Misleading Graphs and Statistics 10-4 Misleading Graphs and Statistics Warm Up Lesson Presentation Lesson Quiz Holt Algebra 1

Warm Up mean median mode Determine the measure of central tendency that best describes each set of data. 1. Home team scores for basketball games: 56, 61, 75, 49, 69, 91, 87, 54, 79, 62 2. Number of scouts in the city’s scouting troops: 10, 8, 21, 11, 9, 7, 5, 10, 6, 9 3. Number of apricots in bags of mixed dried fruit: 3, 3, 3, 4, 3, 3, 2, 0, 3, 3, 4, 6, 3, 2, 3, 3. mean median mode

Objectives Recognize misleading graphs. Recognize misleading statistics.

Vocabulary random sample

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

Example 1A: Misleading Bar Graphs The graph shows customer satisfaction with different brands. % Explain why the graph is misleading. The scale on the vertical axis starts at 76. This exaggerates the difference’s between the sizes of the bars.

Example 1B: Misleading Bar Graphs % The graph shows customer satisfaction with different brands. What might someone believe because of the graph? Someone might believe that the satisfaction with brand B is significantly higher than the other brands. It is only 3 points higher than brand D.

Check It Out! Example 1 Who might want to use the graph at right? Explain. Company D; the fertilizer from company D appears to be more effective than the other fertilizers.

Example 2A: Misleading Line Graphs The graph shows the amount of rainfall by year in a particular metropolitan area. Explain why the graph is misleading. The intervals on the vertical axis are not equal.

Example 2B: Misleading Line Graphs The graph shows the amount of rainfall by year in a particular metropolitan area. What might people be influenced to believe by the graph? Someone might believe the amount of rainfall decreased the most between 1997 and 1998. However, the change between 1997 and 1998 was only 8 inches while the change between 1998 and 1999 was 10 inches.

Check It Out! Example 2 Who might want to use the graph at right? Explain. Possible answer: taxi drivers; the drivers could justify charging higher rates by using this graph, which seems to show that gas prices have increased dramatically.

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

Example 3A: Misleading Circle Graphs The graph shows the allocation of the county budget for 2005. Explain why the graph is misleading. The sections of the graph do not add to 100%, so the expenditures are not accurately represented.

Example 3B: Misleading Circle Graphs The graph shows the allocation of the county budget for 2005. What might people be influenced to believe by the graph? Someone might believe that road maintenance takes more than 50% of the budget.

Check It Out! Example 3 Who might want to use the graph at right? Explain. Smith: Smith might want to show that he or she got many more votes than Atkins or Napier.

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.

Example 4: Misleading Statistics A study of 5 households found the following number of pets per household: 2, 1, 1, 9, and 2. Explain why the following statement is misleading: “The average household has 3 pets.” The sample size of 5 households is too small to achieve accurate results. This sample implies that each household has pets when many probably do not.

Check It Out! Example 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.” The sample size is much too small.

Lesson Quiz: Part I 1. Explain why each graph is misleading. The scale exaggerates the differences between the sitting fees; someone might believe that studio Z charges much less than its competitors.

Lesson Quiz: Part II 2. Explain why the graph is misleading. The vertical scale extends well below the data set; the number of members did not vary much throughout the year.

Lesson Quiz: Part III 3. Explain why the graph is misleading. The sectors do not add to 100%; Someone might believe that Gutierrez would receive most votes.

Lesson Quiz: Part IV 4. A researcher asks 5 people if they like to snow ski. Four people respond yes. Explain why the following statement is misleading: “80% of people like to snow ski.” Only 5 people were asked whether they liked to snow ski. The sample is too small.