Name ________________________________________ Date __________________ Class __________________
LESSON
8-2
Relative Frequency
Practice and Problem Solving: A/B
The two-way frequency table below represents the results of a survey
about favorite forms of entertainment. In Exercises 1–3, write
fractions that are not simplified as responses.
Like Board Games
Like Reading
Yes
No
Total
Yes
48
25
73
No
43
9
52
Total
91
34
125
1. Find the joint relative frequency of people surveyed who like
to read but dislike playing board games.
_______________
2. What is the marginal relative frequency of people surveyed who
like to read?
_______________
3. Given someone interested in reading, is that person more or less likely
to take an interest in playing board games? Explain.
_________________________________________________________________________________________
_________________________________________________________________________________________
4. Given someone interested in board games, is that person more or less
likely to take an interest in reading? Explain your response.
_________________________________________________________________________________________
_________________________________________________________________________________________
The two-way frequency table below represents the results of a survey
about ways students get to school.
Type of Transportation
Grade
On Foot
By Car
By Bus
Total
9
15
28
64
107
10
20
30
43
93
Total
35
58
107
200
5. Find the joint relative frequency of students surveyed who walk to
school and are in grade 9.
_______________
6. Given grade level, is that person more or less likely to travel to school
by bus? Explain your response.
_________________________________________________________________________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
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143
2. 49
Sample explanation: In the Total column,
150 − 78 = 72; so there are 72 boys in all.
In the Boy row, 72 − 23 = 49; so 49 boys
do not play a musical instrument.
Practice and Problem Solving:
Modified
1. 14;
13;
Add the two numbers in the Carrots
column to get 34;
Add the totals in the far right column or
add the totals along the bottom row of the
table to get 100.
Preferred Vegetable
Grade Carrots Celery Cucumber Total
14
18
13
45
9
20
22
13
55
10
34
40
26
100
Total
3. No
Sample explanation: The given data has
only one characteristic, which is the type
of ticket (adult or student). A two-way
frequency table is used when the data has
two characteristics.
LESSON 8-2
Practice and Problem Solving: A/B
2.
Preferred Fruit
Grade
Apple
Orange
Berries
Total
9
21
18
13
52
10
24
19
19
62
Total
45
37
32
114
1.
25
125
2.
73
125
3. Calculate frequencies with a row total as
the denominator.
Likes reading and likes board games:
48
,
73
about 0.658
3.
Likes reading but does not like board
25
games:
, about 0.342
73
Foreign Language
Gender Italian Spanish French Total
6
10
12
28
Boys
19
6
7
32
Girls
25
16
19
60
Total
Those who like reading are more likely to
like board games.
4. Calculate frequencies with a column total
as the denominator.
Reading Strategies
1. A, C, D
Likes board games and likes reading:
2. B, E, F
48
,
91
about 0.527
3. Sample answer: Questions B, E, and F
ask about preferences between and
among the men and women who were
polled. The two-way frequency table
contains data for a second category,
which is the gender of the people who
were polled.
Likes board games but does not like
43
, about 0.472
reading:
91
Those who like board games are more
likely to like reading.
5.
Success for English Learners
15
200
6. Calculate frequencies with a row total as
the denominator.
1. Sample answer: The table would have
another row of frequencies between the
Large row and the Total row. The phrase
Extra Large would be in the left cell of
the row.
Grade 9 and travels by bus:
64
, about
107
0.598
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533
Grade 10 and travels by bus:
43
, about
93
7.
0.462
15
or 0.075
200
8. Calculate frequencies with a row total as
the denominator.
Grade 9 students are more likely to travel
by bus than not. Grade 10 students are
more likely not to travel by bus.
Adult and travels by bus:
0.598
Practice and Problem Solving: C
1.
Child and travels by bus:
Like Televised Sports
Gender
Yes
No
Total
Men
48
25
73
Women
43
9
52
Total
91
34
125
Adults are more likely to travel by bus
than not. Children are more likely not to
travel by bus.
Practice and Problem Solving:
Modified
3. 72.8%
1. 28; 140;
4. Calculate frequencies with a row total as
the denominator.
28
140
2. 56; 140;
56
140
48
,
73
3.
about 65.8%
Male but does not like televised sports:
25
, about 34.2%
73
5.
1.
48
,
91
Likes televised sports but is not male:
43
, about 47.2%
91
6.
Type of Transportation
15
28
64
107
Child
20
30
43
93
Total
35
58
107
200
42 21
=
= 0.42 = 42% ; marginal relative
100 50
frequency
3. Sample answer: What is the conditional
relative frequency that a student plays a
team sport, given that the student plays
chess?
Sample solution:
chess and sport
12 3
=
=
"Yes" chess row total
16 4
= 0.75 = 75%
Those who like televised sports are more
likely to be male.
Adult
8
66
2. The given condition is that the student
plays a team sport, so you are only
looking for a relationship among numbers
in that column.
about 52.7%
On Foot
28
74
Success for English Learners
5. Calculate frequencies with a column total
as the denominator.
Age
30
140
4. 28; 74;
Men are more likely to like televised
sports.
Likes televised sports and is male:
43
, about
93
0.462
2. 38.4%
Male and likes televised sports:
64
, about
107
By Car By Bus Total
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
534