Do social robots walk or roll? Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study on the current trend in the design of social robots, Exercise 2.7

(p. 66). Recall that in a random sample of social robots obtained through a Web search, 28 were built with wheels. The numbers of wheels on each of the 28 robots are listed in the table on p. 105.

a. Generate a histogram for the sample data set. Is the distribution of number of wheels mound shaped and symmetric?

b. Find the mean and standard deviation for the sample data set.

c. Form the interval x { 2s.

d. According to Chebychev’s rule, what proportion of sample observations will fall within the interval in part c?

e. According to the empirical rule, what proportion of sample observations will fall within the interval in part c?

f. Determine the actual proportion of sample observations that fall within the interval in part

c. Even though the histogram in part a is not perfectly symmetric, does the empirical rule provide a good estimate of the proportion?

4 4 3 3 3 6 4 2 2 2 1 3 3 3 3 4 4 3 2 8 2 2 3 4 3 3 4 2