Topic 6: Misleading Graphs
for use before
Samples and Populations
(
Investigation 1
When making graphs, choose an appropriate scale divided into equal
intervals that fit the data being presented. A scale that is too widespread or
too narrow can give the reader a false visual impression. Graphs that use
those techniques are
misleading graphs.
A. Use the bar graph below to answer parts (1)–(6).
1. Which team appears to have won twice as many games as the
Panthers have won?
2. Find the difference in the number of wins between the two teams of
part (1).
3. What do you notice about the vertical scale of the bar graph?
4. Make a table of teams and wins.
5. Draw a bar graph from your table of values using a vertical scale
starting at a zero.
6. Which graph better represents the data? Explain.
B. A
break symbol
is an insertion at the beginning of a scale to indicate
that the scale does not begin at zero.
1. How does a break symbol help you draw a graph?
2. Can a graph with a break symbol be misleading?
C. Kevin states that a graph is misleading if the scale does not begin at
zero. Do you agree or disagree? Explain.
Little League Results
Bears
Number of Games Won
Teams
Badgers
Tigers Panthers
20
22
24
26
28
30
Problem
6.1
Exercises
1. The bar graph shows the results of a survey taken at Brookfield Middle
School.
a. Which subject appears to be twice as popular as science?
b. How is the graph misleading?
c. How can you change the graph so that it is not misleading?
2. Use the table below to answer parts (a)–(d).
a. Make a line graph giving the impression that there have been many
new clients since the television ad first aired.
b. Make a line graph that indicates a small increase in the number of
clients.
c. Which graph more fairly represents the data?
d. Why would someone want to exaggerate the number of new
clients?
Month
Feb. Mar. Apr. May. June.
Company Growth Since Onset of TV Advertisement
Number of
New Clients
35
38
40
42
43
44
Jan.
Favorite Subject
Math
Number of Students
Subject
Social
Studies
Science
30
40
50
60
70
Topic 6: Misleading Graphs
Guided Instruction
Mathematical Goals
• Explain how misleading representations affect interpretations and
conclusions about data.
Vocabulary
•
misleading graphs
•
break symbol
Materials
•
Labsheet 6.1
•
Labsheet 6ACE
Exercise 2
At a Glance
To introduce the topic, discuss the characteristics of a bar graph. Ask:
•
Why do you use a bar graph?
(to compare amounts)
•
What information is placed on the horizontal axis?
(the categories)
•
What information is placed on the vertical axis?
(the amounts)
•
How would you describe the intervals on the vertical axis?
(The intervals are equal in quantity and in height.)
•
Why is it easier to compare quantities with a bar graph than in a table?
(Bar graphs are visual and can be interpreted quickly.)
Review the characteristics of a line graph. Ask:
•
Why do you use a line graph?
(to show changes over time)
•
What information is placed on the horizontal axis?
(measures of time)
•
What information is placed on the vertical axis?
(the amounts)
•
How would you describe the intervals on the vertical axis?
(The intervals are equal in quantity and in height.)
•
Why is it easier to see changes over time with a line graph than in a
table?
(Line graphs are visual and quickly show upward or
downward trends.)
Summarize by asking:
•
How does the data compare in a graph that has been scaled properly
with one that has been scaled improperly?
(The data is the same.)
•
Then why is it so important to scale properly?
(The impressions given
by the properly-scaled and the improperly-scaled graphs are
entirely different.)
•
When would someone choose an inappropriate scale?
(to influence the
person using the graph)
You will find additional work on graphing data in the Grade 7 unit
Data Distributions
.
PACING
1 day
ACE Assignment Guide
for Topic 6
Core
1–2
Answers to Topic 6
Problem 6.1
A. 1.
the Bears
2.
1
3.
The scale goes from 20–30; it does not
start at zero.
4.
5.
6.
The graph of part (5) better represents the
data because the height of each bar is
appropriate for its value. A visual
comparison of the teams is accurate and
not distorted.
B. 1.
You can skip small numbers when the data
represents large numbers.
2.
When there is a break in the graph, the
area of the bars is not proportional to
the values.
C.
Answers may vary. Sample: A graph is
misleading when a scale does not begin at
zero.
Exercises
1. a.
social studies
b.
The vertical scale starts at 30.
c.
Change the vertical scale to start at zero.
2. a.
Answers may vary. Sample:
b.
Answers may vary. Sample:
c.
the second graph
d.
Answers may vary. Sample: A salesman
might want to show that he is doing a
good job by showing a large increase in
new clients.
Number of New Clients
40
45
35
30
Jan
Feb March Apr
May
June
Number of New Clients
38
39
40
41
42
43
44
37
36
35
Jan
Feb March Apr
May
June
Bears
Number of Games Won
Badgers
Tigers Panthers
2
4
6
8
12
10
14
16
18
20
22
24
26
28
Team
Bears
Badgers
Tigers
Wins
22
28
24
Panthers
21
© Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved.
Name
Date
Class
Labsheet 6.1
Topic 6
A. 4.
5.
Bears
Number of Games Won
Badgers
Tigers Panthers
2
4
6
8
12
10
14
16
18
20
22
24
26
28
Team
Bears
Badgers
Tigers
Wins
Panthers
© Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved.
Name
Date
Class
Labsheet 6ACE Exercise 2
Topic 6
2. a.
b.
Number of New Clients
Jan Feb Mar Apr May June
Number of New Clients
Jan Feb Mar Apr May June