4
Answers for Workbooks The answers for Chapter 12 of these workbooks
can be found in the back of this Chapter Resource Masters booklet.
Spanish Assessment Masters Spanish versions of forms 2A and 2C
of the Chapter 12 Test are available in the Pre-Algebra Spanish Assessment
Masters (0-07-830412-1).
Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.
Printed in the United States of America. Permission is granted to reproduce the
material contained herein on the condition that such material be reproduced only
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and be used solely in conjunction with Glencoe Pre-Algebra. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher.
Send all inquiries to:
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ISBN: 0-07-827778-7
1 2 3 4 5 6 7 8 9 10 047 11 10 09 08 07 06 05 04 03 02
Pre-Algebra Chapter 12 Resource Masters
CONTENTS
Vocabulary Builder............................vii
Lesson 12-7
Lesson 12-1
Study Guide and Intervention ........................697
Skills Practice.................................................698
Practice ..........................................................699
Reading to Learn Mathematics ......................700
Enrichment .....................................................701
Study Guide and Intervention ........................667
Skills Practice.................................................668
Practice ..........................................................669
Reading to Learn Mathematics ......................670
Enrichment .....................................................671
Lesson 12-2
Study Guide and Intervention ........................672
Skills Practice.................................................673
Practice ..........................................................674
Reading to Learn Mathematics ......................675
Enrichment .....................................................676
Lesson 12-3
Study Guide and Intervention ........................677
Skills Practice.................................................678
Practice ..........................................................679
Reading to Learn Mathematics ......................680
Enrichment .....................................................681
Lesson 12-4
Study Guide and Intervention ........................682
Skills Practice.................................................683
Practice ..........................................................684
Reading to Learn Mathematics ......................685
Enrichment .....................................................686
Lesson 12-5
Study Guide and Intervention ........................687
Skills Practice.................................................688
Practice ..........................................................689
Reading to Learn Mathematics ......................690
Enrichment .....................................................691
Lesson 12-8
Study Guide and Intervention ........................702
Skills Practice.................................................703
Practice ..........................................................704
Reading to Learn Mathematics ......................705
Enrichment .....................................................706
Lesson 12-9
Study Guide and Intervention ........................707
Skills Practice.................................................708
Practice ..........................................................709
Reading to Learn Mathematics ......................710
Enrichment .....................................................711
Chapter 12 Assessment
Chapter 12 Test, Form 1 ........................713–714
Chapter 12 Test, Form 2A ......................715–716
Chapter 12 Test, Form 2B ......................717–718
Chapter 12 Test, Form 2C......................719–720
Chapter 12 Test, Form 2D......................721–722
Chapter 12 Test, Form 3 ........................723–724
Chapter 12 Open-Ended Assessment ...........725
Chapter 12 Vocabulary Test/Review ..............726
Chapter 12 Quizzes 1 & 2..............................727
Chapter 12 Quizzes 3 & 4..............................728
Chapter 12 Mid-Chapter Test.........................729
Chapter 12 Cumulative Review .....................730
Chapter 12 Standardized
Test Practice...........................................731–732
Lesson 12-6
Study Guide and Intervention ........................692
Skills Practice.................................................693
Practice ..........................................................694
Reading to Learn Mathematics ......................695
Enrichment .....................................................696
Standardized Test Practice Student
Recording Sheet ..............................................A1
ANSWERS ................................................A2–A34
iii
Teacher’s Guide to Using the
Chapter 12 Resource Masters
The Fast File Chapter Resource system allows you to conveniently file the resources you
use most often. The Chapter 12 Resource Masters includes the core materials needed for
Chapter 12. These materials include worksheets, extensions, and assessment options. The
answers for these pages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing and printing in the
Pre-Algebra TeacherWorks CD-ROM.
Vocabulary Builder
Pages vii-viii
include a student study tool that presents
up to twenty of the key vocabulary terms
from the chapter. Students are to record
definitions and/or examples for each term.
You may suggest that students highlight
or star the terms with which they are
not familiar.
When to Use Give these pages to students
before beginning Lesson 12-1. Encourage them
to add these pages to their Pre-Algebra Study
Notebook. Remind them to add definitions and
examples as they complete each lesson.
Study Guide and Intervention
Each lesson in Pre-Algebra addresses one or
two objectives. There is one Study Guide and
Intervention master for each lesson.
When to Use Use these masters as reteaching activities for students who need additional reinforcement. These pages can also
be used in conjunction with the Student
Edition as an instructional tool for students
who have been absent.
Skills Practice There is one master for
each lesson. These provide computational
practice at a basic level.
When to Use These masters can be used
with students who have weaker mathematics
backgrounds or need additional reinforcement.
Practice
There is one master for each
lesson. These problems more closely follow
the structure of the Practice and Apply
section of the Student Edition exercises.
These exercises are of average difficulty.
When to Use These provide additional
practice options or may be used as homework for second day teaching of the lesson.
Reading to Learn Mathematics
One master is included for each lesson. The
first section of each master asks questions
about the opening paragraph of the lesson in
the Student Edition. Additional questions
ask students to interpret the context of and
relationships among terms in the lesson.
Finally, students are asked to summarize
what they have learned using various representation techniques.
When to Use This master can be used as
a study tool when presenting the lesson or
as an informal reading assessment after
presenting the lesson. It is also a helpful
tool for ELL (English Language Learner)
students.
Enrichment
There is one extension
master for each lesson. These activities
may extend the concepts in the lesson, offer
an historical or multicultural look at the
concepts, or widen students’ perspectives
on the mathematics they are learning.
These are not written exclusively for honors
students, but are accessible for use with all
levels of students.
When to Use These may be used as extra
credit, short-term projects, or as activities
for days when class periods are shortened.
iv
Assessment Options
Intermediate Assessment
• Four free-response quizzes are included
to offer assessment at appropriate intervals in the chapter.
• A Mid-Chapter Test provides an option
to assess the first half of the chapter. It is
composed of both multiple-choice and
free-response questions.
The assessment masters in the Chapter 12
Resource Masters offer a wide range of
assessment tools for intermediate and final
assessment. The following lists describe each
assessment master and its intended use.
Chapter Assessment
Continuing Assessment
Chapter Tests
• Form 1 contains multiple-choice questions
and is intended for use with basic level
students.
• Forms 2A and 2B contain multiple-choice
questions aimed at the average level
student. These tests are similar in format
to offer comparable testing situations.
• Forms 2C and 2D are composed of freeresponse questions aimed at the average
level student. These tests are similar in
format to offer comparable testing situations. Grids with axes are provided for
questions assessing graphing skills.
• Form 3 is an advanced level test with
free-response questions. Grids without
axes are provided for questions assessing
graphing skills.
• The Cumulative Review provides
students an opportunity to reinforce and
retain skills as they proceed through
their study of Pre-Algebra. It can also
be used as a test. This master includes
free-response questions.
• The Standardized Test Practice offers
continuing review of pre-algebra concepts
in various formats, which may appear on
the standardized tests that they may
encounter. This practice includes multiplechoice, grid-in, and open-ended questions.
Bubble-in and grid-in answer sections are
provided on the master.
Answers
• Page A1 is an answer sheet for the
Standardized Test Practice questions
that appear in the Student Edition on
pages 664–665. This improves students’
familiarity with the answer formats they
may encounter in test taking.
• The answers for the lesson-by-lesson
masters are provided as reduced pages
with answers appearing in red.
• Full-size answer keys are provided for the
assessment masters in this booklet.
All of the above tests include a freeresponse Bonus question.
• The Open-Ended Assessment includes
performance assessment tasks that are
suitable for all students. A scoring rubric is
included for evaluation guidelines. Sample
answers are provided for assessment.
• A Vocabulary Test, suitable for all students, includes a list of the vocabulary
words in the chapter and ten questions
assessing students’ knowledge of those
terms. This can also be used in conjunction with one of the chapter tests or as a
review worksheet.
v
NAME ______________________________________________ DATE ____________ PERIOD _____
12
Reading to Learn Mathematics
This is an alphabetical list of key vocabulary terms you will learn in Chapter 12.
As you study this chapter, complete each term’s definition or description.
Remember to add the page number where you found the term. Add these pages to
your Pre-Algebra Study Notebook to review vocabulary at the end of the chapter.
Vocabulary
Term
Found
on Page
Definition/Description/Example
back-to-back stemand-leaf plot
box-and-whisker plot
combination
compound events
dependent events
factorial
fak-TOHR-ee-uhl
Fundamental
Counting Principle
histogram
independent events
vii
Vocabulary Builder
Vocabulary Builder
NAME ______________________________________________ DATE ____________ PERIOD _____
12
Reading to Learn Mathematics
Vocabulary Builder
Vocabulary
Term
Found
on Page
(continued)
Definition/Description/Example
interquartile range
IN-tuhr-KWAWR-tyl
measures of
variation
mutually exclusive
events
odds
outliers
permutation
PUHR-myoo-TAY-shuhn
quartiles
range
stem-and-leaf plot
tree diagram
upper and lower
quartiles
viii
NAME ______________________________________________ DATE
____________ PERIOD _____
12-1 Study Guide and Intervention
Stem-and-Leaf Plots
Words One way to organize and display data is to use a stem-and-leaf plot.
In a stem-and-leaf plot, numerical data are listed in ascending or
descending order.
Model
The next greatest
place value forms
the leaves.
The greatest place
value of the data is
used for the stems.
Example
ZOOS Display the data shown at the
right in a stem-and-leaf plot.
Stem
Leaf
Step 1 The least and the greatest
numbers are 55 and 95. The
5
8 5
greatest place value digit in
6
4
each number is in the tens.
7
5
Draw a vertical line and write
8
5 0 0
the stems from 5 to 9 to the left
of the line.
9
5 0 2
Step 2 Write the leaves to the right of
the line, with the corresponding
stem. For example, for 85, write
5 to the right of 8.
Step 3 Rearrange the leaves so they
are ordered from least to
greatest. Then include a key or
an explanation.
Stem
5
6
7
8
9
Exercises
Size of U. S. Zoos
Leaf
58
4
5
00 5
02 5
8 | 5 85 acres
Zoo
Size
(acres)
Audubon
(New Orleans)
58
Cincinnati
85
Dallas
95
Denver
80
Houston
55
Los Angeles
80
Oregon
64
St. Louis
90
San Francisco
75
Woodland
Park (Seattle)
92
Display each set of data in a stem-and-leaf plot.
1. {27, 35, 39, 27,
24, 33, 18, 19}
2. {94, 83, 88, 77,
95, 99, 88, 87}
ROLLER COASTERS For Exercises 3 and 4, use the
stem-and-leaf plot shown.
3. What is the speed of the fastest roller coaster?
The slowest? 100 mph; 83 mph
4. What is the median speed?
©
Glencoe/McGraw-Hill
92 mph
667
The Fastest Roller Coasters
Stem
8
9
10
Leaf
35
25
0
8 | 3 83 mph
Glencoe Pre-Algebra
Lesson 12-1
Stem-andLeaf Plot
NAME ______________________________________________ DATE
____________ PERIOD _____
12-1 Skills Practice
Stem-and-Leaf Plots
Display each set of data in a stem-and-leaf plot.
1. {7, 2, 3, 11, 20, 21,
17, 15, 15, 14}
2. {8, 2, 14, 27, 7, 2,
16, 13, 29, 16}
3.
4.
Amount of Fresh Fruit Consumed per
Person in the United States, 1998
Fruit
Pounds Consumed
per Person
Winning Scores in College Football
Bowl Games, 1999
Game and Winning School
Points
Scored
Apples
19
Aloha Bowl, Wake Forest
23
Bananas
29
Cotton Bowl, Texas
38
Cantaloupes
11
Fiesta Bowl, Tennessee
23
Grapefruit
6
Florida Citrus Bowl, Michigan
45
Grapes
7
Gator Bowl, Georgia Tech.
35
Oranges
15
Holiday Bowl, Kansas St.
24
Peaches and
nectarines
5
Liberty Bowl, So. Mississippi
23
Orange Bowl, Florida
31
Pears
3
Outback Bowl, Penn. St.
26
Pineapples
3
Peach Bowl, Mississippi St.
27
Plums and prunes
1
Rose Bowl, Wisconsin
38
Strawberries
4
Sugar Bowl, Ohio St.
24
Watermelons
15
Source: World Almanac
Source: U.S. Census Bureau
HUMIDITY For Exercises 5–7, use the information in the back-to-back
stem-and-leaf plot. Source: The New York Public Library Desk Reference
U.S. Average Relative Humidity (percent)
5. What is the highest morning relative humidity? 89%
6. What is the lowest afternoon relative humidity? 51%
7. Does relative humidity tend to be higher in the
morning or afternoon? morning
©
Glencoe/McGraw-Hill
668
Morning
5
6
88 4 7
94 0 8
8 | 7 78%
Afternoon
1 23 47 9
5 | 3 53%
Glencoe Pre-Algebra
NAME ______________________________________________ DATE
____________ PERIOD _____
12-1 Practice
Stem-and-Leaf Plots
Display each set of data in a stem-and-leaf plot.
1. {68, 63, 70, 59,
78, 64, 68, 73,
61, 66, 70}
4.
Major League Baseball
Leading Pitchers, 2000
Player and Team
Average Prices Received by
U.S. Farmers, 1999
Price
(dollars per
100 pounds)
Wins
Commodity
T. Glavine, Atlanta
21
T. Hudson, Oakland
20
Beef Cattle
63
R. Johnson, Arizona
19
Hogs
30
D. Kile, St. Louis
20
Lambs
75
G. Maddux, Atlanta
19
Milk
15
P. Martinez, Boston
18
Sheep
31
C. Park, Los Angeles
18
Veal Calves
88
A. Pettite, New York Y.
19
A. Sele, Seattle
17
D. Wells, Toronto
20
Source: World Almanac
Source: World Almanac
RECREATION For Exercises 5–7, use the information
in the back-to-back stem-and-leaf plot
shown at the right.
Total U.S. Spending on Personal Recreation (by Category)
5. The category with the lowest total expenditure
in 1992 was motion pictures. What was its
total? $5 billion
1992
7 5 5
8 7 2 0
7 2
4 0
6. What is the median total recreational spending
for 1992? For 1998? $17.5 billion; $26 billion
1
7. Compare the total spending on recreation in
1992 with that in 1998. In general, spend-
ing on recreation increases between
1992 and 1998.
©
Glencoe/McGraw-Hill
669
7 | 2 $27 billion
1998
0 7 8 9
1 5 7
2 4 8
3 2
4 7
5 6 8
6
7
8
9 3
2 | 4 $24 billion
Glencoe Pre-Algebra
Lesson 12-1
3.
2. {27, 32, 42, 31, 36,
37, 47, 23, 39,
31, 41, 38, 30,
34, 29, 42, 37}
NAME ______________________________________________ DATE
____________ PERIOD _____
12-1 Reading to Learn Mathematics
Stem-and-Leaf Plots
Pre-Activity
How can stem-and-leaf plots help you understand an election?
Do the activity at the top of page 606 in your textbook. Write
your answers below.
a. Is there an equal number of electors in each group? Explain.
Sample answer: Even though the intervals are the same,
the data are not distributed evenly as the number of
pieces of data in each interval are not the same.
b. Name an advantage of displaying the data in groups.
Sample answer: You can see how the data are distributed.
Reading the Lesson 1–4. See students’ work.
Write a definition and give an example of each new vocabulary word or phrase.
Vocabulary
Definition
Example
1. stem-andleaf plot
2. stems
3. leaves
4. back-toback stemand-leaf plot
Helping You Remember
5. How will you remember
which numbers of a stemand-leaf plot represent
the greater place value?
Using the data at right,
draw a back-to-back
stem-and-leaf plot to look
like actual leaves on
stems. Then to read the
data, start from the tree
trunk and move outward.
©
Glencoe/McGraw-Hill
Ages of Persons
Apartment
Building A
Apartment
Building B
33, 16, 19,
39, 21, 20,
1,
26, 23, 11,
10, 21, 36, 37,
34, 24, 37,
32, 22, 11,
17, 29
10,
2,
1, 32, 38,
12, 36, 39
670
Glencoe Pre-Algebra
NAME ______________________________________________ DATE
____________ PERIOD _____
12-1 Enrichment
Statistical Graphs
Bar graphs and pictographs are used to compare quantities. Line graphs are used to show
changes. Circle graphs compare parts to parts, or parts to the whole.
Solve. Use the pictograph.
English
Hindi
Arabic
Portuguese
Chinese
Russian
Spanish
French
Bengali
A
A
A
A
A
A
A
A
A
1. How many people speak Portuguese?
AAA
AB
B
B
AAAAAAB
AB
AB
150,000,000
2. What is the ratio of people who speak
Spanish to those who speak Russian?
1:1
3. What three languages are each spoken
by about 150 million people? Arabic,
Portuguese, Bengali
4. How many fewer people speak Arabic
than Hindi? 100,000,000
B
A = 100 million
Australia
0.3%
Solve. Use the circle graph.
5. Which continent has the smallest
population? Australia
Europe
15.1%
North Am.
8.3%
6. How does the population of South
America compare to that of Africa?
South Am.
5.5%
South America has about half
as many people.
7. What is the population of Australia if
the world’s population is about 6 billion?
about 18,000,000
Africa
10.9%
Asia
59.7%
Population
by Continent
Solve. Use the line graph.
8. During which ten-year period was the
increase in the price of eggs greatest?
Price Received by Farmers
for One Dozen Eggs
1940–1950
70¢
9. What was the price of a dozen eggs
in 1940? 16¢
60¢
50¢
10. What was the percent of increase in
the price of eggs from 1940 to 1950?
40¢
30¢
about 220–240%
20¢
10¢
11. What was the increase in cents from
1930 to 1980? about 32¢
0¢
1940 1960 1980 2000
1930 1950 1970 1990
©
Glencoe/McGraw-Hill
671
Glencoe Pre-Algebra
Lesson 12-1
Principal Languages of the World
(to nearest fifty million)
NAME ______________________________________________ DATE
____________ PERIOD _____
12-2 Study Guide and Intervention
Measures of Variation
The range and the interquartile range describe how a set of data varies.
Measures of Variation
Term
Definition
range
The difference between the greatest and the
least values of the set
median
The value that separates the data set in half
lower quartile
The median of the lower half of a set of data
upper quartile
The median of the upper half of a set of data
interquartile range
The difference between the upper quartile
and the lower quartile
Example
Find the range and interquartile range for each set of data.
a. {3, 12, 17, 2, 21, 14, 14, 8}
b. Stem
2
3
4
5
Step 1 List the data from least to
greatest. The range is 21 – 2
or 19. Then find the median.
2
3
8 12 14 14 17 21
median
14
2
12 or 13
The stem-and-leaf plot displays the data in
order. The greatest value is 56. The least
value is 22. So, the range is 56 – 22 or 34.
Step 2 Find the upper and lower
quartiles.
2
LQ
3
The median is 42. The LQ is 31 and the UQ
is 48. So, the interquartile range is 48 – 31
or 17.
8 12 14 14 17 21
3
8 median
2
or 5.5
UQ
Leaf
2 6 9
1 1 34 9
0 2 55 7 78
3 4 66
3 | 4 34
14
17
2
or 15.5
The interquartile range is 15.5 – 5.5 or 10.
Exercises
WEATHER For Exercises 1 and 2, use the data in the stem-and-leaf plot at the right.
1. Find the range, median, upper quartile,
lower quartile, and the interquartile
range for each set of data. July lows:
Average Extreme July Temperatures in World Cities
Low Temps.
range: 30°F; median: 73; UQ: 76;
LQ: 59; interquartile range: 17°F;
July highs: range: 43°F; median: 83;
UQ: 91; LQ: 79; interquartile range: 12°F
9 1 1 0
4
9 8 6 5 5 4 3 0 0
0
2. Write a sentence that compares the data.
July highs vary more widely than
July lows.
©
Glencoe/McGraw-Hill
0 | 8 80°F
672
High Temps.
5
6
7
8
9
10
4 7 9
9
1 1 3 3 4 8
0 1 2 5
7
7 | 9 79°F
Glencoe Pre-Algebra
NAME ______________________________________________ DATE
____________ PERIOD _____
12-2 Skills Practice
Measures of Variation
Find the range and interquartile range for each set of data.
1. {7, 9, 21, 8, 13, 19}
2. {33, 34, 27, 40, 38, 35}
14; 11
13; 5
3. {37, 29, 42, 33, 31, 36, 40}
4. {87, 72, 104, 94, 85, 71, 80, 98}
13; 9
33; 20
5. {92, 89, 124, 114, 98, 118, 115, 106, 101, 109}
6. {6.7, 3.4, 3.8, 4.2, 5.1, 5.8, 6.0, 4.5}
35; 17
3.3; 1.9
7. {4.3, 1.9, 6.3, 5.1, 2.1, 1.6, 2.4, 5.6, 5.9, 3.5}
8. {127, 58, 49, 101, 104, 98, 132, 111}
9. Stem
1
2
3
12. Stem
0
1
2
3
4
Leaf
00 3 8 9
05
12 4
2 | 0 20
83; 41
10. Stem
24; 18
7
8
9
Leaf
13. Stem
6
1133 79
7
2678 99
8
0122 45 79 99
9
2467 8
42;
16
013
2 | 0 20
Leaf
89
137
356
9 | 3 93
Leaf
0 6
1
4 99
1 37778
8 | 4 84
11. Stem
0
1
2
3
18; 14
14. Stem
4
5
6
7
38; 19.5
HEALTH For Exercises 15–17, use the data
Activity
15. What is the range of the data?
16. What is the interquartile range of the data?
285 Calories
17. Which activity burns the most calories per
hour? The least calories per hour?
running; yoga
32; 22
Leaf
8
1 2 4 7 7
0 2 5
4
6 | 2 62
26; 10
Estimated Calories Burned
in the table showing the calories burned by
a 125-pound person.
420 Calories
Leaf
236 8 9
225
6
234
1 | 5 15
Calories Burned
per Hour
Basketball
480
Bicycling
600
Hiking
360
Mowing the Lawn
270
Running
660
Soccer
420
Swimming
600
Weight Training
360
Yoga
240
Source: www.fitresource.com
©
Glencoe/McGraw-Hill
673
Glencoe Pre-Algebra
Lesson 12-2
4.7; 3.5
NAME ______________________________________________ DATE
____________ PERIOD _____
12-2 Practice
Measures of Variation
Find the range and interquartile range for each set of data.
1. {3, 9, 11, 8, 6, 12, 5, 4}
2. {8, 3, 9, 14, 12, 11, 20, 23, 5, 26}
9; 5.5
18; 12
3. {42, 50, 46, 47, 38, 41}
4. {10.3, 9.8, 10.1, 16.2, 18.0, 11.4, 16.0, 15.8}
12; 6
8.2; 5.9
5. {107, 82, 93, 112, 120, 95, 98, 86, 109, 110} 6. {106, 103, 112, 109, 115, 118, 113, 108}
38; 17
7. Stem
1
2
3
10. Stem
6
7
8
9
15; 7
13;
Leaf
78
23 56 8
0
19 | 2 192
7
Leaf
31;
47 9
9
11 33 46
01 25
7 | 9 79
11
8. Stem
5
6
7
11. Stem
3
4
5
6
7
8
21;
Leaf
6 7
0 114 88 9
0 235 67
6 | 1 61
Leaf
01 6 8
4
2
15. Where does the city with the
fastest growth rate fall in terms
of population? The city with the
slowest growth rate? near the
median; at the LQ
4
5
6
7
59; 39.5
12. Stem
4
5
6
7
8
9
39;
Leaf
000 25 7
26
188
019
5 | 2 52
26
Leaf
52;
335 7 9
001
2
446 8
42
011 2 25
5 | 1 51
Populations of the World’s Largest Cities
2000
13. What is the range of populations
shown? 13.8 million
1.3%
9. Stem
33
9
5 | 2 52
POPULATION For Exercises 13–15,
use the data in the table at the
right.
14. What is the interquartile range
for the annual growth rate?
12
City
Population
(millions)
Annual
Growth
Rate (%)
Tokyo, Japan
26.4
0.51
Mexico City, Mexico
18.1
1.81
Mumbai, India
18.1
3.54
Sao Paulo, Brazil
17.8
1.43
New York City, U.S.
16.6
0.37
Lagos, Nigeria
13.4
5.33
Los Angeles, U.S.
13.1
1.15
Calcutta, India
12.9
1.60
Shanghai, China
12.9
0.35
Buenos Aires, Argentina
12.6
1.14
Source: World Almanac
©
Glencoe/McGraw-Hill
674
Glencoe Pre-Algebra
NAME ______________________________________________ DATE
____________ PERIOD _____
12-2 Reading to Learn Mathematics
Measures of Variation
Pre-Activity
Why are measures of variation important in interpreting data?
Do the activity at the top of page 612 in your textbook. Write
your answers below.
a. What is the fastest speed? 173 mph
b. What is the slowest speed?
142 mph
c. Find the difference between these two speeds.
31 mph
d. Write a sentence comparing the fastest winning average speed and
the slowest winning average speed. The fastest winning
average speed and the slowest winning average speed
are within 31 miles per hour of each other.
Write a definition and give an example of each new vocabulary word or phrase.
Vocabulary
Definition
Example
1. measures
of variation
2. range
3. quartiles
4. lower
quartile
5. upper
quartile
6. interquartile
range
Helping You Remember
7. Complete the following
diagram by filling in the
boxes with the appropriate
vocabulary words.
©
Glencoe/McGraw-Hill
Diagram Title:
675
1 2
4 6
6 7
9 11 16 17 17 20 21 21 30
Glencoe Pre-Algebra
Lesson 12-2
Reading the Lesson 1–6. See students’ work.
NAME ______________________________________________ DATE
____________ PERIOD _____
12-2 Enrichment
Variance
Another way to measure the variation of a set of data is by
computing the variance. The higher the variance is for a group
of numbers, the more “spread out” the data will be.
The table below shows the price of the stock for two companies
during one week.
Monday Tuesday Wednesday Thursday
Friday
Acme Computer Systems
$10
$7
$3
$8
$12
Baker Pencil Company
$7
$8
$7
$9
$9
1. What is the mean average price for the week for each company?
$8 for both companies
Computing the variance will show which company’s stock has the
greater variation. To compute the variance, follow these steps:
Step 1
Subtract the mean from each number in the set.
Step 2
Multiply each difference in step 1 by itself.
Step 3
Add these differences.
Step 4
Divide the total by the number of members of the set.
Example
Find the variance for Acme Computer Systems.
(10 8) (10 8) (7 8) (7 8) (3 8) (3 8) (8 8) (8 8) (12 8) (12 8)
4
1
25
0
16
46
The variance is 46 5, or 9.2.
Solve.
2. Do you think the variance for Baker
Pencil Company will be higher than the
variance for Acme Computer Systems?
Why? Compute the variance for Baker
Pencil Company to see whether you are
correct. No; the prices are closer
3. Consolidated Airlines also had an
average price last week of $8 per share,
but its variance was 10.8. Indicate five
stock prices that could produce this
variance. (Hint: Change only the
Monday and Tuesday prices for Acme.)
4. Sleepy Mattress Company’s stock had an
average price last week of $8 per share
and a variance of 0. What was the price
of shares each day last week?
5. Are there any values that the variance
cannot equal? If so, what are these
values? yes; values less than zero
Answers may vary. Sample
answer: $11, $6, $3, $8, $12
together; 0.8
$8 each day
©
Glencoe/McGraw-Hill
676
Glencoe Pre-Algebra
NAME ______________________________________________ DATE
____________ PERIOD _____
12-3 Study Guide and Intervention
Box-and-Whisker Plots
Words
Box-andWhisker
Plot
A box and whisker plot divides a set of data into four parts using
the median and quartiles. Each of these parts contains 25% of
the data.
Model
LQ
median
UQ
upper extreme,
or greatest value
lower extreme,
or least value
Example
FOOD The heat levels of popular chile peppers are shown in the
table. Display the data in a box-and-whisker plot.
Heat Level of Chile Peppers
Name
0
50,000
25,000
100,000
150,000
200,000
250,000
75,000
125,000
175,000
225,000
Step 2 Mark the median, the extremes, and the quartiles.
Mark these points above the number line.
lower extreme: 0
LQ: 4000
upper extreme: 210,000
median: 12,500
UQ: 75,000
0
50,000
25,000
75,000
100,000
150,000
200,000
250,000
125,000
175,000
225,000
Step 3 Draw a box and the whiskers.
Heat Level*
Aji escabeche
17,000
Bell
0
Cayenne
8,000
Habañero
210,000
Jalapeño
25,000
Mulato
1,000
New Mexico
4,500
Pasilla
5,500
Serrano
4,000
Tabasco
120,000
Tepín
75,000
Thai hot
60,000
Source: Chile Pepper Institute
*Scoville heat units
0
50,000
25,000
75,000
100,000
150,000
200,000
250,000
125,000
175,000
225,000
Exercises
Draw a box-and-whisker plot for each set of data.
1. {17, 5, 28, 33, 25, 5, 12, 3, 16, 11, 22, 31, 9, 11}
2. {$21, $50, $78, $13, $45, $5, $12, $37, $61, $11, $77, $31, $19, $11, $29, $16}
©
Glencoe/McGraw-Hill
677
Glencoe Pre-Algebra
Lesson 12-3
Step 1 Find the least and greatest number. Then draw
a number line that covers the range of the data.
NAME ______________________________________________ DATE
____________ PERIOD _____
12-3 Skills Practice
Box-and-Whisker Plots
Draw a box-and-whisker plot for each set of data.
1. {6, 9, 22, 17, 14, 11, 18, 28,
19, 21, 16, 15, 12, 3}
2. {$45, $37, $50, $53, $61, $95, $46,
$40, $48,$62}
3. {14, 9, 1, 16, 20, 17, 18, 11, 15}
4. {$20, $35, $42, $26, $53, $18, $36, $27,
$21, $32}
5. {97, 83, 100, 99, 102, 104, 97, 101,
115, 106, 94, 108, 102, 100, 109,
103, 102, 98, 108}
6. {188, 203, 190, 212, 214, 217, 174, 220,
219, 211, 201, 210, 214, 217, 213, 204,
187, 206, 210}
7.
8.
Goals Scored by MLS Leading
Scorers, 2000
Number of 300 Games per
Person in Women’s International
Bowling Congress
26
15
12
16
15
1
12
17
23
18
11
10
21
17
23
16
15
5
14
21
12
16
13
9
17
19
24
18
27
13
14
20
12
16
12
16
Source: World Almanac
Source: World Almanac
©
Glencoe/McGraw-Hill
678
Glencoe Pre-Algebra
NAME ______________________________________________ DATE
____________ PERIOD _____
12-3 Practice
Box-and-Whisker Plots
Draw a box-and-whisker plot for each set of data.
1. {14, 30, 35, 8, 29, 28, 31, 42,
20, 36, 32}
2. {$105, $98, $83, $127, $115, $114,
$132, $93, $107, $101, $119}
3. {211, 229, 196, 230, 240, 212, 231, 233,
243, 214, 239, 238, 228, 237, 230, 234,
239, 240, 212, 232, 239, 240, 237}
4. {3.7, 6.2, 4.1, 2.4, 1.0, 1.5, 1.4, 2.1,
2.6, 3.0, 1.3, 1.7}
For Exercises 5–7, use the box-and-whisker plot shown.
5. How tall is the highest peak
of the Hindu Kush? about 25,200 ft
Major Peaks of the Hindu Kush
(height in feet)
6. What is the median height of the
major peaks? about 23,200 ft
19,000 20,000 21,000 22,000 23,000 24,000 25,000 26,000
Lesson 12-3
Source: www.peakware.com
7. Write a sentence describing what the
box-and-whisker plot tells about the major peaks of the Hindu Kush.
Sample answers: About 75% of the peaks are taller than 22,300 ft;
most peaks are between 22,300 and 24,300 ft tall.
For Exercises 8–10, use the box-and-whisker plot shown.
8. In which year was the corn yield more
varied? Explain. 1999; The range
and the interquartile range
are greater in 1999 than in 1997.
9. How does the median yield in 1999
compare with the median yield in 1997?
The median yield is seven
bushels per acre greater in 1999
than in 1997.
Corn Yield by State
(bushels per acre)
1997
1999
70
80
90
100
110
120
130
140
150
Source: U.S. Census Bureau
10. Write a few sentences that compare the 1997 yields with the 1999 yields.
Sample answer: Yields are slightly higher in 1999 than in 1997. For
example, 50% of the 1997 yields are between 122 and 146 bushels per
acre, and 50% of the 1999 yields are between 129 and 150 bushels per
acre. Both the range and the interquartile range are greater in 1999 than
in 1997, meaning 1999 yields are more varied.
©
Glencoe/McGraw-Hill
679
Glencoe Pre-Algebra
NAME ______________________________________________ DATE
12-3
____________ PERIOD _____
Reading to Learn Mathematics
Box-and-Whisker Plots
How can box-and-whisker plots help you interpret data?
Pre-Activity
Do the activity at the top of page 617 in your textbook. Write
your answers below.
a. Find the low, high, and the median temperature, and the upper and
lower quartile for each city.
Tampa, FL
Caribou, ME
Low
LQ
60
64.5
73
81
82
20
40.5
57.5
66
9
Median
UQ
High
b. Draw a number line extending from 0 to 85. Label every 5 units.
c. About one-half inch above the number line, plot the data found in
part a for Tampa. About three-fourths inch above the number line,
plot the data for Caribou.
d. Write a few sentences comparing the average monthly temperatures.
Sample answer: The average monthly temperatures vary
greatly in Caribou, ME, whereas the average monthly temperatures in Tampa, FL, are more consistent.
Reading the Lesson
Write a definition and give an example for the new vocabulary phrase.
1.
Vocabulary
Definition
Example
box-andwhisker plot
See students’ work.
Helping You Remember
2. Complete the following concept map of how to make a box-and-whisker plot.
Step 1
Find the least number and
the greatest number out of
the set of data. These are the
. Then
draw a
covers the
©
that
of data.
Glencoe/McGraw-Hill
Step 3
Draw a box by marking vertical lines through
Step 2
Find the
,
the
and the upper and
,
the points above the
, the
and the
lower
.
Mark these points
above the number line.
680
.
Draw whiskers extending from each
to the
data points.
Glencoe Pre-Algebra
NAME ______________________________________________ DATE
____________ PERIOD _____
12-3 Enrichment
Mental Math: Compensation
To add or subtract in your head, work with multiples of 10 (20, 30, 40, . . .) or
100 (200, 300, 400, . . .) and then adjust your answer.
To add 52, first add 50, then add 2 more.
To subtract 74, first subtract 70, then subtract 4 more.
To subtract 38, first subtract 40, then add 2.
To add 296, first add 300, then subtract 4.
Write the second step you would use to do each of the following.
1. Add 83.
2. Add 304.
3. Subtract 62.
1) Add 80.
1) Add 300.
1) Subtract 60.
2) Add 3 more.
2) Add 4 more.
2) Subtract 2 more.
4. Add 27.
5. Subtract 79.
6. Subtract 103.
1) Add 30.
1) Subtract 80.
1) Subtract 100.
2) Subtract 3.
2) Add 1.
2) Subtract 3 more.
7. Add 499.
8. Add 294.
9. Subtract 590.
1) Add 300.
1) Subtract 600.
2) Subtract 1.
2) Subtract 6.
2) Add 10.
Lesson 12-3
1) Add 500.
Use the method above to add 59 to each of the following.
10. 40
11. 72
40 60 1 99
12. 53
72 60 1 131
13. 15
53 60 1 112
15 60 1 74
Use the method above to subtract 18 from each of the following.
14. 96
15. 45
96 20 2 78
16. 71
45 20 2 27
17. 67
71 20 2 53
©
Glencoe/McGraw-Hill
67 20 2 49
681
Glencoe Pre-Algebra
NAME ______________________________________________ DATE
____________ PERIOD _____
12-4 Study Guide and Intervention
Histograms
Histograms
Example
A histogram uses bars to display numerical data that have been organized into
equal intervals.
• There is no space between bars.
• Because the intervals are equal, all of the bars have the same width.
• Intervals with a frequency of 0 have no bar.
ELEVATIONS The frequency table shows the highest elevations in
each state. Display the data in a histogram.
Highest Elevation in Each State
Highest Elevation in Each State
Tally
Frequency
0–3999
22
4000–7999
14
8000–11,999
2
12,000–15,999
11
16,000–19,999
0
20,000–23,999
1
Number of States
Elevation (ft)
22
20
18
16
14
12
10
8
6
4
2
0
0–
4,000– 8,000– 12,000– 16,000– 20,000–
3,999 7,999 11,999 15,999 19,999 23,999
Elevation (ft)
Source: www.peakware.com
Step 1 Draw and label the axes as shown.
Include the title.
Step 2 Show the frequency intervals on the horizontal axis and an interval of 2 on the
vertical axis.
Step 3 For each elevation interval, draw a bar whose height is given by the frequency.
Exercises
For Exercises 1–3, use the information shown in the table below.
1. The frequency table shows voter participation in 1998. Display the data in a histogram.
Voter Participation by State (1998)
Percent voting
2. How many states had a voter turnout greater
than 50 percent? 11
3. How many states had fewer than 40 percent
voting? 13
©
Glencoe/McGraw-Hill
682
Tally
Frequency
30–34
4
35–39
9
40–44
10
45–49
16
50–54
9
55–59
1
60–64
1
Source: U.S. Census Bureau
Glencoe Pre-Algebra
NAME ______________________________________________ DATE
____________ PERIOD _____
12-4 Skills Practice
Histograms
Display each set of data in a histogram.
Number of
Shots
Employees in Each Office
Frequency
Number of
Employees
1–7
5
10–19
2
8–14
1
20–29
6
15–21
8
30–39
9
22–28
2
40–49
8
29–35
4
50–59
1
3.
Tally
4.
Basketball Backboards
on Each Playground
Number of
Backboards
©
2.
Shots per Hockey Game
Tally
Frequency
Population of Loons on Local Lakes
Number of
Loons
Frequency
Tally
Tally
Frequency
30–39
2
0–4
16
40–49
0
5–9
3
50–59
6
10–14
8
60–69
9
15–19
11
70–79
17
20–24
0
80–89
4
25–29
4
Glencoe/McGraw-Hill
683
Glencoe Pre-Algebra
Lesson 12-4
1.
NAME ______________________________________________ DATE
____________ PERIOD _____
12-4 Practice
Histograms
Display each set of data in a histogram.
1.
Ages of Zoo Volunteers
Age
Tally
2.
Frequency
Crossword Puzzle Solving Times
Time (min)
Tally
Frequency
18–27
3
0–4
3
28–37
8
5–9
1
38–47
16
10–14
6
48–57
12
15–19
14
58–67
5
20–24
0
68–77
2
25–29
2
For Exercises 3–6, use the histogram at the right.
3. What size are the intervals? 5 species
5. Which interval contains the median number of
endangered species? 5–9
6. Can you tell from the histogram whether any of the
countries have zero threatened species? Explain.
No; seven countries have 0–4 threatened
species, but you cannot tell the specific
number of threatened species in any
country from the histogram.
©
Glencoe/McGraw-Hill
684
Number of Countries
4. How many countries have nine or fewer threatened
species? 26 countries
Threatened Species of
Mammals in Europe
20
18
16
14
12
10
8
6
4
2
0
0–4
5–9
10–14 15–19 20–24
Number of Threatened Species
Source: www.redlist.org
Glencoe Pre-Algebra
NAME ______________________________________________ DATE
____________ PERIOD _____
12-4 Reading to Learn Mathematics
Histograms
Pre-Activity
How are histograms similar to frequency tables?
Do the activity at the top of page 623 in your textbook. Write
your answers below.
a. What does each tally mark represent?
a state
b. What does the last column represent?
the totals in the row of tally marks
c. What do you notice about the intervals that represent the counties?
They are equal.
Reading the Lesson
Write a definition and give an example of the new vocabulary word.
Vocabulary
1.
Definition
Example
See students’ work.
histogram
Complete the following statements about frequency tables and histograms.
2. If the first frequency interval goes from 1 to 50, the next frequency interval
goes from 51–100 .
3. Because the intervals in a histogram are equal , all of the bars have
the same width .
no space between
4. In a histogram, there is
5. Intervals that have a frequency of 0 have
bars.
no bar
.
6. The height of a bar in a histogram corresponds to the
interval
of the data for
.
Helping You Remember
Number of Respondents
7. Label the following in the histogram at right: interval, frequency, bar, and histogram.
Then make a frequency table showing the
My Survey
same information as the histogram.
My Survey
Age
©
Tally
Frequency
0–19
9
20–39
6
40–59
11
60–79
3
Glencoe/McGraw-Hill
12
10
8
6
4
2
0
0–19
20–39
40–59
60–79
Age
685
Glencoe Pre-Algebra
Lesson 12-4
that
frequency
NAME ______________________________________________ DATE
____________ PERIOD _____
12-4 Enrichment
Histograms
A histogram is a type of bar graph that displays the frequencies in a distribution of data
that has been divided into equal intervals. Notice that there is no space between the bars.
(A boundary grade, like 200 or 240, is included in the lower interval. 200 would be included
in the 180–200 interval.)
The table at the right shows the weights of the players on the
Mather Jr. High football team separated into 20-pound intervals.
The histogram below shows this data.
Weight
Frequency
180–200
200–220
220–240
240–260
260–280
280–300
2
10
9
7
4
2
Use the graph to answer each of the following.
1. Give the histogram a name.
10
Weight of Players Mather Jr. High
Football Team
9
2. What does the vertical scale represent?
7
8
6
number of players
5
3. What does the horizontal scale represent?
4
3
weight of the players
2
4. How many weigh between 220 and 240? 9
1
5. How many players are there on the team? 34
180
6. How many weigh over 240 lb? 13
200
220
240
260
280
300
7. How many weigh 227 lb? cannot be determined
Make a histogram using the given data.
8. Grades in Mr. Miner’s Math Class
9. Grades in Mrs. Colburn’s Math Class
Grade
Frequency
Grade
Frequency
90–100
80–90
70–80
60–70
50–60
4
8
17
5
2
90–100
80–90
70–80
60–70
50–60
6
10
14
8
3
10. How many students in each class received a grade above 70? Miner: 29; Colburn: 30
11. How many students in each class had a grade of 60 or below?
©
Glencoe/McGraw-Hill
686
Miner: 2; Colburn: 3
Glencoe Pre-Algebra
NAME ______________________________________________ DATE
____________ PERIOD _____
12-5 Study Guide and Intervention
Misleading Statistics
Example
The graphs below show the increase in the number of events held
in the Summer Olympics from 1948 to 1996.
Events in Summer Olympics
Graph A
257
250
225
198
200
172
175
149
150
150
125
100
145
136
196
525
271
221
Number of Events
Number of Events
275
Events in Summer Olympics
Graph B
237
203
163
'48 '52 '56 '60 '64 '68 '72 '76 '80 '84 '88 '92 '96
Year
450
375
300
225
150
149
198
172
150
203
221
257
237
271
196
163
75 136 145
0
'48 '52 '56 '60 '64 '68 '72 '76 '80 '84 '88 '92 '96
Year
a. What causes the graphs to differ in their appearance?
Different vertical scales and the lack of a zero on Graph A’s axis result in different
visual impressions.
b. Which graph appears to show a more rapid increase in the number of events
held in the Summer Olympics? Explain.
Graph A; the steeper slope of the line and the higher position of the line relative to
the scale make it appear that the number of events is greater and increasing faster.
Exercises
Alaska
California
Florida
Hawaii
Texas
State
140
120
100
80
60
40
20
0
Alaska
California
Florida
Hawaii
Texas
State
1. What is the highest recorded temperature in California? In Alaska? 134°F; 100°F
2. In which graph does the difference between these two temperatures appear to be
minimized? Graph B
3. How do the graphs create different appearances? The vertical scale on Graph A
has a smaller range than the scale on Graph B.
©
Glencoe/McGraw-Hill
687
Glencoe Pre-Algebra
Lesson 12-5
135
130
125
120
115
110
105
100
95
90
85
80
Highest Temperatures
Graph B
Temperature (˚F)
Source: National Oceanic and Atmospheric Administration
Highest Temperatures
Graph A
Temperature (˚F)
Source: National Oceanic and Atmospheric Administration
For Exercises 1–3, refer to the graphs below.
NAME ______________________________________________ DATE
____________ PERIOD _____
12-5 Skills Practice
Misleading Statistics
For Exercises 1–3, refer to the graphs below.
Most Common Lake Names
in Wisconsin
Graph B
150
Number of Lakes
Number of Lakes
Most Common Lake Names
in Wisconsin
Graph A
115
105
95
85
75
65
55
Bass Lake
Long Lake
100
50
0
Bass Lake
Mud Lake
Long Lake
Mud Lake
Name
Name
Source: Wisconsin Department of Natural Resources
Source: Wisconsin Department of Natural Resources
1. How many lakes in Wisconsin are named Bass Lake? Long Lake? Mud Lake?
82; 59; 116
2. Which graph gives the impression that only a few lakes are called Long Lake, while
numerous lakes are called Bass Lake? Graph A
3. What causes the graphs to differ in their appearance? The vertical axis of
Graph A starts at 55 instead of zero. This makes it appear that the
name Long Lake is used much less frequently than Bass Lake.
For Exercises 4–6, refer to the graphs below.
U.S. Corn Production, 1991–2001
Graph B
Amount Produced
(billion bushels)
Amount Produced
(billion bushels)
U.S. Corn Production, 1991–2001
Graph A
11
10
9
8
7
6
15
12
9
6
3
0
'91 '92 '93 '94 '95 '96 '97 '99 '98 '99 '01
Year
'91 '92 '93 '94 '95 '96 '97 '99 '98 '99 '01
Year
Source: USDA
Source: USDA
4. Do these graphs show the same information? yes
5. Which graph suggests that U.S. corn production is relatively stable?
Graph B
6. What causes the graphs to differ in their appearance? The vertical scales are
different. Graph A runs from 6 billion bushels to 11 billion bushels, while
Graph B runs from 0 to 15 billion bushels.
©
Glencoe/McGraw-Hill
688
Glencoe Pre-Algebra
NAME ______________________________________________ DATE
____________ PERIOD _____
12-5 Practice
Misleading Statistics
For Exercises 1–3, refer to the graphs below.
U.S. Consumption of Hydroelectric
Power, 1960–1999 Graph B
400
350
300
250
200
150
100
50
0
Amount Consumed
(billion kilowatthours)
Amount Consumed
(billion kilowatthours)
U.S. Consumption of Hydroelectric
Power, 1960–1999 Graph A
'60'65'70'75'80'85'90'91'92'93'94'95'96'97'98'99
Year
Source: Energy Information Administration
400
350
300
250
200
150
100
50
0
1960 1965 1970 1975 1980 1985 1990 1995 1999
Year
Source: Energy Information Administration
1. What was the U.S. consumption of hydroelectric power in 1990? 300 billion
kilowatt hours
2. Which graph gives the impression that the use of hydroelectric power in the United
States has experienced many dips as well as rises between 1975 and 1999? Graph A
3. What causes the graphs to differ in their appearance? The scale on the horizontal
axis of Graph A is inconsistent. The same interval size represents five
years between 1960 and 1990 and one year between 1990 and 1999.
For Exercises 4–6, refer to the graphs below.
World Population
Graph B
2050
2000
1950
1900
1850
1800
1750
1700
Year
Year
World Population
Graph A
1
2
3
4
5
Population (billions)
6
2000
1975
1950
1925
1900
1875
1850
1825
1800
1
2
3
4
5
6
Population (billions)
Source: www.pbs.org
Source: www.pbs.org
4. What was the world’s population in 1999?
about 6 billion
years than the vertical axis in Graph A.
6. Are the vertical axis and the horizontal axis in either graph misleading? Explain.
Sample answer: The most misleading aspect of the axes is the placement
of population along the horizontal and year along the vertical. Placing
population on the vertical axis, running from zero to seven in one billion
person increments, would improve the display.
©
Glencoe/McGraw-Hill
689
Glencoe Pre-Algebra
Lesson 12-5
5. Which graph gives the impression that the world’s population skyrocketed between 1800
and 1925? Explain. Graph B; The vertical axis in Graph B shows fewer
NAME ______________________________________________ DATE
____________ PERIOD _____
12-5 Reading to Learn Mathematics
Misleading Statistics
Pre-Activity
How can graphs be misleading?
Do the activity at the top of page 630 in your textbook. Write
your answers below.
yes
a. Do both graphs show the same information?
b. Which graph suggests a dramatic increase in sales from May to June?
Graph B
c. Which graph suggests steady sales? Graph A
d. How are the graphs similar? How are they different?
Sample answer: The graphs differ in that Graph A shows
a gradual increase and decrease over the year; Graph B
shows a drastic increase and decrease. They are similar
in that each graph contains labeled axes and a title.
Reading the Lesson
Complete the following statements by filling in the blanks with the following words.
different
gradually
horizontal
interval(s)
label(s)
rapidly
title(s)
vertical
1. If two graphs showing the same information have different vertical scales, that means
that on the vertical axis, the intervals are different.
2. If two graphs showing the same information have different horizontal scales, that means
that on the horizontal axis, the intervals are
different .
3. A graph can be misleading if it has no title or if it has no labels on the scales.
4. If a graph shows steady change, the plotted values should increase or
decrease
gradually .
5. If a graph shows dramatic change, the plotted values should increase or
decrease
rapidly
.
Helping You Remember
6. Use a dictionary and a book of synonyms to rewrite the following sentence by replacing
the underlined words with ones you are more familiar with.
Statistics or statistical graphs can be misleading when the same data are represented
in different ways, so that each graph gives a different visual impression.
Sample answer: A collection of numerical information or statistical
graphs can be deceptive when the same facts are shown in different
ways, so that each graph gives a different effect to the eyes.
©
Glencoe/McGraw-Hill
690
Glencoe Pre-Algebra
NAME ______________________________________________ DATE
____________ PERIOD _____
12-5 Enrichment
Using and Misusing Graphs
Graph A: Vans Sold In June
Use the graphs at the right. Complete
the following to discover which graph
is misleading.
1. Do Graphs A and B give the same
information on sales? yes
Hilly’s
Van
Sales
2. Find the ratio of Hilly’s sales to Valley’s
sales. 3:1
3. In Graph A, the Hilly van is about
2.5 cm high by 6 cm long. What is
its area? 15 cm2
Valley’s
Van
Sales
4. The Valley van is about 0.75 cm high by
2 cm long. What is its area? 1.5 cm2
0
5. In Graph B, both vans are about 1.5 cm
high. The Hilly van is about 6 cm long.
What is its area? 9 cm2
6. The Valley van is about 2 cm long.
What is its area? 3 cm2
2
4
6
Number of Vans
8
10
Graph B: Vans Sold In June
Hilly’s
Van
Sales
7. Compute the following ratios.
10
Area of Valley 1
Area of H illy 3
Graph B: Area of Valley 1
Area of H illy
Graph A: Valley’s
Van
Sales
8. Compare the results of Exercises 2
and 7. Which graph is misleading?
Explain your answer.
0
A; The actual number of vans
sold by Hilly’s is 3 times greater,
but Graph A appears to show
the sales as 10 times greater.
Which graph is easier to read? C
Which graph gives a better impression of
the trend in sales? Explain.
Sample answer: Neither; the sales
increase is overstated by Graph C
and understated by Graph D.
©
40
39
Sales 38
37
36
35
Compare the vertical scales. How do they
differ? The units on Graph C increase
by 1, while the units on Graph D
increase by 10.
11.
Glencoe/McGraw-Hill
8
10
691
J
F
M
A
M
J
J
A
J
A
Month
Graph D: Total Sales
50
40
Sales 30
20
10
0
J
F
M
A
M
J
Month
Glencoe Pre-Algebra
Lesson 12-5
10.
4
6
Number of Vans
Graph C: Total Sales
Use Graphs C and D to answer each question.
9.
2
NAME ______________________________________________ DATE
____________ PERIOD _____
12-6 Study Guide and Intervention
Counting Outcomes
Example 1
List each
beverage
choice.
How many
different combinations of
beverage and bread can
be made from 3 beverage
choices and 3 bread
choices?
Beverage
Coffee
Draw a tree diagram
to find the number of
different combinations.
Tea
Juice
Each beverage choice
is paired with each
bread choice.
Bread
Outcome
Bagel
Coffee, Bagel
Muffin
Coffee, Muffin
Scone
Coffee, Scone
Bagel
Tea, Bagel
Muffin
Tea, Muffin
Scone
Tea, Scone
Bagel
Juice, Bagel
Muffin
Juice, Muffin
Scone
Juice, Scone
There are
9 possible
outcomes.
The Fundamental Counting Principle also relates the number of outcomes to the number of choices.
When you know the number of outcomes, you can find the probability that an event will occur.
Example 2
Refer to Example 1. What is the probability of randomly selecting
coffee with a scone?
Use the Fundamental Counting Principle to find the number of outcomes.
beverage
choices
times
3
bread
choices
3
equals
total number
of possible
outcomes
9
Only one of the 9 possible outcomes is coffee and a scone.
1
So, the probability of randomly selecting coffee with a scone is .
9
Exercises
Find the number of possible outcomes for each situation.
1. one six-sided number cube is rolled, and one card is drawn from a 52-card deck
312
2. There are 512 juniors and 498 seniors. One junior and one senior are randomly drawn
as raffle winners. 254,976
Find the probability of each event.
3. A coin is tossed and a card is drawn from a 52-card deck. What is the probability of
getting tails and the ten of diamonds?
1
104
1
16
4. Four coins are tossed. What is the probability of four tails? ©
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Glencoe Pre-Algebra
NAME ______________________________________________ DATE
____________ PERIOD _____
12-6 Skills Practice
Draw a tree diagram to find the number of outcomes for each situation.
1. Three coins are tossed.
2. A number cube is rolled and a coin is tossed.
Find the number of possible outcomes for each situation.
3. One card is drawn from a standard deck
of cards. 52 outcomes
4. Three six-sided number cubes are rolled.
5. One coin is flipped three consecutive
times. 8 outcomes
6. One coin is flipped and one eight-sided
die is rolled. 16 outcomes
7. A sweater comes in 3 sizes and 6 colors.
8. A restaurant offers dinners with a
choice each of two salads, six entrees,
and five desserts. 60 outcomes
216 outcomes
18 outcomes
Find the probability of each event.
9. Draw the ace of spades from a standard
deck of cards. 1
10. A coin is tossed twice. What is the
probability of getting two tails? 1
52
4
11. Draw the six of clubs from a standard
deck of cards. 1
12. Roll a 4 or higher on a six-sided
number cube. 1
13. Roll a 7 or an 8 on an eight-sided
die. 1
14. Roll an even number on an eight-sided
die. 1
15. Draw a club from a standard deck
of cards. 1
16. Roll an odd number on a six-sided
number cube. 1
17. A coin is tossed and an eight-sided die is
rolled. What is the probability that the
coin lands on tails, and the die lands on
a 2? 1
18. A coin is tossed and a card is drawn
from a standard deck of cards. What is
the probability of landing on tails and
choosing a red card? 1
52
2
4
2
4
16
©
Glencoe/McGraw-Hill
2
693
4
Glencoe Pre-Algebra
Lesson 12-6
Counting Outcomes
NAME ______________________________________________ DATE
____________ PERIOD _____
12-6 Practice
Counting Outcomes
Find the number of possible outcomes for each situation.
1. Joan randomly dials a seven-digit phone number. 10,000,000 outcomes
2. First-year students at a school must choose one each of 5 English classes, 4 history
classes, 5 math classes, and 3 physical education classes. 300 outcomes
3. One card each is drawn from four different standard decks of cards.
7,311,616 outcomes
4. A store offers running shoes with either extra stability or extra cushioning from four
different manufacturers. 8 outcomes
5. A winter sweater comes in wool or fleece, with a zipper or a crew neck, and in
three colors. 12 outcomes
6. One spinner can land on red, green, blue, or yellow and another can land on right
foot, left foot, right hand, or left hand. Each spinner is spun once. 16 outcomes
Find the probability of each event.
2
3
7. A number cube is rolled. What is the probability of rolling a 4 or lower? 1
3
8. A number cube is rolled. What is the probability of getting a five or higher? 9. An eight-sided die is rolled and a coin is tossed. What is the probability
of landing on an even number and getting heads?
1
4
1
8
10. A coin is tossed and a card is drawn from a standard deck of cards. What is the
probability of landing on heads and choosing a heart?
11. REFRESHMENTS How many fruit smoothies are possible from 6 choices of fruit,
4 choices of milk, and 3 sizes? 72 fruit smoothies
12. MONOGRAMS A school’s class rings can include a student’s initials in an engraved
monogram on the ring. How many different monograms are possible from 2 sizes, 5 type
styles, and 3 border styles? 30 monograms
13. MOBILE PHONES The table shows
the features you can choose for a
pay-as-you go phone plan.
a. How many phone plans have
national long distance? 18 plans
Phone
Features
Brand A;
Brand B
e-mail only;
paging only;
deluxe:
paging and
e-mail
b. How many customized phone plans
include 100 minutes per month
talkingtime and paging
capabilities? 12 plans
©
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694
Calling
Area
local only;
local and
regional;
national
long
distance
Monthly
Talk
Time
30 min;
60 min;
100 min
Glencoe Pre-Algebra
NAME ______________________________________________ DATE
____________ PERIOD _____
12-6 Reading to Learn Mathematics
Pre-Activity
How can you count the number of skateboard designs that
are available from a catalog?
Do the activity at the top of page 635 in your textbook. Write
your answers below.
a. Write the names of each deck choice on 5 sticky notes of one color.
Write the names of each type of wheel on 3 notes of another color.
See students’ work.
b. Choose one deck note and one wheel note. One possible skateboard is
Alien, Eagle. See students’ work.
c. Make a list of all the possible skateboards. alien-eagle, alien-
cloud, alien-red hot, birdman-eagle, birdman-cloud, birdman-red hot, candy-eagle, candy-cloud, candy-red hot,
radical-eagle, radical-cloud, radical-red hot, trickstereagle, trickster-cloud, trickster-red hot
d. How many different skateboard designs are possible? 15
Reading the Lesson 1–2. See students’ work.
Write a definition and give an example of each new vocabulary phrase.
Vocabulary
Definition
Example
1. tree diagram
2. Fundamental
Counting
Principle
Helping You Remember
3. Complete the two diagrams below by filling in each blank with one of the following
words. Some words may be used more than once.
choices
favorable
Fundamental
Counting
Principle
number of
m
choices
for event 1
Probability
possible
©
Glencoe/McGraw-Hill
choices
for event 2
possible
outcomes
outcomes
Probability
n
695
number of
favorable outcomes
number of
possible outcomes
Glencoe Pre-Algebra
Lesson 12-6
Counting Outcomes
NAME ______________________________________________ DATE
____________ PERIOD _____
12-6 Enrichment
Outcomes
Complete.
1. Complete the spinner so that it will have
six different possible outcomes.
2. List the numbers
that could be
placed on the die
to provide only
four different
possible outcomes.
Answers will vary.
Sample answer: 1, 1, 1, 2, 3, 4
The six sections do not
have to be the same size.
3. Complete the spinner so that it is more
likely to land on red than blue.
4. List the months in which you could choose
a date and have 30 possible outcomes.
April, June, September, November
Red section must be larger than
blue section.
5. There are white, green, and blue marbles
in a bag. What is the minimum number of
each so that it is twice as likely that you
draw a green one as a white one, and
three times as likely that you draw a blue
one as a green one? 1 white, 2 green,
6. A year between 1950 and 2001 is chosen
at random. How many possible outcomes
are there where the year is a leap year?
List them. 13 outcomes; 1952, 1956,
1960, 1964, 1968, 1972, 1976, 1980,
1984, 1988, 1992, 1996, 2000
and 6 blue
©
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696
Glencoe Pre-Algebra
NAME ______________________________________________ DATE
____________ PERIOD _____
12-7 Study Guide and Intervention
Permutations
Combinations
Words
An arrangement or listing in which order is important is
called a permutation.
Symbols
P(m, n) means m number of choices taken n at a time.
Example
P(3, 2) 3 2 6
Words
An arrangement or listing where order is not important is
called a combination.
Symbols
C(m, n) Example
Example 1
P(m, n)
n!
P(6, 2)
65
C(6, 2) or 15
2!
21
SPORTS How many ways can the top five finishers be arranged in
a 20-person cross-country race?
20 runners
Order is important.
So, this arrangement is a permutation.
choose 5
P(20, 5)
Example 2
20 19 18 17
1,860,480 ways
16
20 choices for 1st place
19 choices for 2nd place
18 choices for 3rd place
17 choices for 4th place
16 choices for 5th place
SCHOOL In a science class with 42 students, how many 3-person
lab teams can be formed?
From 42 students, take 3 at a time.
Order is not important.
So, this arrangement is a combination.
C(42, 3)
P(42, 3)
3!
42 41
3 2
40
or 11,480 lab teams
1
Exercises
Tell whether each situation is a permutation or combination. Then solve.
1. How many ways can three people be selected from a group of seven?
C; 35 ways
2. How many ways can a 6-person kickball team be chosen from 27 students?
C; 296,010 ways
3. How many ways can 15 actors fill 6 roles in a play? P; 3,603,600 ways
4. How many ways can 5 books be borrowed from a collection of 40 books? C; 658,008 ways
5. JOBS A telemarketing firm has 35 applicants for 8 identical entry-level positions.
How many ways can the firm choose 8 employees? C; 23,535,820 ways
6. FOOD A pizza place sends neighbors a coupon for a 4 topping pizza of any size. If the
pizzeria has 15 toppings and 3 sizes to choose from, how many possible pizzas could be
purchased using the coupon? C; 4,095 pizzas
©
Glencoe/McGraw-Hill
697
Glencoe Pre-Algebra
Lesson 12-7
Permutations and Combinations
NAME ______________________________________________ DATE
____________ PERIOD _____
12-7 Skills Practice
Permutations and Combinations
Tell whether each situation is a permutation or combination. Then solve.
1. How many ways can 6 student desks be arranged in a row? P; 720 ways
C; 153 ways
2. How many ways can 18 baseball cards be passed out to 2 students?
3. How many ways can 10 students line up for lunch? P; 3,628,800 ways
4. How many ways can you choose 4 CDs from a stack of 8 CDs? C; 70 ways
5. How many ways can 3 pairs of shoes be chosen from 8 pairs? C; 56 ways
6. How many ways can 9 runners be arranged on a 4-person relay team? P; 3024 ways
Find each value.
7. 9!
10. 4!
362,880
24
8. 5!
120
9. 3!
11. 6! 720
12. 12!
6
479,001,600
13. SPORTS The Eastern Division of a baseball league is composed of 5 teams.
How many different ways can teams of the Eastern Division finish? 120 ways
14. LEISURE The local hobby store has 17 model airplanes to display. If the front case
holds 6 models, how many ways can 6 planes be chosen for the front of the store?
12,376 ways
15. ZOOS The local zoo has 23 animals it can take on visits to schools and other
community centers. How many ways can the zoo directors choose 9 animals for
a trip to a middle school? 817,190 ways
16. CULTURE There are 15 Irish dancers in a championship-level competition.
How many ways can the top 3 finishers be arranged? 2730 ways
17. RACING In an auto race, the cars start in 11 rows of 3. How many ways
can the front row be made from the field of 33 race cars? 32,736 ways
TELEVISION For Exercises 18 and 19, use the following information.
A television network has a choice of 11 new shows for 4 consecutive time slots.
18. How many ways can four shows be chosen, without considering the age of the
viewers or the popularity of the time slots? 330 ways
19. How many ways can the shows be arranged if the time slots are during prime time
and in competition for viewers? 7920 ways
©
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698
Glencoe Pre-Algebra
NAME ______________________________________________ DATE
____________ PERIOD _____
12-7 Practice
Permutations and Combinations
Tell whether each situation is a permutation or combination. Then solve.
1. How many ways can you make a sandwich by choosing 4 of 10 ingredients? C; 210
2. How many ways can 11 photographs be arranged horizontally? P; 39,916,800
4. How many ways can a baseball manager make a 9-player batting order from a
group of 16 players? P; 4,151,347,200 ways
5. How many ways can 30 students be arranged in a 4-student line? P; 657,720 ways
6. How many ways can 3 cookie batches be chosen out of 6 prize-winning batches?
C; 20 ways
7. SCHOOL TRIPS Students are chosen in groups of 6 to tour a local business.
How many ways can 6 students be selected from 3 classes totaling 53 students?
22,957,480 ways
8. CONTESTS In a raffle, 5 winners get to choose from 5 prizes, starting with
the first name drawn. If 87 people entered the raffle, how many ways can the
winners be arranged? 4,433,982,840 ways
9. RESTAURANTS A local restaurant specializes in simple and tasty meals.
a. How many sandwiches are possible if the restaurant lets you build a sandwich
by choosing any 4 of 10 sandwich ingredients? 210 sandwiches
b. If there are 6 soups to choose from, how many soup-and build-a-sandwich specials
are possible? 1260 specials
10. SPORTS An inline skate has 4 wheels. How many ways could 4 replacement wheels
be chosen from a pack of 10 wheels and fitted to a skate? 5040 ways
GIFT WRAPPING For Exercises 11–14, use the following information.
An upscale department offers its customers free gift wrapping on any day that
they spend at least $100. The store offers 5 box sizes (XS, S, M, L, XL), 6 wrapping
themes (birthday, wedding, baby girl, baby boy, anniversary, and all-occasion),
and 3 styles of bow (classic, modern, and jazzy).
11. How many ways can packages be gift-wrapped at the store? 90 ways
1
5
12. What is the probability that any wrapped package will be in a large box? 2
3
13. What is the probability that any wrapped package will not have a jazzy bow? 1
6
14. What is the probability that a customer will request wrapping for a baby-boy gift? ©
Glencoe/McGraw-Hill
699
Glencoe Pre-Algebra
Lesson 12-7
3. How many ways can you buy 2 software titles from a choice of 12? C; 66 ways
NAME ______________________________________________ DATE
____________ PERIOD _____
12-7 Reading to Learn Mathematics
Permutations and Combinations
Pre-Activity
Why is order sometimes important when determining outcomes?
Do the activity at the top of page 641 in your textbook. Write your
answers below.
a. Make a list of all possible pairs for class offices. (Note: Lenora-Michael
is different than Michael-Lenora.) Lenora-Michael, Lenora-Nate,
Lenora-Olivia, Lenora-Patrick, Michael-Lenora, MichaelNate, Michael-Olivia, Michael-Patrick, Nate-Michael, NateLenora, Nate-Olivia, Nate-Patrick, Olivia-Michael, OliviaLenora, Olivia-Nate, Olivia-Patrick, Patrick-Lenora, PatrickMichael, Patrick-Nate, Patrick-Olivia
b. How does the Fundamental Counting Principle relate to the number of
pairs you found? The results are the same.
c. Make another list for student council seats. (Note: For this list, LenoraMichael is the same as Michael-Lenora.) Lenora-Michael,
Lenora-Nate, Lenora-Olivia, Lenora-Patrick, Michael-Nate,
Michael-Olivia, Michael-Patrick, Nate-Olivia, Nate-Patrick,
Olivia-Patrick
d. How does the answer in part a compare to the answer in part c?
The answer in part c equals the answer in part a divided by 2.
Reading the Lesson 1–3. See students’ work.
Write a definition and give an example of each new vocabulary word.
Vocabulary
Definition
Example
1. permutation
2. factorial
3. combination
Helping You Remember
4. Complete the diagram at right by writing the words
combinations and permutations in the correct blanks.
Then write a sentence based on the diagram stating how
to remember the difference between permutations and
combinations. Sample answer: Permutations are
Possible Outcomes or
all of the possible outcomes, and both start
with the letter p. Because the set of permutations contains all possible outcomes, it must be the larger set. Therefore,
the smaller set of outcomes must be the set of combinations.
©
Glencoe/McGraw-Hill
700
Glencoe Pre-Algebra
NAME ______________________________________________ DATE
____________ PERIOD _____
12-7 Enrichment
Permutations and Combinations
An arrangement of objects in a given order is called a permutation of the objects.
A symbol for the number of permutations is P(n, x), where x represents the number of
objects to be arranged in order and n reminds us that these objects are chosen from an
original set of n objects.
n!
Example 1
If gold, silver, and bronze medals are to be awarded to the first 3 finishers in
an 8-person race, in how many ways can the medals be awarded?
8!
P(8, 3) 5!
87654321
876
336 ways in which the medals may be awarded
A selection of x objects taken from a set of n objects without regard for order of the selection
is called a combination. A symbol for the number of combinations is C(n, x).
n!
C(n, x) x!(n x)!
Example 2
In how many ways can you choose 3 people from a group of 12 without
regard for order?
12!
C(12, 3) 3!9!
12 11 10 9 8 7 6 5 4 3 2 1
12 11 10
32
220 possible groups of 3 people
Find each value.
1. P(7, 2) 42
2. P(7, 5) 2520
3. C(7, 2) 21
4. C(7, 5) 21
5. P(13, 2) 156
6. C(13, 11) 78
©
Glencoe/McGraw-Hill
701
Glencoe Pre-Algebra
Lesson 12-7
P(n, x) (n x)!
NAME ______________________________________________ DATE
____________ PERIOD _____
12-8 Study Guide and Intervention
Odds
The odds in favor of an outcome is the ratio of the number of ways the outcome can occur
to the number of ways the outcome cannot occur.
Odds in favor number of successes : number of failures
Odds
The odds against an outcome is the ratio of the number of ways the outcome cannot occur
to the number of ways the outcome can occur.
Odds against number of failures : number of successes
Example 1
Example 2
Find the odds of a
sum of 11 if a pair of number cubes
are rolled.
In a bag of marbles,
30 are blue, 15 are orange, 20 are
yellow, and 10 are green. What are the
odds against drawing a green marble
from the bag?
There are 6 • 6 or 36 sums possible for
rolling a pair of number cubes. There are 2
sums of 11. They are (5, 6) and (6, 5). There
are 36 – 2 or 34 sums that are not 11.
There are 75 – 10 marbles that are
not green.
Odds of rolling a sum of 11
numbers of
ways to roll
a sum of 11
to
:
2
2:34 or 1:17
Odds against drawing a green marble
numbers of
ways to roll
any other sum
numbers of ways
to draw a marble
that is not green
to
numbers of
ways to draw a
green marble
:
65
65:10 or 13:2
34
The odds of rolling an 11 are 1:17.
10
The odds against drawing a green
marble are 13:2.
Exercises
Find the odds of each outcome if a pair of number cubes are rolled.
1. not a sum of 7 5:1
2. a sum less than 5 or greater than 9
3. a sum that is a multiple of 3 1:2
4. a double number 1:5
5. not a double number 5:1
6. double twos
1:2
35:1
7. A hockey team scores 3 goals for every 30 shots taken. What are the odds in favor of
the next shot being a goal? 1:9
8. A bookshelf holds 12 mysteries, 3 history books, 4 how-to books, and 11 self-help books.
What are the odds of randomly picking a how-to book? 2:13
9. A professional football team finished the season with a record of 10 wins and 6 losses.
What were its odds that season of winning a game? 5:3
10. After many sessions of playing rock-paper-scissors with Joe, you discover that he
throws “rock” 55 percent of the time. What are the odds in favor of his next throw
being “rock”? 11:9
©
Glencoe/McGraw-Hill
702
Glencoe Pre-Algebra
NAME ______________________________________________ DATE
____________ PERIOD _____
12-8 Skills Practice
Odds
Find the odds of each outcome if an eight-sided die is rolled.
1. three 1:7
2. not three
4. not 7 or 8 3:1
5. 1 or 2
7:1
1:3
3. an even number 1:1
6. a number less than 6 5:3
Find the odds of each outcome if the spinner at the right is spun.
7. yellow
1:3
9. not blue 3:1
8. red
1:3
RED
GREEN
BLUE
YELLOW
10. not blue or green 1:1
A card is selected from a standard deck of 52 cards.
11. What are the odds of selecting a black jack? 1:25
12. What are the odds of selecting a 3? 1:12
Lesson 12-8
13. What are the odds of not selecting a club? 3:1
14. What are the odds of selecting a 6 or an 8? 2:11
15. What are the odds of not selecting a king? 12:1
16. If aces are counted as higher than a king, what are the odds of selecting a card
lower than a 10? 8:5
BASEBALL For Exercises 17 and 18, use the following information.
A baseball team finished the season with a record of 92 wins and 70 losses.
17. What were the odds in favor of this team winning any given game during the season?
46:35
18. If a player on this team got 150 hits in 500 at bats (a .300 batting average), what
were the odds in favor of a hit when he got an at bat? 3:7
NUMBER CUBES For Exercises 19–21, use the following information.
Two number cubes are rolled. The chart at the right
shows the outcomes.
19. How many ways can two number cubes total 11? What
are the odds of rolling a sum of 11? 2; 1:17
20. What are the odds in favor of rolling doubles? 1:5
21. What are the odds of not rolling a double?
©
Glencoe/McGraw-Hill
5:1
703
Roll
1
2
3
4
5
6
1
1,1
1,2
1,3
1,4
1,5
1,6
2
2,1
2,2
2,3
2,4
2,5
2,6
3
3,1
3,2
3,3
3,4
3,5
3,6
4
4,1
4,2
4,3
4,4
4,5
4,6
5
5,1
5,2
5,3
5,4
5,5
5,6
6
6,1
6,2
6,3
6,4
6,5
6,6
Glencoe Pre-Algebra
NAME ______________________________________________ DATE
____________ PERIOD _____
12-8 Practice
Odds
Find the odds of each outcome if the spinner at the right is spun.
1. an odd number
3. not 7 or 8 3:1
1:1
1
2. a number less than 6 5:3
8
4. a number greater than 5 3:5
7
3
4
6
A card is selected from a standard deck of 52 cards.
2
5
5. What are the odds of selecting a red king? 1:25
6. What are the odds of selecting a 4 of diamonds? 1:51
7. What are the odds of not selecting an even club (not a face card)? 47:5
8. What are the odds of selecting a diamond or an 8 of spades? 7:19
9. What are the odds of not selecting a queen of hearts? 51:1
10. What are the odds of selecting a jack? 1:12
11. SURVEYS One opinion poll revealed that 41 percent of Americans are completely
satisfied with their jobs and that 44 percent are somewhat satisfied. What are the
odds of an American worker, chosen at random, being completely satisfied?
Somewhat satisfied? Source: www.gallup.com 41:59; 44:56
SURVEYS For Exercises 12–14, use the information
in the table at the right.
Gallup Poll, August 2001
12. What are the odds against a randomly chosen
respondent being a sports fan? 43:57
Sports
Fan
Not a
Fan
No
Opinion
13. What are the odds against a person having no
opinion? 99:1
57%
42%
1%
14. Based on this poll, in a group of 1000 people, how
many would you expect not to be sports fans?
420 people
SCIENCE For Exercises 15–18, use the information
in the table at the right. Assume that one sample
is drawn randomly from a bag containing one
sample of each of the minerals in the table.
15. What are the odds in favor of drawing a mineral
harder than topaz? 1:4
16. What are the odds in favor of drawing quartz? 1:9
17. What are the odds against drawing a mineral softer
than quartz? 2:3
18. What are the odds against drawing a mineral
harder than apatite? 1:1
Source: www.gallup.com
Mohs Scale of Mineral
Hardness
Mineral
Hardness
(hardest rank
is 10)
Diamond
Corundum
Topaz
Quartz
Orthoclase
Apatite
Fluorite
Calcite
Gypsum
Talc
10
9
8
7
6
5
4
3
2
1
Source: The Sizesaurus
©
Glencoe/McGraw-Hill
704
Glencoe Pre-Algebra
NAME ______________________________________________ DATE
____________ PERIOD _____
12-8 Reading to Learn Mathematics
Odds
How are odds related to probability?
Pre-Activity
Do the activity at the top of page 646 in your textbook. Write
your answers below.
a. Roll the number cubes 50 times. Record whether you win or lose each
time. See students’ work.
b. What is the experimental probability of winning the game based on
your results in part a? See students’ work; theoretical
5
12
probability is .
c. Write the ratio of wins to losses using your results in part a.
Reading the Lesson
Write a definition and give an example of the new vocabulary word.
Vocabulary
1.
Definition
Example
See students’ work.
odds
2. The odds
in favor of
an outcome is the ratio of the number of successes to the
number of failures.
3. The odds
against
an outcome is the ratio of the number of failures to the number
of successes.
4. The number of successes added to the number of failures equals the number
total possible
of
odds
5. To find the
outcomes.
of an outcome, compare the number of successes with the number
of failures.
Helping You Remember
6. Study the spinner below, then complete the following.
The number of total possible outcomes =
1
2
0
3
7
4
6
5
8
1:1
The odds in favor of spinning an even number =
The probability of spinning an even number =
1
2
The odds in favor of spinning a number less than 5 =
The odds against spinning a number less than 5 =
©
Glencoe/McGraw-Hill
705
5:3
3:5
Glencoe Pre-Algebra
Lesson 12-8
See students’ work; based on theoretical probability, the
ratio is 5:7.
NAME ______________________________________________ DATE
____________ PERIOD _____
12-8 Enrichment
Odds
The odds for an event can be found as follows.
odds for an event number of ways that event can occur: number of ways that event
cannot occur
If a number cube is rolled once, find the odds for a 4.
1
→
A 4 can occur only in one way.
5
→
The other events are 1, 2, 3, 5, and 6.
The odds of rolling a 4 are 1 to 5 or 1:5.
odds against an event number of ways that event cannot occur: number of ways
that event can occur
Stop
Find the odds for spinning each of the following.
1. for a 6
1:15
2. not for a 13 15:1
3. for a prime number 3:5
4. for a 4, 8, or 12 3:13
15
1:1
7. for an odd number less than 14 7:9
2
3
14
13
4
12
11
5
6
10
5. not for an odd number
16 1
6. for a 7 or 9 1:7
9
7
8
8. not for a number greater than 11 11:5
A pair of number cubes are rolled. Find the odds for each of the following.
9. for a sum of 6 5:31
10. for a sum of 2 or 10 1:8
11. not for a sum of 3 17:1
12. for matching numbers (doubles) 1:5
13. for a sum of 7, with a 2 on one die
14. for a sum of 10 with a 4 on one die
1:17
1:17
15. not for a sum greater than 9 5:1
©
Glencoe/McGraw-Hill
16. for a sum greater than 9 1:5
706
Glencoe Pre-Algebra
NAME ______________________________________________ DATE
____________ PERIOD _____
12-9 Study Guide and Intervention
Probability of Compound Events
Probability
of Two
Independent
Events
Probability
of Two
Dependent
Events
Words
The probability of two independent events is found by
multiplying the probability of the first event by the
probability of the second event.
Symbols
P(A and B) P(A) P(B)
Words
If two events, A and B, are dependent, then the probability of
events occurring is the product of the probability of A and the
probability of B after A occurs.
Symbols
P(A and B) P(A) P(B following A)
Example 1
GAMES A card is drawn from a standard deck of 52 cards. The card
is replaced and another is drawn. Find the probability if the first card is the 3 of
hearts and the second card is the 2 of clubs.
Probability
of Mutually
Exclusive
Events
P(3 of hearts and 2 of clubs)
P(3 of hearts)
P(2 of clubs)
1
2704
The probability is .
1
1
52 52
1
2704
Words
The probability of one or the other of two mutually exclusive events
can be found by adding the probability of the first event to the probability
of the second event.
Symbols
P(A or B) P(A) P(B)
Example 2
The spinner at the right is spun. What is the probability that the
spinner will stop on 7 or an even number?
1
The events are mutually exclusive because the spinner cannot stop on
both 7 and an even number at the same time.
1
1
5
P(7 or even) = P(7) + P(even) = + = 8
2
8
2
8
3
7
4
5
The probability that the spinner will stop on 7 or an even number is .
8
6
5
Exercises
A card is drawn from a standard deck of cards. The card is not replaced and a
second card is drawn. Find each probability.
1. P(4 and 8)
4
663
1
663
2. P(queen of hearts and 10) A card is drawn from a standard deck of cards. Find each probability.
27
52
3. P(queen of clubs or a red card) ©
Glencoe/McGraw-Hill
5
52
4. P(queen of hearts or 10) 707
Glencoe Pre-Algebra
Lesson 12-9
Since the first
card is replaced,
the events are
independent.
NAME ______________________________________________ DATE
____________ PERIOD _____
12-9 Skills Practice
Probability of Compound Events
A number cube is rolled and the spinner is spun.
Find each probability.
BROWN
SQUARE
1
1. P(2 and green triangle) 48
1
8
2. P(an odd number and a circle) 1
4
3. P(a prime number and a quadrilateral) 4. P(a number greater than 4 and a parallelogram)
1
8
YELLOW
TRIANGLE
ORANGE
TRAPEZOID
BLUE
CIRCLE
WHITE
CIRCLE
RED
RHOMBUS
GREEN
TRIANGLE
WHITE
RECTANGLE
There are 5 yellow marbles, 1 purple marble, 3 green marbles, and 3 red marbles in
a bag. Once a marble is drawn, it is replaced. Find the probability of each outcome.
1
48
6. a red then a green marble 1
16
1
16
8. two red marbles in a row 5. a purple then a red marble 1
16
7. two green marbles in a row 1
48
5
48
9. a purple then a green marble 10. a red then a yellow marble There are 4 yellow marbles, 3 purple marbles, 1 green marble, and 1 white
marble in a bag. Once a marble is drawn, it is not replaced. Find the probability
of each outcome.
1
24
1
72
11. a purple then a white marble 12. a white then a green marble 1
12
1
6
13. two purple marbles in a row 14. two yellow marbles in a row 1
6
1
72
15. a yellow then a purple marble 16. a green then a white marble A card is drawn from a standard deck of cards. Find the probability of each outcome.
3
4
1
2
17. P(a red card or a club) 18. P(a diamond or a spade) 4
13
2
13
19. P(a face card or a 2) 20. P(a 7 or a 9) 27
52
21. P(a red card or a king of spades) ©
Glencoe/McGraw-Hill
7
26
22. P(a heart or a queen of diamonds) 708
Glencoe Pre-Algebra
NAME ______________________________________________ DATE
____________ PERIOD _____
12-9 Practice
Probability of Compound Events
An eight-sided die is rolled and the spinner
is spun. Find each probability.
1
1. P(4 and yellow fruit or vegetable) 32
2. P(an odd number and a pumpkin)
YELLOW
SQUASH
1
16
1
8
3. P(a prime number and a red fruit or vegetable) RED
APPLE
BLUE
BERRY
RED
PEPPER
ORANGE
CARROT
GREEN
SQUASH
3
64
4. P(a number less than 4 and a blue fruit or vegetable) YELLOW
BANANA
ORANGE
PUMPKIN
There are 6 orange marbles, 2 red marbles, 3 white marbles, and 4 green marbles in a
bag. Once a marble is drawn, it is replaced. Find the probability of each outcome.
2
75
4
75
5. a red then a white marble 6. a white then a green marble 4
25
16
25
7. two orange marbles in a row 8. two marbles in a row that are not white 44
225
16
1125
9. a green then a not green marble 10. a red then an orange then a green marble 1
40
11. a green then a white marble 7
40
7
60
12. a blue then a purple marble 11
20
13. two blue marbles in a row 14. two marbles in a row that are not purple 1
20
15. a white then a purple marble 1
140
16. three purple marbles in a row The chart shows the letter-number combinations for
bingo. The balls are randomly drawn one at a time.
Balls are not replaced after they are drawn.
Find the probability of each outcome.
17. a B-1
1
60
18. a G
13
60
19. an N or a B-2 21. not a G
4
5
1
5
2
5
20. an I or an O 22. a B-6, then a G, then
11
17,110
another G ©
Glencoe/McGraw-Hill
709
B
I
N
G
O
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Glencoe Pre-Algebra
Lesson 12-9
There are 2 green marbles, 7 blue marbles, 3 white marbles, and 4 purple marbles in a
bag. Once a marble is drawn, it is not replaced. Find the probability of each outcome.
NAME ______________________________________________ DATE
____________ PERIOD _____
12-9 Reading to Learn Mathematics
Probability of Compound Events
Pre-Activity
How are compound events related to simple events?
Do the activity at the top of page 650 in your textbook. Write
your answers below.
a. What was your experimental probability for the red then white
1
outcome? See students’ work; theoretical probability is .
4
b. Would you expect the probability to be different if you did not place
the first counter back in the bag? Explain your reasoning. Yes;
by not replacing the first counter drawn, you affect the
possibilities for the second draw.
Reading the Lesson 1–4. See students’ work.
Write a definition and give an example of each new vocabulary phrase.
Vocabulary
Definition
Example
1. compound
events
2. independent
events
3. dependent
events
4. mutually
exclusive
events
You are finding the probability of choosing the following arrangements of counters
from a bag containing red, orange, and blue counters. Label each situation with
independent events, dependent events, or mutually exclusive events.
5. a red counter, which is replaced, followed by a blue counter independent events
6. an orange counter or a primary color mutually exclusive events
7. an orange counter, which is kept out of the bag, followed by a red counter
dependent events
Helping You Remember
8. Complete the concept map below with
the vocabulary
One event, then the other
phrases from
P(A AND B)
this lesson.
yes
Does the outcome
of the first event
influence the outcome
of the second event?
no
Probability
of Two Events
One event, or the other
P(A OR B)
©
Glencoe/McGraw-Hill
710
Glencoe Pre-Algebra
NAME ______________________________________________ DATE
____________ PERIOD _____
12-9 Enrichment
Probability of Dependent Events
Look at the letters in the word MATHEMATICAL. If these letters were placed in a hat,
what would be the probability of drawing a vowel and then, without replacing the vowel,
drawing a consonant? These are dependent events since the letter selected on the first
draw affects the probability for the second draw.
5
7
35
P(vowel, then consonant) 1
2 11
132
Find the probability of drawing each of the following from the letters in
MATHEMATICAL if the letters are not replaced.
1
66
1
3. three As 220
1
22
1. two Ms 2. two As 1
22
4. three vowels 7
264
1
990
5. five consonants 6. the letters MATH in that order Now, think of using variables instead of numbers. This is very useful, since this is the way
formulas are developed. Once a formula is found, it can be used for any numbers. Begin by
examining the following example.
Example
3
10
6
2 1
1
9 8 , or 120
7. If box containing n socks has k blue
ones, what is the probability of picking
3 blue socks in 3 drawings?
k
n
k1
©
8. If a box containing n socks has k blue
ones, what is the probability of picking
x blue socks in x drawings?
k2
k
n
n1 n2
9. Use your formula from Exercise 7 to
find the probability of picking 3 blue
socks in 3 drawings from a box
containing 6 socks, 4 of them blue.
4
6
720
3
2
10. Use your formula from Exercise 8 to
find the probability of picking 4 blue
socks in 4 drawings from a box
containing 6 socks, 5 of them blue.
1
5
6
5 4 5
Glencoe/McGraw-Hill
k1 k2
k (x 1)
n1 n2
n (x 1)
711
4
3
2
1
5 4 3 3
Glencoe Pre-Algebra
Lesson 12-9
Three of 10 socks in a box are blue. If socks are drawn without looking and
not replaced, what is the probability of picking 3 blue socks in 3 drawings?