Q5. Do social robots walk or roll? A... [FREE SOLUTION]

91影视

Statistics For Business And Economics

James T. McClave, P. George Benson, Terry Sincich

$Math Studyset 91影视 Explanations$ Math

13th Edition 路 888 pages

ISBN: 9780134506593

Chapter 2: Q5. (page 72)

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

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

Step by step solution

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.

Specifying the variable

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

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.

Computing class relative frequencies

The class relative frequencies of each design are calculated below:

$Relative class frequency = \frac{Total number of robots of one design}{Total number of robots} 脳100 Relative class frequency of the robots having no limbs = \frac{15}{106} 脳100 = 14.15 % Relative class frequency of the robots having both limbs = \frac{8}{106} 脳100 = 7.55 % Relative class frequency of the robots having only legs = \frac{63}{106} 脳100 = 59.43 % Relative class frequency of the robots havingonlywheels= \frac{20}{106} 脳100 = 18.87 %$

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: