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Algebra1 Misleading Graphs and Statistics. Warm Up. Solve each inequality and graph the solutions. 1) 2x - 3 < 7. 2) 3 (t - 1) ≥ -15. 3) 6 - n < 2n + 9. Misleading Graphs and Statistics.

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Presentation Transcript
warm up
Warm Up

Solve each inequality and graph the solutions.

1) 2x - 3 < 7

2) 3 (t - 1) ≥ -15

3) 6 - n < 2n + 9

CONFIDENTIAL

slide3

Misleading Graphs and Statistics

Graphs can be used to influence what people believe. The way data is displayed can influence how the data is interpreted.

CONFIDENTIAL

slide4

Misleading 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 begins

at 80. This exaggerates the differences

between the sizes of the bars.

B) What might someone believe because of the graph?

Someone might believe that the

tomato treated with fertilizer D is

much larger than the other tomatoes. It is only 4 grams larger than the tomato treated with fertilizer B.

CONFIDENTIAL

slide5

Now you try!

1. Who might want to use the graph below? Explain.

CONFIDENTIAL

slide6

Misleading 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 are

not 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

slide7

Now you try!

2. Who might want to use the graph below? Explain.

CONFIDENTIAL

slide8

A circle graph compares each category of a data set to the whole. When any

category is not represented in the graph, it may appear that another category

represents a greater percentage of the total than it should.

CONFIDENTIAL

slide9

Misleading 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

slide10

Now you try!

3. Who might want to use the graph below? Explain.

CONFIDENTIAL

slide11

Statistics can be misleading because of the way the data is collected or the way

the 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 equal

chance of being selected.

CONFIDENTIAL

slide12

Misleading Statistics

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.

CONFIDENTIAL

slide13

Now you try!

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.”

CONFIDENTIAL

slide14

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

slide15

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

slide16

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

slide17

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

slide18

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

slide19

Let’s review

Misleading 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 begins

at 80. This exaggerates the differences

between the sizes of the bars.

B) What might someone believe because of the graph?

Someone might believe that the

tomato treated with fertilizer D is

much larger than the other tomatoes. It is only 4 grams larger than the tomato treated with fertilizer B.

CONFIDENTIAL

slide20

Misleading 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 are

not 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

slide21

Misleading 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

slide22

Misleading Statistics

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.

CONFIDENTIAL