Lesson 27-2
Types of Variables and Graphs
Activity 27
continued
My Notes
Learning Targets:
Identify types of statistical variables.
Write statistical questions.
Construct graphs to represent statistical data.
•
•
•
SUGGESTED LEARNING STRATEGIES: Marking the Text, Create
Representations, Sharing and Responding
The answer to each question in your class survey represents a variable.
Gender and eye color are examples of categorical variables, because they
place each individual into a category, such as people with blue eyes.
Categorical variables can be summarized to show how often each
category occurs.
Another type of variable is a numerical variable. Numerical variables
occur when the data collected results in numbers. Weight and age are
examples of numerical variables.
1. Identify each question in your class survey as an example of a
categorical (C) variable or a numerical (N) variable.
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Question
C
N
Question
1. Gender
7. Superpower
2. Eye Color
8. Room number
3. Height
9. Minutes to get ready
4. Number of people
10. Computer hours
5. Birth month
11. Pieces of gum
6. Number of pets
12. Hand span
C
N
A variable with values represented by numbers is not automatically
a numerical variable. Numerical variables have values for which
numerical calculations, such as averages or addition, would make
sense. If either of those operations does not make sense, the variable
is categorical. For example, a zip code is a number, but it is a
categorical variable.
2. Review your answers to Item 1. Should any of your numerical
variables be changed to a categorical variable?
CONNECT TO AP
Key concepts in AP Statistics
include summarizing data,
creating graphical displays, and
recognizing the difference
between numerical (also called
quantitative) and categorical
variables.
3. Write a new question to add to the class survey.
Activity 27 • Summarizing Data Graphically 351
Lesson 27-2
Types of Variables and Graphs
Activity 27
continued
My Notes
4. Do the answers to your new question produce a categorical or a
numerical variable?
Data needs to be organized to analyze it and see patterns. One way to
organize data is to create a table. Marshall collected the following
categorical data about the eye color of the students in his class.
• Number of students with blue eyes: 6 girls, 7 boys
• Number of students with brown eyes: 9 girls, 6 boys
• Number of students with hazel eyes: 3 girls, 4 boys
Study the table below to see how this data can be organized.
Eye Color
Gender
Girls
Boys
Total
Blue
6
7
13
Brown
9
6
15
Hazel
3
4
7
18
17
35
Total
With the data organized, you can now use it to make calculations.
Example A
Step 1:
Eye Color
Step 2:
The total number of girls is 18, so the fraction of girls with
blue eyes is 6 , or 33.3%
18
Calculate the percentage of girls with brown and hazel eyes.
Girls
Count
Fraction
Percent
Blue
6
6
18
33.3%
Brown
9
9
18
50%
Hazel
3
3
18
16.7%
Total
18
18
18
100%
By looking at the data about eye color for girls, you can quickly see
which eye color is the most common for girls in your class.
352 Unit 6 • Data Analysis
© 2014 College Board. All rights reserved.
Calculate the percentage of girls with each eye color.
Lesson 27-2
Types of Variables and Graphs
Activity 27
continued
My Notes
Try These A
Create a table for boys with each eye color in Marshall’s class.
Boys
Count
Fraction
MATH TERMS
Percent
A bar chart (also called a bar
graph) is used to graph categorical
data.
Eye Color
Blue
Brown
Hazel
Total
The preceding table of percentages is a relative frequency chart. Since it
shows what frequencies are calculated, a percent bar chart can be created
as a visual display of the results. For example, look at the bar chart below.
Female Eye Color
MATH TERMS
The mode is the value in the data
that occurs most often.
Percent
50
40
30
20
10
0
Blue
Brown
Hazel
© 2014 College Board. All rights reserved.
Eye Color
The category of brown eyes is the mode for the females in the class since
that eye color occurred most frequently in this group.
5. Create a percent bar graph for males based on the relative frequency
chart and identify the mode.
6. Compare and contrast the eye color distributions for males and
females in Marshall’s class.
In earlier grades, you used bar charts to graph categorical data. In
describing a bar chart, you would discuss which category occurred the
most often or the least often. Distributions for numerical data are created
using dot plots and stem-and-leaf plots.
Activity 27 • Summarizing Data Graphically 353
Lesson 27-2
Types of Variables and Graphs
Activity 27
continued
My Notes
Suppose the students in Douglas’s class have the following heights.
57
56
58
55
56
60
56
58
57
55
61
57
53
58
58
56
57
59
57
59
60
59
54
7. How might these heights have been measured? In what units were
the heights measured?
8. You might wonder what a typical height is or whether height values
vary a lot. Could you easily give answers for typical height and
variability by looking at a list of values like the one above?
MATH TERMS
Dot plots (also called line plots)
are used to graph numerical data.
Be sure to include a scale on the
dot plot.
Data needs to be organized to help you analyze it and see patterns. One
way to organize data is to show it in a graph. Graphical displays, such
as dot plots, help you to easily see how the data are distributed—where
the data are centered and how spread out the data are. You can also see
the overall shape of the distribution and whether any values appear
unusual. To create a dot plot:
• Draw a number line with an appropriate scale.
• Place a dot above the appropriate value on the number line for each
piece of data. If the value occurs more than once, stack the dots
vertically.
10. Reason abstractly and quantitatively. How would you describe
the shape of this distribution? Is the distribution shape easier to see
in the dot plot or in the list of numbers?
11. List the heights of students in your class from the class survey.
354 Unit 6 • Data Analysis
© 2014 College Board. All rights reserved.
9. Create a dot plot for the heights of students in Douglas’s class.
Lesson 27-2
Types of Variables and Graphs
ACTIVITY 27
continued
My Notes
12. Create a dot plot for the heights of students in your class.
13. Describe the shape of the distribution of heights for students in
your class.
Another type of graph that can quickly reveal the shape of the distribution
for a numerical variable is a stem plot.
Example B
Draw a stem plot for the baseball games won for each of the 20 seasons
that Curt Schilling pitched in the major leagues, shown below.
© 2014 College Board. All rights reserved.
0
15
0
15
1
11
3
22
14
23
16
8
2
21
7
8
9
15
17
9
Step 1:
Draw a vertical line. On the left side, write the tens digits of
the numbers in the data set.
Step 2:
Next to each number in the stem, write the units digit of each
corresponding number in the data set. These numbers are the
leaf. There will be as many leaves as there are numbers in the
data set, which in this example is 20.
Stem Leaf
0
1
2
0
1
1
0
4
2
1
5
3
2
5
3
5
7
6
8
7
8
9
MATH TERMS
A stem plot (also called a stemand-leaf plot) displays data that is
organized by place value. The
stem, which is to the left,
represents the first digit (or digits)
and the leaf represents the last
digit of the number. For example,
the number 14 is represented by a
1 on the left with a 4 on the right
separated by a vertical line: 1 | 4.
9
Try These B
a. Create a stem-and-leaf plot of the recorded low temperatures for the
past 15 days.
39
51
42
32
38
38
46
42
50
45
43
53
47
50
46
b. Create a stem-and-leaf plot for the number of boxes of cookies sold
in the fundraiser by each member of the class.
6
2
13
0
0
2
11
21
15
8
11
1
3
1
7
15
16
12
20
9
30
17
22
21
Activity 27 • Summarizing Data Graphically
355
Lesson 27-2
Types of Variables and Graphs
Activity 27
continued
My Notes
Check Your Understanding
14. Write three questions to add to the class survey that lead to
categorical variables.
15. Write three questions to add to the class survey that lead to
numerical variables.
16. Write a few sentences explaining what a dot plot is and how it helps
to organize numerical data.
LESSON 27-2 PRACTICE
17. Model with mathematics. Construct a bar chart for the following
information: There are 20 students in Mrs. Smith’s class, 30 students
in Mr. Yu’s class, and 40 students in Ms. York’s class.
Female
Count
Blue
13
Brown
15
Hazel
 7
Total
35
Fraction
Percent
19. Why would it not be appropriate to create a dot plot for
Items 17 and 18?
20. Consider the daily high temperatures over the last fifteen days.
Create a dot plot to represent this information.
86
90
  88
96
90
88
90
  92
94
90
90
90
100
92
98
21. Describe the shape of the distribution of temperatures. What
conclusions can you draw from the graph?
356 Unit 6 • Data Analysis
© 2014 College Board. All rights reserved.
Eye Color
18. Construct a relative frequency chart and percent bar graph for the
eye color of all students in Marshall’s class. Identify the mode for the
eye color distribution of the class.