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 mean x¯.
(c) Calculate the sample standard deviation s.
(d) Determine the proportion of the data values that lies within x¯ ± 1.5s and compare with the lower bound given by Chebyshev's inequality.
(e) Determine the proportion of the data values that lies within x¯ ± 2s and compare with the lower bound given by Chebyshev's inequality.