6-3 Additional Data and Outliers Learn the effect of additional data and outliers

6-3 Additional Data and Outliers

Learn the effect of additional data and outliers.


Vocabulary

outlier


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


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, and the median remained the same.


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. 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.


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


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



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:


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:

35 + 42 + 75 + 40 + 47 + 34 + 45 + 40

8

The mean is $44.75.

= 358 8

= 44.75

The mean is higher than most of the prices because of the $75 skates, and the mode doesn’t consider all of the data.


Additional Example 3 Continued


$35, $42, $75, $40, $47, $34, $45, $40


Median:

34, 35, 40, 40, 42, 45, 47, 75

40 + 42 2

The median is $41.= 82 2

= 41

The median price is the best description of the prices. Most of the skates cost about $41.


Additional Example 3 Continued


$35, $42, $75, $40, $47, $34, $45, $40


mode:

The value $40 occurs 2 times, and is more than any other value. The mode is $40.

The mode represents only 2 of the 8 values. The mode does not describe the entire data set.


Mean:

17 + 15 + 3 + 12 + 13 + 16 + 19 + 19

8

The mean is $14.25.

= 114 8

= 14.25

The mean is lower than most of the prices because of the $3 glove, so the mean does not describe the data set best.


The Oswalds are shopping for gloves. They found 8 pairs of gloves with the following prices:

$17, $15, $3, $12, $13, $16, $19, $19



Median:

3, 12, 13, 15, 16, 17, 19, 19

15 + 16 2

The median is $15.50.= 31 2

= 15.5

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

Check It Out: Example 3 Continued


$17, $15, $3, $12, $13, $16, $19, $19



mode:

The value $19 occurs 2 times, and is more than any other value. The mode is $19.

The mode represents only 2 of the 8 values. The mode does not describe the entire data set.



$17, $15, $3, $12, $13, $16, $19, $19





$17, $15, $3, $12, $13, $16, $19, $19


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.


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.


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

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6-3 Additional Data and Outliers Learn the effect of additional data and outliers