1. 6-2 Additional Data and Outliers Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. 6-2 Additional Data and Outliers Warm Up Use the numbers to answer the questions. 146, 161, 114, 178, 150, 134, 172, 131, 128 1. What is the greatest number? 2. What is the least number? 3. How can you find the median? 178 114 Order the numbers and find the middle value.

3. 6-2 Additional Data and Outliers Problem of the Day Ms. Green has 6 red gloves and 10 blue gloves in a box. She closes her eyes and picks some gloves. What is the least number of gloves Ms. Green will have to pick to ensure 2 gloves of the same color? 3

4. 6-2 Additional Data and Outliers MA.6.S.6.2 Select and analyze the measures of central tendency… Sunshine State Standards

5. 6-2 Additional Data and Outliers Vocabulary outlier

6. 6-2 Additional Data and Outliers The mean, median, and mode may change when you add data to a data set.

7. 6-2 Additional Data and Outliers Additional Example 1: Sports Application A. Find the mean, median, and mode of the data in the table. 757511Games 20022001200019991998Year EMS Football Games Won mean = 7 modes = 5, 7 median = 7 B. EMS also won 13 games in 1997 and 8 games in 1996. Add this data to the data in the table and find the mean, median, and mode. mean = 8 modes = 5, 7 median = 7 The mean increased by 1. The modes remained the same. The median remained the same.

8. 6-2 Additional Data and Outliers Check It Out: Example 1 A. Find the mean, median, and mode of the data in the table. 1164613Games 20022001200019991998Year MA Basketball Games Won mean = 8 mode = 6 median = 6 B. EMS won 26 games in 2003. Add this data to the table and find the mean, median, and mode. mean = 11 mode = 8.5 median = 6

9. 6-2 Additional Data and Outliers An outlier is a value in a set that is very different from the other values.

10. 6-2 Additional Data and Outliers Additional Example 2: Application Ms. Gray is 25 years old. She took a class with students who were 55, 52, 59, 61, 63, and 58 years old. Find the mean, median, and mode with and without Ms. Gray’s age. mean ≈ 53.3 no modemedian = 58 mean = 58 no modemedian = 58.5 When you add Ms. Gray’s age, the mean decreases by about 4.7, the mode stays the same, and the median decreases by 0.5. The mean is the most affected by the outlier. The median t is closer to most of the students’ ages. Data with Ms. Gray’s age: Data without Ms. Gray’s age: Ms. Gray’s age is an outlier because she is much younger than the others in the group. Helpful Hint

11. 6-2 Additional Data and Outliers Check It Out: Example 2A Ms. Pink is 56 years old. She volunteered to work with people who were 25, 22, 27, 24, 26, and 23 years old. Find the mean, median, and mode with and without Ms. Pink’s age. mean = 29 no modemedian = 25 mean = 24.5 no modemedian = 24.5 Data with Ms. Pink’s age: Data without Ms. Pink’s age:

12. 6-2 Additional Data and Outliers Check It Out: Example 2B Use the data from Exercise 2a. Suppose Ms. Pink and the same volunteers are still working together in 3 years. What do you think the value of the mean without Ms. Pink’s age will be? Explain. 27.5; because each data value will increase by 3, the mean will increase by 3.

13. 6-2 Additional Data and Outliers Additional Example 3: Describing a Data Set The Yorks found 8 pairs of skates with the following prices: $35, $42, $73, $40, $47, $35, $45, and $41. What are the mean, median, and mode of this data set? Which statistic best describes the data set? mean: 35 + 42 + 73 + 40 + 47 + 35 + 45 + 41 8 The mean is $44.75. = 358 8 = 44.75 The mean is higher than most of the prices because of the $75 skates, so the mean does not describe the data set best.

14. 6-2 Additional Data and Outliers Additional Example 3 Continued median: 35, 35, 40, 41, 42, 45, 47, 73 41 + 42 2 The median is $41.50. = 83 2 = 41.5 The median price is the best description of the prices. Most of the skates cost about $41.50. mode: The value $35 occurs 2 times. The mode is $35. The mode does not describe the data well because it is lower than the prices of the other pairs of skates.

15. 6-2 Additional Data and Outliers mean = $18.25; this is higher than most of the prices. median = $16; this is close to many prices. mode = $13; this is lower than most of the prices. The median price is the best description of the prices. Check It Out: Example 3A The Oswalds found 8 pairs of gloves with the following prices: $17, $15, $39, $12, $13, $18, $19, and $13. What are the mean, median, and mode of this data set? Which statistic best describes the data set?

16. 6-2 Additional Data and Outliers $39; the outlier causes the mean to be greater than all but two of the data values. Check It Out: Example 3B Identify the outlier from Exercise 3a. How does it make the mean fail to represent the data well? Justify your answer.

17. 6-2 Additional Data and Outliers Some data sets, such as {red, blue, red}, do not contain numbers. In this case, the only way to describe the data set is with the mode.

18. 6-2 Additional Data and Outliers Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

19. 6-2 Additional Data and Outliers Lesson Quiz At the college bookstore, your brother buys 6 textbooks at the following prices: $21, $58, $68, $125, $36, and $140. 1. Find the mean. 2. Find the median. 3. Find the mode. 4. Your brother signs up for an additional class, and the textbook costs $225. Recalculate the mean, including the extra book. $63 $74.67 none $96.14

20. 6-2 Additional Data and Outliers 1. The weights of 7 members of a family are 48 kg, 52 kg, 63 kg, 75 kg, 52 kg, 64 kg, and 67 kg. Identify the median. A. 48 kg B. 52 kg C. 63 kg D. 75 kg Lesson Quiz for Student Response Systems

21. 6-2 Additional Data and Outliers 2. The heights of seven dogs at a vet are 17 inches, 14 inches, 13 inches, 21 inches, 17 inches, 15 inches, and 22 inches. Identify the mode. A. 17 in. B. 16 in. C. 15 in. D. none Lesson Quiz for Student Response Systems

22. 6-2 Additional Data and Outliers 3. Lopez buys 5 collectibles at the following prices: $15, $12, $15, $13 and $16. He then buys another collectible at $75. Identify the mean with and without the sixth collectible. A. $24.33; $14.20 B. $14.20; $13.83 C. $14.20; $12.64 D. $24.33; $29.20 Lesson Quiz for Student Response Systems