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)
• Dana: 68, 74, 83, 80, 81, 82
• Jose: 91, 93, 97, 96, 96, 96
• Theo: 84, 88, 81, 85, 77, 76
• Ara: 100, 98, 99, 97, 100, 100
To calculate whose mean test score will increase the most, we need to find the difference between their previous mean test score and their mean test score after receiving a 100.
1. For Dana:
Previous mean test score = (68 + 74 + 83 + 80 + 81 + 82) / 6 = 78
Mean test score after receiving a 100 = (68 + 74 + 83 + 80 + 81 + 82 + 100) / 7 = 79.14
Increase in mean test score = 79.14 - 78 = 1.14
2. For Jose:
Previous mean test score = (91 + 93 + 97 + 96 + 96 + 96) / 6 = 95.5
Mean test score after receiving a 100 = (91 + 93 + 97 + 96 + 96 + 96 + 100) / 7 = 95.57
Increase in mean test score = 95.57 - 95.5 = 0.07
3. For Theo:
Previous mean test score = (84 + 88 + 81 + 85 + 77 + 76) / 6 = 81.83
Mean test score after receiving a 100 = (84 + 88 + 81 + 85 + 77 + 76 + 100) / 7 = 84.57
Increase in mean test score = 84.57 - 81.83 = 2.74
4. For Ara:
Previous mean test score = (100 + 98 + 99 + 97 + 100 + 100) / 6 = 98.33
Mean test score after receiving a 100 = (100 + 98 + 99 + 97 + 100 + 100 + 100) / 7 = 99
Increase in mean test score = 99 - 98.33 = 0.67
Therefore, Theo's mean test score will increase the most with a difference of 2.74.