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(a) Write the advantage of preparing a stem-and-leaf display have over grouping a data set using a frequency distribution? Give one example. (4 marks) (b) The following data give the times served (in months) by 35 prison inmates who were released recently. 37 10 13 86 36 6 12 22 70 32 20 20 72 40 5 24 80 92 45 25 8 96 36 38 30 26 33 28 18 24 15 84 90 9 72 i. ii. Prepare a stem-and-leaf display for these data. Arrange the leaves for each stem in increasing order. (4 marks) Produce the condensed stem-and-leaf display by grouping the stems as 0-2, 3- 5, and 6-9. (4 marks) (e) The number of tornadoes that touched down during 1950 to 1994 in the 12 states that had the most tornadoes during this period is represented by the following data. 1113 1166 2009 1374 1137 2110 1086 1039 1673 2300 1139 5490 The data for these 12 states are given in the following order: CO, FL, IA, IL, KS, LA, MO, MS, NE, OK, SD, RX. i. Calculate the mean and the median for these data (2 marks) ii. Identify the outlier in this data set. Drop the outlier and recalculate the mean and median. (3 marks) iii. Based on your answer in (i) and (ii), point out the best summary measure for these data. Explain your answer. (2 marks) Calculate the range, variance, and standard deviation. (3 marks) iv. (d) The following data give the numbers of computer keyboards assembled at the Twentieth Century Electronics Company for a sample of 25 days. 45 46 51 52 44 53 52 47 48 42 51 50 50 41 48 48 54 49 56 53 46 47 52 43 44 i. Calculate the values of the three quartiles and the interquartile range. (4 marks) Calculate the value of the 53rd percentile. (1 mark) Calculate the percentile rank of 50. (1 mark) ii. 111