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Chapter 2: Q62E (page 103)

Using only integers between 0 and 10, construct two data sets with at least 10 observations each so that the two sets have the same mean but different variances. Construct dot plots for each of your data sets and mark the mean of each data set on its dot diagram.

Short Answer

Expert verified

Set A: 1, 0, 3, 2, 4, 2, 2, 3, 3, 0

Set B: 0, 4, 4, 4, 4, 3, 2, 0, 0, 0

Step by step solution

01

Creating 2 data sets only by using integers between 0 and 10

Set A: 1, 0, 3, 2, 4, 2, 2, 3, 3, 0

Mean = 2

Variance = 1.77

Variance=鈭�(x-x炉)2n-1=(1-2)2+(0-2)2+(3-2)2+(2-2)2+(4-2)2+(2-2)2+(2-2)2+(3-2)2+(3-2)2+(0-2)210-1=1+4+1+0+4+0+0+1+1+49=169=1.77

Set B: 0, 4, 4, 4, 4, 3, 2, 0, 0, 0

Mean = 2

Variance = 3.66

Variance=鈭�(x-x炉)2n-1=(0-2)2+(4-2)2+(4-2)2+(4-2)2+(4-2)2+(3-2)2+(2-2)2+(0-2)2+(0-2)2+(0-2)210-1=4+4+4+4+4+1+0+4+4+49=339=3.66

02

Constructing a dot plot for Set A

03

Creating a dot plot for Set B

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Do social robots walk or roll? A social (or service) robot is designed to entertain, educate, and care for human users. In a paper published by the International Conference on Social Robotics (Vol. 6414, 2010), design engineers investigated the trend in the design of social robots. Using a random sample of 106 social robots obtained through a Web search, the engineers found that 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. This information is portrayed in the accompanying graph.

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State

Status

Number of Power Plants

Alabama

Regulated

2

Arizona

Regulated

1

Arkansas

Regulated

1

California

Regulated

1

Connecticut

Deregulated

1

Florida

Regulated

3

Georgia

Regulated

2

Illinois

Deregulated

6

Iowa

Deregulated

1

Kansas

Regulated

1

Louisiana

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2

Maryland

Deregulated

1

Massachusetts

Deregulated

1

Michigan

Deregulated

3

Minnesota

Regulated

2

Mississippi

Regulated

1

Missouri

Regulated

1

Nebraska

Regulated

2

New Hampshire

Deregulated

1

New Jersey

Deregulated

3

New York

Deregulated

4

North Carolina

Regulated

3

Ohio

Deregulated

2

Pennsylvania

Deregulated

5

South Carolina

Regulated

4

Tennessee

Regulated

2

Texas

Deregulated

2

Virginia

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2

Washington

Regulated

1

Wisconsin

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