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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? 178
2. What is the least number? 114
3. How can you find the median?
Order the numbers and find the middle value.
6-2 Additional Data and Outliers
Sunshine State Standards
MA.6.S.6.2 Select and analyze the measures
of central tendency…
6-2 Additional Data and Outliers
Vocabulary
outlier
6-2 Additional Data and Outliers
The mean, median, and mode may
change when you add data to a data
set.
6-2 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
mean = 7
5
7
modes = 5, 7
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
The mean increased by 1.
modes = 5, 7
The modes remained the same.
median = 7
The median remained the same.
6-2 Additional Data and Outliers
An outlier is a value in a set that is
very different from the other values.
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.
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
t
is closer to most of the students’ ages.
Helpful Hint
Ms. Gray’s age is an outlier because she is much younger than the
others in the group.
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, $75, $40, $47, $34, $45, and $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 = 358 = 44.75
8
8
The mean is $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.
6-2 Additional Data and Outliers
Additional Example 3 Continued
median:
34, 35, 40, 40, 42, 45, 47, 75
40 + 42 = 82
= 41
2
2
The median is $41.
The median price is the best description of the prices. Most
of the skates cost about $41.
mode:
The value $40 occurs 2 times, which 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.
6-2 Additional Data and Outliers
Check It Out: Example 3
The Oswalds found 8 pairs of gloves with the following
prices: $17, $15, $3, $12, $13, $16, $19, and $19.
What are the mean, median, and mode of this data set?
Which statistic best describes the data set?
mean:
17 + 15 + 3 + 12 + 13 + 16 + 19 + 19 = 114 = 14.25
8
8
The mean is $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.
6-2 Additional Data and Outliers
Check It Out: Example 3 Continued
median:
3, 12, 13, 15, 16, 17, 19, 19
15 + 16 = 31
= 15.5
2
2
The median is $15.50.
The median price is the best description of the prices. Most
of the gloves cost about $15.50.
mode:
The value $19 occurs 2 times, which 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.
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.
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.
$74.67
2. Find the median.
$63
3. Find the mode.
none
4. Your brother signs up for an additional class,
and the textbook costs $225. Recalculate the
mean, including the extra book.
$96.14
6-2 Additional Data and Outliers
Lesson Quiz for Student Response Systems
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
6-2 Additional Data and Outliers
Lesson Quiz for Student Response Systems
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
6-2 Additional Data and Outliers
Lesson Quiz for Student Response Systems
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
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
6-2 Additional Data and Outliers
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
6-2 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
mean = 8
6
mode = 6
4
6
11
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
The mean increased by 1.
mode = 6
The modes remained the same.
median = 8
The median increased by 2.
6-2 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.
Data with Ms. Pink’s age:
mean = 29
no mode
median = 25
Data without Ms. Pink’s age:
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.
6-2 Additional Data and Outliers
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems