Chapter 6 – Lessons 6.2 and 6.3 Mean, Median, Mode and Range Additional Data andOutliers.

Chapter 6 – Lessons 6.2 and 6.3

Mean, Median, Mode and Range

Additional Data andOutliers

6-2 Mean, Median, Mode and Range

Learn to find the mean, median, mode and range of a data set.

Learn the effect of additional data and outliers.


Vocabulary

meanmedianmoderangeoutlier


Example 1: Finding the Mean of a Data Set

1245385

Depths of Puddles (in.)

mean: 5 + 8 + 3 + 5 + 4 + 2 + 1 = 28

28 ÷ 7 = 4

The mean is 4 inches.

Add all values.

Divide the sum by the number of items.

Find the mean of each data set.


White board (or mental) practice:

Find the mean of each data set.

96521021

Rainfall per month (in.)

mean: 1 + 2 + 10 + 2 + 5 + 6 + 9 = 35

35 ÷ 7 = 5

The mean is 5 inches.

Add all values.

Divide the sum by the number of items.


Some other descriptions of a set of data are called the median, mode, and range.

•The range is the difference between the least and greatest values in the set.

•The median is the middle value when the data are in numerical order, or the mean of the two middle values if there are an even number of items.

•The mode is the value or values that occur most often. There may be more than one mode for a data set. When all values occur an equal number of times, the data set has no mode.


Example 2: Finding the Mean, Median, Mode, and Range of a Data Set

Write the data in numerical order. 11, 12, 14, 15

range: 15 – 11 = 4

mean: 12 + 11 + 14 + 15 4

= 13

median: 11, 12, 14, 15

12 + 14 2

= 13

mode: none

The mean is 13, the median is 13, there is no mode, and the range is 4.

There are an even number of items, so find the mean of the two middle values.

Find the mean, median, mode, and range of the data set.

9th Grade 158th Grade 14


Car Wash Totals


White board practice:

Write the data in numerical order. 11, 14, 17, 22

range: 22 – 11 = 11

mean: 17 + 11 + 22 + 14 4

= 16

median: 11, 14, 17, 22

14 + 17 2

= 15.5

mode: none

The mean is 16, the median is 15.5, there is no mode, and the range is 11.

There are an even number of items, so find the mean of the two middle values.

Find the mean, median, mode, and range of the data set.



Bake Sale Totals


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


Example 3: 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.




1164613Games

20022001200019991998Year

MA Basketball Games Won

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.


White board practice: Solution


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.


Example 4: 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 = mode = median =

mean = mode = median =

Data with Ms. Pink’s age:

Data without Ms. Pink’s age:


White board practice: Solution

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:


Example 5: 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.


Example 5 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.


Example 5 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.


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 QuizUse the following data set: 18, 20, 56, 47, 30, 18, 21.

1. Find the range. 2. Find the mean.

3. Find the median. 4. Find the mode.

5. Bonnie ran a mile in 8 minutes, 8 minutes, 7

minutes, 9 minutes, and 8 minutes. What was her

mean time?

38 30

21 18

8 minutes


6. Identify the range of the following data set.

20, 22, 58, 48, 32, 20, 23

A. 38

B. 28

C. 18

D. 8


7. Identify the mean of the following data set.

20, 25, 60, 42, 30, 20, 20

A. 31

B. 34

C. 38

D. 42


8. Identify the median of the following data set.

20, 22, 58, 48, 32, 20, 23

A. 48

B. 32

C. 23

D. 20


9. Identify the mode of the following data set.

20, 28, 55, 48, 30, 20, 25

A. 20

B. 23

C. 25

D. 32


10. Rebecca spent $7, $12, $8, and $13 over the past 4 days buying vegetables. What was the mean amount spent on vegetables?

A. $10

B. $9

C. $8

D. $7


At the college bookstore, your brother buys 6 textbooks at the following prices: $21, $58, $68, $125, $36, and $140.

11. Find the mean.

12. Find the median.

13. Find the mode.

14. 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


15. 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


16. 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


17. 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

Chapter 6 – Lessons 6.2 and 6.3 Mean, Median, Mode and Range Additional Data andOutliers.

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Transcript of Chapter 6 – Lessons 6.2 and 6.3 Mean, Median, Mode and Range Additional Data andOutliers.