The following scores represent the final examination grades for an elementary statistics course (treated as population): 57 74 52 70 23 80 52 41 60 60 77 10 79 32 81 64 83 95 89 75 54 41 76 78 64 65 25 72 92 48 74 80 88 85 84 98 71 78 84 34 67 17 82 69 (a) Construct a stem-and-leaf display representing the given data set. Use the tens digits for the stem. (b) Construct a frequency distribution table for the given data set. Use class size of 10 and start from 10 (i.e. 10-19, 20-29 etc.). (c) Determine the following summary measures considering the provided frequency distribution from (b): (c.1) arithmetic mean, 12% trimmed mean, median, and mode (c.2) range, variance, standard deviation, and coefficient of variation (c.3) classification of data set in terms of its skewness and kurtosis. For skewness, use 1st coefficient of skewness. (d) How many percent of the students have their grades within three standard deviations considering the actual data? Compare the determined percentage with Chebysh (e) Determine the z-score of the second lowest and the second highest grades among the population. (f) What should be the minimum grade of the student in order for him/her to have a grade: (f.1) higher than 40% of the student population? (f.2) higher than 75% of the student population? (f.3) higher than 90% of the student population? Consider the frequency distribution from (b) for the calculations. 62 90 82 63 80 55 81 74 15 36 76 67 85 43 79 61