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) Responses Jose: 91, 93, 97, 96, 96, 96 Jose: 91, 93, 97, 96, 96, 96 Theo: 84, 88, 81, 85, 77, 76 Theo: 84, 88, 81, 85, 77, 76 Dana: 68, 74, 83, 80, 81, 82 Dana: 68, 74, 83, 80, 81, 82 Ara: 100, 98, 99, 97, 100, 100
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 their latest test.
Jose:
Mean before = (91 + 93 + 97 + 96 + 96 + 96) / 6 = 95.5
New mean = (91 + 93 + 97 + 96 + 96 + 96 + 100) / 7 = 95.14
Increase = 95.14 - 95.5 = -0.36
Theo:
Mean before = (84 + 88 + 81 + 85 + 77 + 76) / 6 = 82.83
New mean = (84 + 88 + 81 + 85 + 77 + 76 + 100) / 7 = 83
Increase = 83 - 82.83 = 0.17
Dana:
Mean before = (68 + 74 + 83 + 80 + 81 + 82) / 6 = 78
New mean = (68 + 74 + 83 + 80 + 81 + 82 + 100) / 7 = 81.43
Increase = 81.43 - 78 = 3.43
Ara:
Mean before = (100 + 98 + 99 + 97 + 100 + 100) / 6 = 98.33
New mean = (100 + 98 + 99 + 97 + 100 + 100 + 100) / 7 = 98.57
Increase = 98.57 - 98.33 = 0.24
Therefore, Dana's mean test score will increase the most, with an increase of 3.43.