Ch. 10 Pretest
Two Categorical Variables
Name ______________________________
Period _________
1. Richard plans to write a sports article for the school newspaper, but he isn’t sure which sport
to write about. To help in making the decision, he surveys a random group of students about
which sport they like best, and whether they prefer to watch it at the college or professional
level. The table shows the results.
a. Create a Frequency Marginal Distribution of the Data.
b. Identify the variables of the data from Richard’s findings. Are the variables in the
table numerical or categorical? Explain your reasoning.
c. Identify the groups for the variable, ____________ . What are the groups for this
variable?
d. Identify the groups for the variable, ____________ . What are the groups for this
variable?
e. How many people did Richard survey?
f. Make 4 different observations from the data.
2. Richard plans to choose a book for his advanced reading group, but he isn’t sure genre to
choose. To help in making the decision, he surveys a random group of students about which
genre they like best.
a. The table shows the results. Complete the frequency marginal distribution table.
b.
c.
d.
e.
f.
g.
How many Boys participated in the survey?
How many students prefer Science Fiction?
How many students prefer Non-Fiction?
How many Girls prefer Historical Fiction?
Which Genre of book is the least favorite of all students?
Which Genre of book is the most favorite of Girls?
h. Construct a bar graph of the
frequencies. Let the x-axis
represent the Gender.
i. Construct a bar graph of the
frequencies. Let the x-axis represent
the Genre.
j. Which genre of book would you recommend he pick? Explain your reasoning.
3. Karl is opening his own bakery. He is able to make a number of different desserts but he
wants to make sure he sells desserts that his customers like. He notices that most of the people
around town are either young families or older couples. He takes a survey asking people to
choose their favorite from four desserts he can make and organizes the data by the age of the
person surveyed. The frequency marginal distribution shows the results of his survey.
a. Construct a relative frequency marginal distribution for the data.
b. Construct a stacked bar graph of the
frequencies. Let the x-axis represent
the Age Group.
c. Construct a stacked bar graph of the
frequencies. Let the x-axis represent
the Favorite Dessert.
d. Karl wants to focus on 2 desserts to highlight at a local festival. Which two do you
recommend that he choose? Explain your reasoning.
4. A gym teacher is trying to decide which sport to play during class for the last week of
school. She surveys the students in her 9th and 10th grade class and organizes the data
according to the grade level of the students. The marginal frequency table shows the results of
her survey.
a. Construct a relative frequency conditional distribution of the data given the Grade.
b. Construct a relative frequency conditional distribution of the data given the Preferred Sport.
c. Which sport is most preferred by 9th graders? by 10th graders?
d. Which sport is least preferred by 9th graders? by 10th graders?
e. Of the students who like Baseball, what percent are 9th graders? What percent are 10th?
e. The gym teacher wants both grades to play the same sport. Which sport should she
choose? Explain your reasoning.
Review
5. Evaluate the following expressions.
1
3
3
4
a. − −
1
2
5
3
b. − +
1
6. Solve.
a. 2 − 5(𝑥 − 3) = −7𝑥 + 9
d.
5
4
÷
9
e.
3
0
8
4
f.
0
b. 3(2 + 3𝑥) = 1 − 𝑥 + 5
−2(𝑥 − 5) + 5 = 29
c.
3
c. − (− )
4
5
d.
1
2
𝑥+3=𝑥−1
7. Find the slope and then write the equation of the line
a.
(17, 5) & (22 , 11)
b.
(11, -5) & (6 , 2)
8. Interpret the following correlation coefficients (r-value).
a. 𝑟 = 0.8534
b. 𝑟 = −0.0045
c. 𝑟 = 0.3914
d. 𝑟 = −0.802
9. Simplify/Evaluate each of the following
a.
f. 5
3
𝑥 ∙𝑥
5
3
k. (2𝑥 2 𝑦 −3 )4
b.
(𝑥 6 )4
g. (𝑥 3 )4
𝑥 −3
l. ( )
4
c.
15𝑦 8
20𝑦 2
1 −2
𝑥 4 ∙𝑥 3
d.
(𝑥 −2 )−5
7 3 2
𝟑 −𝟐
e) ( )
𝒙
20𝑥 12 𝑦 5
h. ( )
7
i. 2𝑥 𝑥 𝑥
j.
m. (𝐴𝐵3 )0
n. −24
p. (−2)4
5𝑥 2 𝑦 11