1. CONFIDENTIAL 1 Algebra1 Misleading Graphs and Statistics

2. CONFIDENTIAL 2 Warm Up 1) 2x - 3 < 7 2) 3 (t - 1) ≥ -15 1) x < 5 2) t ≥ -4 Solve each inequality and graph the solutions. 3) 6 - n < 2n + 9 3) n > -1

3. 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 Statistics

4. CONFIDENTIAL 4 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.

5. CONFIDENTIAL 5 Now you try! 1. Who might want to use the graph below? Explain. 1) Company D; the fertilizer from company D appears to be more effective than the other fertilizers.

6. CONFIDENTIAL 6 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.

7. CONFIDENTIAL 7 Now you try! 2. Who might want to use the graph below? Explain. 2) Taxi driver; the taxi driver could justify charging higher rates by using this graph showing the gas prices have increased.

8. CONFIDENTIAL 8 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.

9. CONFIDENTIAL 9 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.

10. CONFIDENTIAL 10 Now you try! 3. Who might want to use the graph below? Explain. 3) Smith; Smith might want to show that he or she got many more votes than Atkins or Napier.

11. CONFIDENTIAL 11 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.

12. 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 Statistics

13. 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! 4) The sample size is much too small.

14. 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? 1)a) The vertical scale does not start at 0. This exaggerates the difference in heights of the bar. b) someone might believe that employee at company Y make about twice as much as employee at company Z. c) company Y

15. 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? 2) a) The vertical scale does not start at 0 and the categories on the horizontal scale are not at equal time intervals. b) someone who wants to run a campaign to increase tourism. c) Tourism is decreasing rapidly.

16. 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? 3)a) The sectors of the graph do not add to 100%. b) The Granola bar is almost half protein. c) The Granola bar company might want their product to look healthful.

17. 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.” 4) the sample size is too small.

18. 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.” 5) people shopping at the mall are more likely to favor a larger parking lot.

19. CONFIDENTIAL 19 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. Let’s review

20. CONFIDENTIAL 20 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.

21. CONFIDENTIAL 21 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.

22. 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 Statistics

23. CONFIDENTIAL 23 You did a great job today!