please show each step clearly. especially the standard deviation. DON NOT USE EXCEL

. In an attempt to judge and monitor the quality of instruction, the administration of Mega-Byte Academy devised an exami- nation to test students on the basic concepts that all should have learned. Each year, a random sample of 10 graduating students is selected for the test. The average score is used to track the quality of the educational process. Test results for the past 10 years are shown in Table 3.2. Use these data to estimate the center and standard deviation for this distribution. Then, calculate the two-sigma control limits for the process average. What comments would you make to the administration of the Mega-Byte Academy? TABLE 3.2 TEST SCORES ON EXIT EXAM STUDENT Year 1 2 3 4 5 6 7 8 9 10 Average 69.7 1 63 57 92 87 70 61 75 58 63 71 2 90 77 59 88 48 83 63 94 72 70 74.4 3 3 67 81 93 55 71 71 86 98 60 90 77.2 4 62 67 78 61 89 93 71 59 93 84 75.7 5 85 88 77 69 58 90 97 72 64 60 76.0 6 60 57 79 83 64 94 86 64 92 74 75.3 7 94 85 56 77 89 72 71 61 92 97 79.4 8 97 86 83 88 65 87 76 84 81 71 81.8 8 9 9 94 90 76 88 65 93 86 87 94 63 83.6 10 88 91 71 89 97 79 93 87 69 85 84.9