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Chapter 2: Q35E (page 94)
Calculate the mean and median of the following grade point averages:
3.2, 2.5, 2.1, 3.7, 2.8, 2.0
The mean is 2.71.
The median is 2.65.
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Compute xbar, s2, and sfor each of the following data sets. If appropriate, specify the units in which your answer is expressed.
a.3, 1, 10, 10, 4
b.8 feet, 10 feet, 32 feet, 5 feet
c.-1, -4, -3, 1, -4, -4
d.1/5 ounce, 1/5 ounce, 1/5 ounce, 2/5 ounce, 1/5 ounce, 4/5 ounce
If the range of a set of data is 20, find a rough approximation to the standard deviation of the data set.
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, Exercises 2.47 and 2.65 (pp. 96 and 104). Recall that slices of sandstone blocks were measured 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).
a.Combine the mean (from Exercise 2.47) and standard deviation (from Exercise 2.65) to make a statement about where most of the permeability measurements for Group A sandstone slices will fall. Which rule did you use to make this inference and why?
b.Repeat part afor Group B sandstone slices.
c.Repeat part afor Group C sandstone slices.
d.Based on all your analyses, which type of weathering (type A, B, or C) appears to result in faster decay (i.e., higher permeability measurements)?
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.
Question: Given a data set with a largest value of 760 and a smallest value of 135, what would you estimate the standard deviation to be? Explain the logic behind the procedure you used to estimate the standard deviation. Suppose the standard deviation is reported to be 25. Is this feasible? Explain
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