confidential 1 algebra1 misleading graphs and statistics
TRANSCRIPT
CONFIDENTIAL 2
Warm UpWarm Up
1) 2x - 3 < 7
2) 3 (t - 1) ≥ -15
Solve each inequality and graph the solutions.
3) 6 - n < 2n + 9
CONFIDENTIAL 3
Graphs can be used to influence what people believe. The way data is displayed can influence how the data is interpreted.
Misleading Graphs and StatisticsMisleading Graphs and Statistics
CONFIDENTIAL 4
Misleading Bar GraphsMisleading Bar Graphs
The graph shows the size of tomatoes on plants that were treated with different fertilizers.
A) Explain why the graph is misleading.
The scale on the vertical axis beginsat 80. This exaggerates the differencesbetween the sizes of the bars.
B) What might someone believe because of the graph?
Someone might believe that thetomato treated with fertilizer D ismuch larger than the other tomatoes. It is only 4 grams larger than the tomato treated with fertilizer B.
CONFIDENTIAL 6
Misleading line GraphsMisleading line Graphs
The graph shows the average price of gasoline in the U.S. in September.
A) Explain why the graph is misleading.
The intervals on the vertical axis arenot equal.
B) What might people be influenced to believe by the graph?
Someone might believe that the price of gasoline increased the most between 1995 and 1997. However, the change between 1995 and 1997 was only $0.14/gal while the change between 1999 and 2001 was $0.17/gal.
CONFIDENTIAL 8
A circle graph compares each category of a data set to the
whole. When anycategory is not represented in the graph, it may appear that another
categoryrepresents a greater percentage
of the total than it should.
CONFIDENTIAL 9
Misleading Circle GraphsMisleading Circle Graphs
The graph shows what percent of the total votes were received by three candidates for student council president.
A) Explain why the graph is misleading.
The sections of the graph do not add to 100%, so the votes for at least one of the candidates is not represented.
B) What might someone believe because of the graph?
Someone might believe that Smith won the election.
CONFIDENTIAL 11
Statistics can be misleading because of the way the data is
collected or the waythe results are reported. A
random sample is a good way to collect unbiased data.
In a random sample , all members of the group being surveyed have
an equalchance of being selected.
CONFIDENTIAL 12
A researcher surveys people leaving a basketball game about what they like to watch on TV. Explain why the following statement is misleading: “80% of
people like to watch sports on TV.”
The sample is biased because people who attend sporting events are more likely to watch sports on TV than people
who watch TV but do not attend sporting events.
Misleading StatisticsMisleading Statistics
CONFIDENTIAL 13
4) A researcher asks 4 people if they have seasonal allergies. Three people respond yes. Explain why the
following statement is misleading: “75% of people have seasonal allergies.”
Now you try!
CONFIDENTIAL 14
Assessment
1 )The graph shows the average salaries of employees at three companies.
a. Explain why the graph is misleading.b. What might someone believe because of the graph?c. Who might want to use this graph?
CONFIDENTIAL 15
2) The graph shows hotel occupancy in San Francisco over four years.
a. Explain why the graph is misleading.b. What might someone believe because of the graph?c. Who might want to use this graph?
CONFIDENTIAL 16
3 )The graph shows the nutritional information for a granola bar .
a. Explain why the graph is misleading.b. What might someone believe because of the graph?c. Who might want to use this graph?
CONFIDENTIAL 17
4) Three students were surveyed about their favorite teacher. Two students
answer Mr. Gregory, and one answers Mr. Blaine. Explain why the following
statement is misleading: “Mr. Gregory is the favorite teacher of a majority
of the students.”
CONFIDENTIAL 18
5) A researcher surveys people at a shopping mall about whether they favor enlarging
the size of the mall parking lot. Explain why the following statement is misleading:
“85% of the community is in favor of enlarging the parking lot.”
CONFIDENTIAL 19
Misleading Bar GraphsMisleading Bar Graphs
The graph shows the size of tomatoes on plants that were treated with different fertilizers.
A) Explain why the graph is misleading.
The scale on the vertical axis beginsat 80. This exaggerates the differencesbetween the sizes of the bars.
B) What might someone believe because of the graph?
Someone might believe that thetomato treated with fertilizer D ismuch larger than the other tomatoes. It is only 4 grams larger than the tomato treated with fertilizer B.
Let’s review
CONFIDENTIAL 20
Misleading line GraphsMisleading line Graphs
The graph shows the average price of gasoline in the U.S. in September.
A) Explain why the graph is misleading.
The intervals on the vertical axis arenot equal.
B) What might people be influenced to believe by the graph?
Someone might believe that the price of gasoline increased the most between 1995 and 1997. However, the change between 1995 and 1997 was only $0.14/gal while the change between 1999 and 2001 was $0.17/gal.
CONFIDENTIAL 21
Misleading Circle GraphsMisleading Circle Graphs
The graph shows what percent of the total votes were received by three candidates for student council president.
A) Explain why the graph is misleading.
The sections of the graph do not add to 100%, so the votes for at least one of the candidates is not represented.
B) What might someone believe because of the graph?
Someone might believe that Smith won the election.
CONFIDENTIAL 22
A researcher surveys people leaving a basketball game about what they like to watch on TV. Explain why the following statement is misleading: “80% of
people like to watch sports on TV.”
The sample is biased because people who attend sporting events are more likely to watch sports on TV than people
who watch TV but do not attend sporting events.
Misleading StatisticsMisleading Statistics