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6-3 Additional Data and Outliers6-3 Additional Data and Outliers

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Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

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6-3 Additional Data and Outliers

Warm UpUse 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.

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6-3 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

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6-3 Additional Data and Outliers

Learn the effect of additional data and outliers.

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6-3 Additional Data and Outliers

Vocabulary

outlier

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6-3 Additional Data and Outliers

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

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6-3 Additional Data and Outliers

Additional Example 1: Sports Application

A. Find the mean, median, and mode of the data in the table.

EMS Football Games Won

Year 1998 1999 2000 2001 2002

Games 11 5 7 5 7

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, and the median remained the same.

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6-3 Additional Data and Outliers

Check It Out: Example 1

A. Find the mean, median, and mode of the data in the table.

MA Basketball Games Won

Year 1998 1999 2000 2001 2002

Games 13 6 4 6 11

mean = 8 mode = 6 median = 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 mode = 6 median = 8

The mean increased by 1, the mode remained the same, and the median increased by 2.

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6-3 Additional Data and Outliers

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

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6-3 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 mode median = 58

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 t 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

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6-3 Additional Data and Outliers

Check It Out: 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 no mode median = 25

mean = 24.5 no mode median = 24.5

When you add Ms. Pink’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.

Data with Ms. Pink’s age:

Data without Ms. Pink’s age:

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6-3 Additional Data and Outliers

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, and the mode doesn’t consider all of the data.

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6-3 Additional Data and Outliers

Check It Out: 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?

mean = $14.25 mode = $19 median = $15.50

The median price is the best description of the prices. Most of the gloves cost about $15.50.

The mean is lower than most of the prices because of the $3 gloves, and the mode is higher because of the two pairs costing $19.

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6-3 Additional Data and Outliers

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.

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6-3 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