Name_________________________________________________________
Date __________
Tables
10.4 Two-Way
For use with Exploration 10.4
Essential Question How can you read and make a two-way table?
1
EXPLORATION: Reading a Two-Way Table
Work with a partner. You are the manager of a sports shop. The two-way tables show
the numbers of soccer T-shirts in stock at your shop at the beginning and end of the
selling season. (a) Complete the totals for the rows and columns in each table. (b) How
would you alter the number of T-shirts you order for next season? Explain your
reasoning.
T-Shirt Size
Color
Beginning of season
S
M
L
XL
XXL
blue/white
5
6
7
6
5
blue/gold
5
6
7
6
5
red/white
5
6
7
6
5
black/white
5
6
7
6
5
black/gold
5
6
7
6
5
145
Total
Color
End of season
Total
T-Shirt Size
S
M
L
XL
XXL
blue/white
5
4
1
0
2
blue/gold
3
6
5
2
0
red/white
4
2
4
1
3
black/white
3
4
1
2
1
black/gold
5
2
3
0
2
Total
Total
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Integrated Mathematics I 205
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10.4
2
Two-Way Tables (continued)
EXPLORATION: Making a Two-Way Table
Work with a partner. The three-dimensional
bar graph shows the numbers of hours
students work at part-time jobs.
a. Make a two-way table
showing the data. Use
estimation to find the
entries in your table.
Part-Time Jobs of Students at a High School
160
140
120
100
80
60
40
20
0
Males
Females
0 hours per week
1–7 hours per week
8+ hours per week
b. Write two observations that summarize the data in your table.
Communicate Your Answer
3. How can you read and make a two-way table?
206 Integrated Mathematics I
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5.
9.
Set Academic Goals
Tablet Computer
Name_________________________________________________________ Date __________
Yes
No
Yes
No
Name_________________________________________________________
Date __________
34
124
≈ 0.65
≈ 0.65
Male
64
168
—
—
Yes Practice
52
191
18
52
Gender
Cell
Phone
Chapter
10.4 7Practice
use after Lesson 10.4
10.4No For
0.35
≈ 0.35
—≈
For use
after
Lesson—
10.4
67
191
Female
54
142
Total
118
310
Concepts
9.
The conditional
relative frequencies for students who
Core
Concepts
Set Academic
Computer
have cell phones
are aboutTablet
the same
whether they have a
So, 232 male students and
196 femaleGoals
studen
Relative
Frequencies
tablet computer
or not. Similarly,
the conditional
relative
they set academic goals. A
total of 118No
studen
Yes
Yes
No
Relative
Frequencies
A
joint relative
frequency
isdo
thenot
ratio
of cell
a frequency
that is not in the “total”
row
or310
thestudents
“total” column
to A total of 4
frequencies
for students
who
have
phones
are
goals,
and
have
not.
34
124
≈or0.65
0.65 orthat
64 to
168
—
—
Yes whether
A
joint
relative
frequency
ishave
the ratio
of a≈
frequency
orMale
“total”
column
the
total
number
of values
observations.
52they
191
about
the
same
a tablet
computer
not.is not in the “total”
were row
asked
ifthe
they
set academic
goals.
the
values
or observations.
So, total
therenumber
is not anofassociation
between 67
owning a tablet
18
Female
54
142
≈
0.35 is the sum
≈ 0.35
—
—
No
A
marginal
relative
frequency
191 of the joint relative frequencies
10. in a row or column.
computer and owning a52cell phone.
A marginal relative frequency is the sum of the joint relative frequencies in a row or column.
Total
118
310
Cat
When
finding relative
frequencies
infor
a two-way
The conditional
relative
frequencies
students table,
who you can use the corresponding decimals or percents.
7.4 Exercises
(pp.
360
–362)
When
finding
relative
frequencies
a two-way
decimals or percents. No
have cell
phones
are about
the sameinwhether
theytable,
haveyou
a can use the corresponding
So, 232 male studentsYes
and 196 female studen
Notes:
tablet
computer
or
not.
Similarly,
the
conditional
relative
Vocabulary
and
Core
Concept
Check
they
set
academic
goals.
118 studen
Notes:
Yes
104 A total of 208
frequencies
for
students
who
do
not
have
cell
phones
are
goals, and 310 students have not. A total of 4
1. Each entry in a two-way table is called a joint frequency.
about the same whether they have a tablet computer or not.
were asked
academic goals.
Noif they set186
98
So,
there
is
not
an
association
between
owning
a
tablet
2. It is appropriate to use a two-way table to organize data
Total
290
306
10.
computer
a cell
phone.
Conditional
Relative
Frequencies
when dataand
are owning
collected
from
one source and belong to two
Conditional
Relative Frequencies
different
categories.
Cat 284 people
312marginal
people have
a dog, while
A
conditional
relative frequency is the ratio of a joint relative frequencySo,
to the
relative
7.4 Exercises
(pp. relative
360 –362)
have
a cat,
306 people
A
conditional
is the
ratio of
a joint relative
to
marginal
relative
No do n
frequency.
You can findfrequency
a conditional
relative
frequency
using afrequency
row total290
or the
apeople
column
total
ofYes
a while
two-way
3. A marginal relative frequency is the sum of the joint relative
596
people
were
asked
whether
they
have a c
frequency.
You
can
find
a
conditional
relative
frequency
using
a
row
total
or
a
column
total
of
a
two-way
table.
Vocabulary
andinCore
Check
frequencies
a rowConcept
or column.
A conditional relative
Yes
104
208
table.
1. Each
entryisinthe
a two-way
called afrequency
joint frequency.
frequency
ratio of atable
jointisrelative
to the
11.
Notes:
No
186
98
marginal
relative
frequency.
Notes:
Participate in Spirit We
2. It is appropriate to use a two-way table to organize data
Total
290
306
data
from
one source
and belong
4. when
In order
to are
findcollected
conditional
relative
frequencies,
you to
cantwo
Yes
No
Undec
different
categories.
use the marginal
relative frequency of each row or of
So, 312 people have a dog, while 284 people
Freshmen
112
56
54
Worked-Out
each column. Or, youExamples
can find the ratio of a joint relative
290 people have a cat, while 306 people do n
3. Worked-Out
A
marginaltorelative
frequency
ismarginal
the sum relative
of the joint
relative
frequency
the corresponding
frequency.
Examples
596Sophomore
people were asked
they have a32
c
92whether68
frequencies
in
a
row
or
column.
A
conditional
relative
Example #1
Worked-Out
Examples
frequencyProgress
is#1
the ratio
of aModeling
joint relative
frequency
to the
Example
Total
204
124
86
11.
Monitoring
and
with
Mathematics
You
conduct
that asks 346 students whether they buy lunch at school. U se the results
marginal
relative
frequency.
Example
#1a survey
Participate
in Spirit
We
of the survey shown in the two-way table.
So, 222 freshmen and
192 sophomores
respo
4. Solve
In order
toequation.
find conditional
frequencies, you can
the
Checkrelative
your solution.
survey. A were
total of
204Yes
students No
say theyUndec
will p
a. How many freshmen
surveyed?
Buy Lunch at School
use the marginal relative frequency of each row or of
in school spirit week, 124 students say they w
Freshmen
112
56
54
were
surveyed?
each column. Or, you canYes
find the ratioNo
of a joint relative b. How many sophomores
86 students are
undecided.
A total of 414 stud
frequency
to the corresponding
c. How many students
buy lunch at school?
surveyed.
Freshmen
92 marginal
86relative frequency.
Sophomore
92
68
32
d. How many students do not buy lunch at school?
12.
Total
204
124
86
MonitoringSophomore
Progress and Modeling
with
116
52 Mathematics
Type of Degree
Table for ExercisesTotal
5–8
208
138
346
So, 222 freshmen and 192 sophomores respo
Bachelor’s
Map
survey. A totalAssociate’s
of 204 students
say they will
Buy Lunch at School
spirit week,
students
a. A total in
of school
178
freshmen
were
surveyed.
5. A total of 178 freshmen were surveyed.
Male
58 124
126say they w
Yes
No
Total
86 students are undecided. A total of 414 stud
b. A total of 168 sophomores were surveyed.
surveyed.
6. A total of
168
sophomores
were
surveyed.
Female
62
118
Freshmen
92
86
178
c. A total of 208 students buy lunch at school.
Total
244
12. of 138
7. A total Sophomore
of 208 students buy
lunch at school.
d. A total
students do120
not buy lunch
116
52
168
Type ofresponded
Degree to
So, 226 males and 228 females
at school.
138at school.346
8. A total of 138 Total
students do208
not buy lunch
A total of 120Associate’s
seniors plan toBachelor’s
receive an asso
Ma
degree, 244 seniors plan to receive a bachelor
5.
Integrated
I
Male Mathematics
58
126
and 90 seniors plan to receive 207
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454Female
seniors
were
surveyed.
All rights
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365
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LLC
6. All
A rights
total reserved.
of 168 sophomores were surveyed.
118
7. A total of 208 students buy lunch at school.
365
Gender
Class
Gender
Class
Class
Class
Dog
Dog
Cell
Phone
Gender
5. Core
Total
All rights reserved.
120
244
4. In order to find conditional relative frequencies, you can
Class
4. In order to find conditional relative
you
can
Yes frequencies,
No
Undecided
Tota
No frequency
186 of each row98or of
284
use the marginal relative frequency of each row or of
use the marginal relative
2. It is appropriate to use a two-way table to organize data
Freshmen
112ratio of a56joint relative
54
222
each column. Or, you can find the ratio of a joint relative
each column. Or,
you
can find the
Total
290 about 52%
306prefer aerobic
596 exerci
13. when data are collected from one source and belong to two
19. Of the students
surveyed,
frequency to the corresponding marginal relative frequency. frequency to the corresponding marginal relative frequency.
andSophomore
about
30% have
are males
who
prefer
68284anaerobic
32doexercise.
192
different
categories. Traveled on an Airplane
So,
312
people
dog,
while
people
not. Also,
Name _________________________________________________________
Datea92
_________
290 people
have
a cat,
306Mathematics
people do86
not. A total414
of
Yes is the sum
Total
204while
Monitoring
Progress
Modeling
withNo
Monitoring20.
Progress
and
Modeling
with
Of the sandwiches
included
in124
the survey, 55%
are on whe
3. A marginal
relative and
frequency
ofMathematics
the jointTotal
relative
596
people
were
asked
whether
they
have
a
cat
or
dog.
10.4
Practice
(continued)
bread and 34% are turkey on white bread.
Tablefrequencies
for Exercises
in a5–8
row or column.
Freshman
90 A conditional
62 relative152
Male
58
126
42
226
Total
80
120
200
#2No
6. Example
A total of 168
sophomores64
were surveyed.
Female
62
118
48
228
82
146
MAKING TWO-WAY TABLES A car dealership has 98 cars on its lot. Fifty-five
cars are new.
Of the new 90 I
Integrated
Mathematics
Menu
Total of the120
244
454
109
136
245
7. cars,
A total36ofare
208domestic
students buy
lunch
at school.
cars.
There
are 15 used foreign cars on the lot. Organize this information
in a two-way
Worked-Out
Solutions
Potluck
Cateredto the survey.
­table.
Include
the marginal frequencies.
Extra
Practice
So, 226 males and 228
females responded
8.
A
total
of
138
students
do
not
buy
lunch
at
school.
16.
36 plan to receive
48 an associate’s
A total of
120 seniors
≈ 0.43
≈ 0.57
—
—
Lunch
84
84
In Exercises 1 and 2, find and interpret the marginal frequencies.
Meal
Practice A
Condition
17.
Used
Attend College
Domestic
ForeignMale
Total
Female
Practice
A
Extra Practice
Total 2.
36 Yes
28 No
64
19 98
15132
34
55
43
98
120
88
Gender
New
Gender
Origin
1.
degree, 244 seniors plan to receive a bachelor’s degree,
44
72
≈ 0.38 a master’s
≈ 0.62
—
Dinnerplan —
and 90 seniors
to receive
degree. A total of
116
Own a Car116
454 seniors were surveyed.
Yesthat an employee
No
So, given
prefers a lunch event, the
118he or she prefers
48
228
conditional relative62
frequency that
a cate
Male
54
136
event is about 0.57, or 57%.
Total
120
244
90
454
Integrated
Mathematics I
45
137
Female
24.
Menu
Worked-Out
Solutions
Potluck Type
Catered
Total
Tiger
Dragon Tot
Type ofHawk
Degree
Lunch
36
48
84
Aerobic
Anaerobic
Total
Associate’s
Bachelor’s
Master’s
Tota
Realistic
67
74
51
192
In Exercises 1 and 2, find and interpret the marginal frequencies.
Dinner
44
72
116
88
104
≈ 0.25that asks
0.30
— ≈85
Male
1.
2. school whether they are
3. You
conduct—
a survey
students0.55
in your
in Math
350
Cartoon
24
100
Own
a CarClub58or Chess 18
Attend350
College
Club. Thirty-five
of the students
are in Math Club, and 20 of those students are also in Chess Club.
96
62
≈ 0.27
≈No
0.18
—
Female
0.45
92
75
292
Yes Total No125
Yes —
350the students
350
Thirty-eight of
are not
in Math Club or Chess Club. Organize the results in a two-way
37
Total
0.52
0.48
table.
Include
marginal
1
Male
54
136
98 frequencies.
132
Male the
Type
Female
120
Meat
Turkey
88
Ham
Total
45
Female
Style
18.
Gender
Gender
Gender
Style
Exercise Preference
Realistic
137Tiger
67
≈ 0.54
—
125
Hawk
74
≈ 0.80
—
92
Dragon
51
=
—
75
37
0.68
Bread
452
146
Mathematics
208 Integrated
≈ 0.34 I—
≈ 0.11
White
—
1348
1348
0.55
Journal
CopyrightStudent
© Big Ideas
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328
422
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366
≈ 0.24that —
Wheat
3. You
conduct—
a survey
asks≈850.31
students0.45
in your school
1348
1348
58
18
≈ 0.46
—
Cartoon —
92
Copyright © Big125
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≈ 0.20
24
= 0.32
—
75
So, given that a student prefers a hawk mascot, the
whetherconditional
they are inrelative
Math Club
or Chess
frequency
that he or she prefers a carto
Club. Thirty-five of the students are in Math Club, and 20 of those students are also in Chess Club.
98
132
Female
120
88
Gend
Gend
Male
Male
54
136
Female
45
137
Name_________________________________________________________
10.4
Date __________
Practice (continued)
3. Make
You conduct
a survey
85the
students
in your
school
whether
they are in Math Club or Chess
4.
a two-way
table that
that asks
shows
joint and
marginal
relative
frequencies.
Gender
Club. Thirty-five of the students are in Math Club, and 20 of those students are also in Chess Club.
Catcher
in theClub.
Rye Organize the results in a two-way
Thirty-eight of the students are not in Read
Math Club
or Chess
table. Include the marginal frequencies. Yes
No
Male
96
80
Female
54
88
Name
__________
Integrated Mathematics I
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Practice (continued)
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366
4. Make a two-way table that shows the joint and marginal relative frequencies.
Read Catcher in the Rye
Yes
No
Gender
5. A company is organizing aMale
baseball game96for their employees.
80 The employees are asked whether
they prefer to attend a day game or a night game. They are also asked whether they prefer to sit
in the upper deck or lower
deck. The results
54 are shown in a88two-way table. Make a two-way table
Female
that shows the conditional relative frequencies based on the row totals. Given that an employee
prefers to go to a day game, what is the conditional relative frequency that he or she prefers to
sit in the lower deck?
Game
Time
Seat
Day
Upper
Lower
28
34
Night
22
52
5. A company is organizing a baseball game for their employees. The employees are asked whether
they prefer to attend a day game or a night game. They are also asked whether they prefer to sit
in the upper deck or lower deck. The results are shown in a two-way table. Make a two-way table
that shows the conditional relative frequencies based on the row totals. Given that an employee
prefers to go to a day game, what is the conditional relative frequency that he or she prefers to
sit in the lower deck?
Game
Time
Seat
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Upper
Lower
Day
28
34
Night
22
52
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Name_________________________________________________________
Date __________
Practice
7.4 BPractice B
In Exercises 1 and 2, find and interpret the marginal frequencies.
1.
2.
Yes
No
Yes
33
112
No
24
20
Airplane
Train
Tea
Coffee
Yes
No
Yes
5
3
No
278
321
In Exercises 3 and 4, complete the two-way table.
3.
Participated in a Triathlon
Gender
Yes
Female
No
Total
24
137
142
Male
306
Total
4.
Dual Enrollment Student
Class
Yes
Total
Total
247
Sophomore
Senior
No
83
432
550
5. You conduct a survey that asks 397 students in your school about whether they have
played a musical instrument or participated in a sport. One hundred eighteen students
have played a musical instrument and 57 of those students have participated in a sport.
Thirty-four of the students have not played a musical instrument or participated in a
sport. Organize the results in a two-way table. Include the marginal frequencies.
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