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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.

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.

Short Answer

Expert verified

a. Bar graph

b. Type of robotic limb

c. 'Legs ONLY' design

d.

Types of Robotic Limbs

Number of Robots

Relative Frequency

None

15

14.15

Both

8

7.55

Legs ONLY

63

59.43

Wheels ONLY

20

18.87

e.

Step by step solution

01

Identifying the type of graph

The type of graph plotted to represent the design of the robots is a bar graph. The total number of robots is represented by the bars each of which is associated with the respective types of robotic limbs.

02

Specifying the variable

Type of robotic limb is the variable that is measured for each robot and is classified into four categories accordingly.

03

Identifying the most used design

It can be inferred from the bar chart that the social robot design that is currently used the most is the 'Legs ONLY' design.

04

Computing class relative frequencies

The class relative frequencies of each design are calculated below:

Relative class frequency =Total number of robots of one designTotal number of robots脳100Relative class frequency of the robots having no limbs =15106脳100=14.15%Relative class frequency of the robots having both limbs =8106脳100=7.55%Relative class frequency of the robots having only legs =63106脳100=59.43%Relative class frequency of the robots havingonlywheels=20106脳100=18.87%

05

Constructing the Pareto diagram

Before constructing the Pareto diagram for the data of the design of the social robots, the calculation of the cumulative frequency and the cumulative percentage is as shown below:

Types of Robotic Limbs

Number of Robots

Cumulative

Frequency

Cumulative Percentage

Legs ONLY

63

63

59.43

Wheels ONLY

20

83

78.30

None

15

98

92.45

Both

8

106

100.00

In the Pareto diagram:

  • The bars represent the relative frequency of each class in descending order
  • The pink line represents the cumulative percentage

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Most popular questions from this chapter

Monitoring weights of flour bags.When it is working properly, a machine that fills 25-pound bags of flour dispenses an average of 25 pounds per fill; the standard deviation of the amount of fill is .1 pound. To monitor the performance of the machine, an inspector weighs the contents of a bag coming off the machine鈥檚 conveyor belt every half hour during the day. If the contents of two consecutive bags fall more than 2 standard deviations from the mean (using the mean and standard deviation given above), the filling process is said to be out of control, and the machine is shut down briefly for adjustments. The data

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8:30

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Question: Permeability of sandstone during weathering.Refer to the Geographical Analysis(Vol. 42, 2010) study of the decay properties of sandstone when exposed to the weather, Exercise 2.47 (p. 96). Recall that slices of sandstone blocks were tested for permeability under three conditions: no exposure to any type of weathering (A), repeatedly sprayed with a 10% salt solution (B), and soaked in a 10% salt solution and dried (C). Measures of variation for the permeability measurements (mV) of each sandstone group are displayed in the accompanying Minitab printout.

Descriptive Statistics: PermA, PermB, PermC

Variable

N

StDev.

Variance

Minimum

Maximum

Range

PermA

100

14.48

209.53

55.20

122.40

67.20

PermB

100

21.97

482.75

50.40

150.00

99.60

PermC

100

20.05

401.94

52.20

129.00

76.80

a.Find the range of the permeability measurements for Group A sandstone slices. Verify its value using the minimum and maximum values shown on the printout.

b.Find the standard deviation of the permeability measurements for Group A sandstone slices. Verify its value using the variance shown on the printout.

c.Which condition (A, B, or C) has the more variable permeability data?

Consider the horizontal box plot shown below.


a.What is the median of the data set (approximately)?

b.What are the upper and lower quartiles of the data set (approximately)?

c.What is the interquartile range of the data set (approximately)?

d.Is the data set skewed to the left, skewed to the right, or symmetric?

e.What percentage of the measurements in the data set lie to the right of the median? To the left of the upper quartile?

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a.4, 6, 6, 5, 6, 7

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Variable

Support

N

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N for mode

992

67.755

0.000

68.000

155.000

64

20

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c.Locate the mode on the printout. Comment on the accuracy of the statement: 鈥淢ost of the 992 senior managers reported a level of support for corporate sustainability below 64 points.鈥

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