6-3 Additional Data and Outliers

Transcription

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

2 Learn the effect of additional data and outliers.

3 6-3 Additional Insert Lesson Data Title and Here Outliers outlier Vocabulary

4 The mean, median, and mode may change when you add data to a data set.

5 Additional Example 1A & 1B: Sports Application A. Find the mean, median, and mode of the data in the table. EMS Football Games Won Year Games mean = 7 modes = 5, 7 median = 7 B. EMS also won 13 games in 1997 and 8 games in 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, and the median remained the same.

6 Try This: Example 1A & 1B A. Find the mean, median, and mode of the data in the table. MA Basketball Games Won Year Games mean = 8 mode = 6 median = 6 B. MA also won 15 games in 1997 and 8 games in Add this data to the data in the table and find the mean, median, and mode. mean = 9 mode = 6 median = 8 The mean increased by 1, the mode remained the same, and the median increased by 2.

7 An outlier is a value in a set that is very different from the other values.

8 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. Data with Ms. Gray s age: mean 53.3 no mode median = 58 Data without Ms. Gray s age: mean = 58 no mode median = 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 is closer to most of the students ages.

9 Try This: 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. Data with Ms. Pink s age: mean = 29 no mode median = 25 Data without Ms. Gray s age: mean = 24.5 no mode median = 24.5 When you add Ms. Gray s age, the mean increases by 4.5, the mode stays the same, and the median increases by 0.5. The mean is the most affected by the outlier. The median is closer to most of the students ages.

10 Additional 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 = $44.75 mode = $40 median = $41 The median price is the best description of the prices. Most of the skates cost about $41. The mean is higher than most of the prices because of the $75 skates.

11 Try This: Example 3 The Oswalds are shopping for gloves. They found 8 pairs of gloves with the following prices: $17, $15, $39, $12, $13, $16, $19, $15 What are the mean, median, and mode of this data set? Which statistic best describes the data set? mean = $18.25 mode = $15 median = $15.50 The median price is the best description of the prices. Most of the gloves cost about $ The mean is higher than most of the prices because of the $39 gloves.

12 Some data sets do not contain numbers. For example, the circle graph shows the result of a survey to find people s favorite color. When it does not contain numbers the only way to describe the data set is with the mode. You cannot find a mean or a median for a set of colors. The mode for this data set is blue. Most people in this survey chose blue as their favorite color.

13 6-3 Additional Insert Lesson Data Title and Here Outliers Lesson Quiz At the college bookstore, your brother buys 6 textbooks at the following prices: $21, $58, $68, $125, $36, and $ Find the mean. 2. Find the median. 3. Find the mode. $74.67 $63 none 4. Your brother signs up for an additional class, and the textbook costs $225. Recalculate the mean, including the extra book. $96.14