Five-Minute Check (over Lesson 8–8)

Main Idea

Example 1: Changing the Interval of Graphs

Example 2: Identify Biased Displays

Example 3: Misleading Statistics

• Recognize when statistics and graphs are misleading.

Changing the Interval of Graphs

BUSINESS The line graphs below show the last 10 weeks of sales for the Crumby Cookie Bakery. Do the graphs show the same data? If so, explain how the graphs differ. Which graph makes it appear that the bakery's sales declined only slightly?

Changing the Interval of Graphs

Answer: The graphs show the same data, but the scale of Graph A has greater intervals and a greater range. Graph A makes it appear that the bakery's sales declined only slightly.

1. A

2. B

3. C

4. D0% 0%0%0%

A. same data; intervals on the graphs are different

B. same data; data in Graph A is graphed incorrectly

C. same data; scale in Graph B is not consistent

D. different data

SOCCER The graphs show the number of wins by four different soccer teams. Do the graphs show the same data? If so, explain how they differ.

Identify Biased Displays

TECHNOLOGY A Web site e-mailed 1,000 of its members to determine its members’ favorite hobbies. The results are shown in the histogram. Identify any sampling errors and explain why the sample and display might be biased.

Identify Biased Displays

Answer: The sample is a biased convenience sample. Members of a Web site probably enjoy computers more than other activities. The display is biased because the data used to create the display came from a biased sample.

1. A

2. B

3. C

4. D0% 0%0%0%

A. The sample is unbiased since it was mailed.

B. The sample is biased because it is a voluntary response sample.

C. The display is unbiased because it came from an unbiased sample.

D. The sample is unbiased because it represents all pet owners.

ANIMALS A pet store owner sent a mail survey to 200 of his customers to what kind of pet is most popular. The results are shown in the graph. Using this information, which of the following statements is true?

Misleading Statistics

GRADES Michael and Melissa both claim to be earning a C average—70% to 79%—in their Latin class. One student is wrong. Which one? Explain how he or she is using a misleading statistic.

Michael Melissa

mean 53.4% 71.9%median 70% 70%

Misleading Statistics

Answer: Michael is wrong. He claimed to be earning a C average because his median was 70%. But his mean, or average, is much less than 70%.

1. A

2. B

3. C

0% 0%0%

A. Store A

B. Store B

C. Both stores have the same average price.

RETAIL SALES Two different grocery stores each claim to have the lowest average prices. Use the table below to determine which store really has the lowest average prices.

End of the Lesson

Five-Minute Check (over Lesson 8–8)

Image Bank

Math Tools

Line Plots

1. A

2. B

3. C

4. D0% 0%0%0%

A. valid, unbiased sample

B. not valid, biased sample

C. valid, biased sample

D. not valid, unbiased sample

A mathematics class decided to find out if students enjoy gym class. The football team had practice that day so they decided to survey them. Fifty-eight of the sixty players all enjoyed gym class, so the class determined that almost all students enjoy gym class. Determine whether the conclusion is valid. Justify your answer.

(over Lesson 8-8)

1. A

2. B

3. C

4. D0% 0%0%0%

A. biased convience sample, invalid

B. unbiased convience sample, valid

C. unbiased convience sample, invalid

D. biased sample, valid

Mr. Brown’s class conducted a survey to determine how many students wanted to listen to music in class. The survey was given to every student in Mr. Brown’s Algebra class. Describe the sample and determine if the sampling method is valid.

(over Lesson 8-8)

1. A

2. B

3. C

4. D0% 0%0%0%

A. Select students from the 49er Cheering Club.

B. Select students from the football team.

C. Select ten students from each class.

D. Select students from the girls’ volleyball team.

Fritz wants to conduct a survey to determine if the San Francisco 49ers is the favorite team at school. Which of the following methods is the best way for him to choose a random sample at his school?

(over Lesson 8-8)