1. 6-2 Additional Data and Outliers I CAN determine the effect of additional data on mean, median, and mode. I CAN identify an outlier. I CAN determine the effect of an outlier on mean, median, and mode. I CAN determine whether the mean or median best describes a set of data.

2. 6-2 Additional Data and Outliers Vocabulary outlier

3. 6-2 Additional Data and Outliers The mean, median, and mode may change when you add data to a data set.

4. 6-2 Additional Data and Outliers Example 1: Using Additional Data A. Find the mean, median, and mode of the data in the table. 757511Games 20022001200019991998Year EMS Football Games Won mean 11 + 5 + 7 + 5 + 7 = 35 ÷ 5 = 7 median 5 5 7 7 11 mode 5, 7

5. 6-2 Additional Data and Outliers 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. The mean increased by 1, the median remained the same, and the mode remained the same. mean 11 + 5 + 7 + 5 + 7 + 13 + 8 = 56 ÷ 7 = 8 median 5 5 7 7 8 11 13 mode 5, 7

6. 6-2 Additional Data and Outliers You Try! Example 1 A. Find the mean, median, and mode of the data in the table. 1164613Games 20022001200019991998Year MA Basketball Games Won mean = 8 median = 6 mode = 6 B. MA also won 15 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 = 9 median = 8 mode = 6 The mean increased by 1, the median increased by 2, and the mode remained the same.

7. 6-2 Additional Data and Outliers An outlier is a value in a set that is very different from the other values.

8. 6-2 Additional Data and Outliers Example 2: Outliers 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 median = 58 no mode mean = 58 median = 58.5 no mode When you add Ms. Gray’s age, the mean decreases by about 4.7, the median decreases by 0.5, and the mode stays the same. The mean is the most affected by the outlier. The median is closer to most of the students’ ages. Data with Ms. Gray’s age: Data without Ms. Gray’s age: Ms. Grey’s age is an outlier because she is much younger than the others in the group. Helpful Hint

9. 6-2 Additional Data and Outliers You Try! Example 2 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 median = 25 no mode mean = 24.5 median = 24.5 no mode When you add Ms. Pink’s age, the mean increases by 4.5, the median increases by 0.5, and the mode stays the same. The mean is the most affected by the outlier. The median is closer to most of the students’ ages. Data with Ms. Pink’s age: Data without Ms. Pink’s age:

10. 6-2 Additional Data and Outliers Example 3: Describing a Data Set The Yorks are shopping for skates. They found 8 pairs of skates with the following prices: $35, $42, $75, $40, $47, $34, $45, $40 What are the mean, median, and mode of this data set? Which statistic best describes the data set? Mean: 35 + 42 + 75 + 40 + 47 + 34 + 45 + 40 The mean is $44.75. = 358 ÷ 8= 44.75

11. 6-2 Additional Data and Outliers Example 3 Continued Median: 34, 35, 40, 40, 42, 45, 47, 75 40 + 42 2 The median is $41. = 82 2 = 41 Mode: The value $40 occurs 2 times, and is more than any other value. The mode is $40.

12. 6-2 Additional Data and Outliers Example 3 Continued The mean is higher than most of the skates. The mode only represents 2 of the 8 values. The median; most of the skates cost about $41. Which one best describes the data set? Which two do not describe the data set best?

13. 6-2 Additional Data and Outliers Mean: 17 + 15 + 3 + 12 + 13 + 16 + 19 + 19 8 The mean is $14.25. = 114 8 = 14.25 You Try! Example 3 The Oswalds are shopping for gloves. They found 8 pairs of gloves with the following prices: $17, $15, $3, $12, $13, $16, $19, $19 What are the mean, median, and mode of this data set? Which statistic best describes the data set?

14. 6-2 Additional Data and Outliers Median: 3, 12, 13, 15, 16, 17, 19, 19 15 + 16 2 The median is $15.50. = 31 2 = 15.5 You Try! Example 3 Continued Mode: The value $19 occurs 2 times, and is more than any other value. The mode is $19.

15. 6-2 Additional Data and Outliers You Try! Example 3 Continued The mean is higher than most of the gloves. The mode only represents 2 of the 8 values. The median; most of the gloves cost about $15.50. Which one best describes the data set? Which two do not describe the data set best?

16. 6-2 Additional Data and Outliers CAN YOU determine the effect of additional data on mean, median, and mode? CAN YOU identify an outlier? CAN YOU determine the effect of an outlier on mean, median, and mode? CAN YOU determine whether the mean or median best describes a set of data?

17. 6-2 Additional Data and Outliers HOMEWORK