MODULE
STUDY GUIDE REVIEW
Multi-Variable Categorical Data
Essential Question: How can you use multi-variable categorical
data to solve real-world problems?
KEY EXAMPLE
(Lesson 8.1)
The principal of a high school surveyed 9th and 10th graders as
to whether they want to go on a field trip to the museum, zoo, or
botanical garden. The results of the survey are in the following
table. Complete the table.
Preferred Field Trip
Grade
Museum
Zoo
Botanical
Garden
9 th
42
28
31
52
62
80
93
10 th
Total
70
42 + 28 + 31 = 101
70 - 42 = 28
Total
142
Key Vocabulary
8
categorical data
(datos categóricos)
conditional relative frequency
(frecuencia relativa
condicional)
frequency table (tabla de
frecuencia)
joint relative frequency
(frecuencia relativa
conjunta)
marginal relative frequency
(frecuencia relativa
marginal)
quantitative data (datos
cuantitativos)
relative frequency (frecuencia
relativa)
Find the 9th grade row total.
Total who prefer the museum - 9th graders who prefer the museum
70 + 80 + 93 = 243 and 101 + 142 = 243
Find the grand total.
© Houghton Mifflin Harcourt Publishing Company
Preferred Field Trip
Grade
Museum
Zoo
Botanical
Garden
Total
9 th
42
28
31
101
10 th
28
52
62
142
Total
70
80
93
243
KEY EXAMPLE
(Lesson 8.2)
The principal wants to know if the percent of 10th graders who prefer the zoo is greater than
the percent of total students who prefer the zoo. Find the conditional relative frequency of 10th
graders who prefer the zoo and the marginal relative frequency of students who prefer the zoo.
Compare the results.
The percent of 10th graders who prefer the zoo is given by the conditional relative frequency:
Number of 10 th graders who prefer the zoo _
____
= 52 ≈ 0.37
142
Total number of 10th graders
The percent of total students who prefer the zoo is given by the marginal relative frequency:
Number of students who prefer the zoo _
____
= 80 ≈ 0.33.
243
Total number of students
Since 37% > 33%, the percent of 10 th graders who prefer the zoo is greater than the percent of
total students who prefer the zoo.
Module 8
371
Study Guide Review
EXERCISES
1.
Complete the two-way frequency table. Interpret the meaning of the number in the starred cell of the
table. (Lesson 8.1)
Preferred Mode of Transportation
Age
Bike
Car
Bus
Adults
25
3
12
Teenagers
5
28
12
Total
2.
Total
*
A middle school student surveyed middle school and high school teachers on whether they preferred
to have their students write in pen. (Lesson 8.2)
Prefer Students Use Pen
Grade Level
Yes
No
Total
Middle School
3
18
21
High School
7
12
19
Total
10
30
40
Are middle school teachers or high school teachers more likely to prefer that their students
use pen? Explain.
MODULE PERFORMANCE TASK
Survey Says?
Visit a Foreign
Country
Attend Camp
Visit a National
Park
Grades 7–9
25
40
15
Grades 10–12
70
20
30
© Houghton Mifflin Harcourt Publishing Company
Students in grades 7–12 were surveyed about which of the following they would most like to do
during 2 weeks of a summer vacation: visit a foreign country, attend camp, or visit a national
park. The students were divided into two groups, Grades 7–9 and Grades 10–12. Here are the
results:
• Make a table showing the relative frequency of each of the six categories in the
table compared to the results for the entire table.
• Make a circle graph, histogram, or bar graph showing the frequencies or
relative frequencies of each of the six categories in the table.
• Write and answer at least five questions involving conditional relative
probability that can be answered by referring to the table.
• Describe any trends you see in the data.
Use your own paper to work on the task. Use numbers, words, or algebra to explain how you
reached your conclusion.
Module 8
372
Study Guide Review
Ready to Go On?
8.1–8.2 Multi-Variable Categorical Data
1.
A researcher surveyed 135 people, 85 females and 50 males. The researcher asked
each person which of the following types of movies they preferred: action, comedy,
or drama. Complete the table. (Lesson 8.1)
• Online Homework
• Hints and Help
• Extra Practice
Favorite Type of Movie
Gender
Action
Female
35
Male
12
Comedy
Total
18
28
Total
2.
Drama
28
Based on the data given in the frequency table below, does a greater percent of
11 th or 12 th graders surveyed like tennis? Use conditional relative frequencies to
support your answer. (Lesson 8.2)
© Houghton Mifflin Harcourt Publishing Company
Like Tennis
Grade
Yes
No
Total
11th
55
55
110
12th
64
32
96
Total
99
97
206
ESSENTIAL QUESTION
3.
How can you compare values in tables of two-variable categorical data?
Module 8
373
Study Guide Review
MODULE 8
MIXED REVIEW
Assessment Readiness
1. Look at each variable. Is the variable best represented by categorical data? Select
Yes or No for each variable.
A. Favorite song
Yes
No
B. Car color
C. Weight
Yes
Yes
No
No
2. Mazin asked his classmates whether they like soccer and whether they like
running. The table shows the results of his survey.
Like Running
Like Soccer
Yes
Yes
12
No
Total
6
18
No
Total
24
31
Complete the table. Choose True or False for each statement.
A. 12 students like soccer but not running.
True
B. Mazin surveyed 55 students in all.
C. 25 students like soccer.
True
True
False
False
False
Use the following information for questions 3 and 4.
Samantha is preparing to do a survey of the language classes taken by ninth and tenth graders
at her high school. Each student in ninth and tenth grade takes one language class. From
school records, she knows there are 158 students in the ninth grade, as shown in the table.
Language
French
Mandarin
Spanish
Total
9
r
s
t
158
10
x
y
z
Total
3. Write an expression to represent the conditional relative frequency that a student
takes Mandarin, given that the student is a tenth grader. Explain how you created
the expression.
4. Based on school records, Samantha finds out that there are 65 students in ninth
grade who take Spanish and 35 students in ninth grade that take French. Find the
conditional probability that a student takes Mandarin, given that the student is a
ninth grader. Show your work.
Module 8
374
Study Guide Review
© Houghton Mifflin Harcourt Publishing Company
Grade