Problems 53
26.The following are the grade point averages of 30 students recently admitted to the
graduate program in the Department of Industrial Engineering and Operations
Research at the University of California at Berkeley.3.46, 3.72, 3.95, 3.55, 3.62, 3.80, 3.86, 3.71, 3.56, 3.49, 3.96, 3.90, 3.70, 3.61,
3.72, 3.65, 3.48, 3.87, 3.82, 3.91, 3.69, 3.67, 3.72, 3.66, 3.79, 3.75, 3.93, 3.74,
3.50, 3.83(a) Represent the preceding data in a stem and leaf plot.
(b) Calculate the sample meanx ̄.
(c) Calculate the sample standard deviations.
(d) Determine the proportion of the data values that lies withinx ̄±1.5sand
compare with the lower bound given by Chebyshev’s inequality.
(e)Determine the proportion of the data values that lies withinx ̄± 2 sand
compare with the lower bound given by Chebyshev’s inequality.
27.Do the data in Problem 26 appear to be approximately normal? For parts (c) and
(d) of this problem, compare the approximate proportions given by the empirical
rule with the actual proportions.
28.Would you expect that a histogram of the weights of all the members of a health
club would be approximately normal?
29.Use the data of Problem 16.
(a) Compute the sample mean and sample median.
(b) Are the data approximately normal?
(c) Compute the sample standard deviations.
(d) What percentage of the data fall withinx ̄±1.5s?
(e)Compare your answer in part (d) to that given by the empirical rule.
(f) Compare your answer in part (d) to the bound given by Chebyshev’s
inequality.
30.Use the data concerning the first 10 states listed in the table given in Problem 15.
(a) Draw a scatter diagram relating the 1992 and 1993 salaries.
(b) Determine the sample correlation coefficient.
31.The following table gives the median salaries for recent U.S. doctorate recipients,
categorized by scientific field and type of employment. Draw a scatter diagram
relating salaries in private firms to those in government, and determine the sample
correlation coefficient.
32.Use the table to find the sample correlation coefficients between salaries in
(a) government and universities
(b) private firms and universities.