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Chapter 2: Q-2- 122E (page 131)

Question: Construct a scatterplot for the data in the following table.

Variable 1: 5 3 -1 2 7 6 4 0 8

Variable 2: 14 3 10 1 8 5 3 2 12

Short Answer

Expert verified

Answer:

The graph is given below:

Step by step solution

01

Scatterplot

Scatter plots are charts that show the connection of two factors in a collection of data. A scatter plot is a graphic that demonstrates the connection (correlation) among two variables by plotting dots.

02

Constructing the scatterplot

The graph is given below:

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Most popular questions from this chapter

Active nuclear power plants.Refer to Exercise 2.54 (p. 98) and the Nuclear Energy Institute’s data on the number of nuclear power plants operating in each of 30 states.

a.Find the range, variance, and standard deviation of this data set.

b.Eliminate the largest value from the data set and repeat part a.What effect does dropping this measurement have on the measures of variation found in part a?

c.Eliminate the smallest and largest value from the data set and repeat part a. What effect does dropping both of these measurements have on the measures of variation found in part a?

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

Regulated

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

Regulated

2

Washington

Regulated

1

Wisconsin

Deregulated

1

Motivation of athletes.A statistician keeps track of every serve that a player hits during the U.S. Open Tennis Championship. The statistician reports that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph.

a.Suppose the statistician also observes that the distribution of serve speeds was mound-shaped and symmetric. What percentage of the player’s serves was between 115 mph and 145 mph?

b.Consider the following serve speeds: 50 mph, 80 mph, and 105 mph. Using the z-score approach for detecting outliers, which of these would represent outliers in the distribution of the player’s serve speeds?

c.If nothing is known about the shape of the distribution, what percentage of the player’s serve speeds are less than 70 mph?

Defects in new automobiles.Consider the following data from the automobile industry. All cars produced on a particular day were inspected for defects. The 145 defects found were categorized by type as shown in the accompanying table.

Defect Type

Number

Accessories

Body

Electrical

Engine

Transmission

50

70

10

5

10

a.Construct a Pareto diagram for the data. Use the graph to identify the most frequently observed type of defect.

b.All 70 car body defects were further classified as to type. The frequencies are provided in the following table. Form a Pareto diagram for the type of body defect. (Adding this graph to the original Pareto diagram of part a is called exploding the Pareto diagram.) Interpret the result. What type of body defect should be targeted for special attention?

Body Defect

Number

Chrome

Dents

Paint

Upholstery

Windshield

2

25

30

10

3

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.

a. What type of graph is used to describe the data?

b. Identify the variable measured for each of the 106 robot designs.

c. Use the graph to identify the social robot design that is currently used the most.

d. Compute class relative frequencies for the different categories shown in the graph.

e. Use the results from part d to construct a Pareto diagram for the data.

Symmetric or skewed?Would you expect the data sets described below to possess relative frequency distributions that are symmetric, skewed to the right, or skewed to the left? Explain.

a.The salaries of all persons employed by a large university

b.The grades on an easy test

c.The grades on a difficult test

d.The amounts of time students in your class studied last week

e.The ages of automobiles on a used-car lot

f.The amounts of time spent by students on a difficult examination (maximum time is 50 minutes)
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