-20
Concept
CCByte
Guided Instruction
Use With Lesson 12-5
A C T I V I T Y
PURPOSE To use two-way frequency tables to
analyze data and to make predictions
PROCESS Students
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calculating ratios and percents.
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trends in two-way frequency tables.
DISCUSS Students first determine what the values
in a two-way frequency table represent. Then they
write ratios and percents to compare data and
draw conclusions.
Two-Way
Frequency Tables
Content Standard
S.ID.5 Summarize categorical data for two
categories in two-way frequency tables . . .
Recognize possible associations and trends in
the data.
Two-way frequency tables are a convenient way to show data.
1
Th
bl at the right gives information about ticket sales for two movies. The table also
The table
separates those sales into ticket purchases by men and ticket purchases by women.
Of the 103 tickets sold for Story of Love, 78 tickets, or 75.7%, were
sold to men. Of the 90 men who purchased tickets, 78 of them, or
86.7%, purchased a ticket for Story of Love.
Movie Ticket Sales
Movie
Gender
Calculate the ratio and percent for each of the following.
1. Men who purchased tickets to Martial Arts Champ to all men.
Martial Arts Champ
Story of Love
Men
78
12
Women
25
86
2. Men who purchased tickets to Martial Arts Champ to all who
purchased tickets to Martial Arts Champ.
Activity 1
In this Activity students write ratios and percents
to analyze the data and draw conclusions about
the data.
3. Women who purchased tickets to Martial Arts Champ to all who purchased tickets
to Martial Arts Champ.
4. Women who purchased tickets to Story of Love to all who purchased tickets to
Story of Love.
Q What is the total number of women who
5. Which movie is more popular with women? With men?
purchased movie tickets? [111]
Q How many people purchased tickets to Martial Arts
Champ? [98]
2
You can use two-way frequency tables to make better predictions.
The citizens of Parkdale are preparing to vote on a bond issue to fund an expansion of
the public library. The table at the right records data about support for the bond issue.
Activity 2
In this Activity students write ratios and percents to
analyze the data and make a prediction.
For each of the following, calculate the ratio and percent in relation to
all people in the given age group.
Support for Bond Issue
Age
6. The people between 18 and 25 who support the bond issue.
7. The people between 26 and 64 who support the bond issue.
Q How many people surveyed were ages
8. The people 65 or older who oppose the bond issue.
18–25? [100]
Q What is the ratio of people 65 or older who
support the bond issue to the total number of
people 65 or older? [33 : 100]
Q What is 10% of 79? [7.9]
Mathematical Practice This Concept Byte
supports students in becoming proficient in
reasoning quantitatively, Mathematical Practice 2.
1
Common Core
26–64
# 65
79
55
33
Oppose
21
45
67
9. The people between 26 and 64 who oppose the bond issue.
10. An expert predicts that 10% of the voters will be between 18 and 25, 40% will be
between 26 and 64, and 50% will be 65 or older. Based on her predictions, she can
calculate the result of the election from the expression 0.1a 0.4b 0.5c where a,
b, and c are the decimal forms of the ratio of people supporting the bond issue in
the three groups. Predict the percent of votes in favor of the bond issue.
ELL SUPPORT
Point out to students that Exercises 6–9 in Activity
2 are similar to Exercises 1–4 in Activity 1. Make
sure students understand what number to use for
the second part of the ratio. For example, Exercise
6 can be written as “The people between 18 and
25 who support the bond issue to all the people
between 18 and 25.”
18–25
Support
1
Common Core
Answers
Activity 1
1.
2.
3.
4.
5.
12 : 90; about 13.3%
12 : 98; about 12.2%
86 : 98; about 87.8%
25 : 103; about 24.3%
Martial Arts Champ; Story of Love
Activity 2
6.
7.
8.
9.
10.
79 : 100; 79%
55 : 100; 55%
67 : 100; 67%
45 : 100; 45%
46.4%