Theo, Ara, Jose, and Dana all got 100 percent on their latest math test. Their scores on the previous six tests are listed. Whose mean test score will increase the most? (1 point)
• Ara: 100, 98, 99, 97, 100, 100
• Jose: 91, 93, 97, 96, 96, 96
• Dana: 68, 74, 83, 80, 81, 82
• Theo: 84, 88, 81, 85, 77, 76
To find out whose mean test score will increase the most, we need to calculate the mean test score for each student before and after the latest test.
Ara:
Mean before = (100 + 98 + 99 + 97 + 100 + 100) / 6 = 98.33
Mean after = (100 + 98 + 99 + 97 + 100 + 100 + 100) / 7 = 98.57
Increase = 98.57 - 98.33 = 0.24
Jose:
Mean before = (91 + 93 + 97 + 96 + 96 + 96) / 6 = 94.83
Mean after = (91 + 93 + 97 + 96 + 96 + 96 + 100) / 7 = 95.14
Increase = 95.14 - 94.83 = 0.31
Dana:
Mean before = (68 + 74 + 83 + 80 + 81 + 82) / 6 = 77.33
Mean after = (68 + 74 + 83 + 80 + 81 + 82 + 100) / 7 = 82.43
Increase = 82.43 - 77.33 = 5.1
Theo:
Mean before = (84 + 88 + 81 + 85 + 77 + 76) / 6 = 81.83
Mean after = (84 + 88 + 81 + 85 + 77 + 76 + 100) / 7 = 83.29
Increase = 83.29 - 81.83 = 1.46
Therefore, Dana's mean test score will increase the most by 5.1.