To determine whose mean test score will increase the most after scoring 100 percent on their latest math test, we first need to calculate the current mean test scores for each person and then find out how their mean will change after adding the test score of 100.
Let's calculate each person's mean test score before the new test:
1. Ara: Scores: 100, 98, 99, 97, 100, 100 Mean = (100 + 98 + 99 + 97 + 100 + 100) / 6 = 594 / 6 = 99
2. Dana: Scores: 68, 74, 83, 80, 81, 82 Mean = (68 + 74 + 83 + 80 + 81 + 82) / 6 = 468 / 6 = 78
3. Jose: Scores: 91, 93, 97, 96, 96, 96 Mean = (91 + 93 + 97 + 96 + 96 + 96) / 6 = 569 / 6 ≈ 94.833
4. Theo: Scores: 84, 88, 81, 85, 77, 76 Mean = (84 + 88 + 81 + 85 + 77 + 76) / 6 = 491 / 6 ≈ 81.833
Now we add the new score of 100 to each person's scores and recalculate the mean:
New mean for Ara: New Scores: 100, 98, 99, 97, 100, 100, 100 New Mean = (594 + 100) / 7 = 694 / 7 ≈ 99.143
Mean increase for Ara: 99.143 - 99 = 0.143
New mean for Dana: New Scores: 68, 74, 83, 80, 81, 82, 100 New Mean = (468 + 100) / 7 = 568 / 7 ≈ 81.143
Mean increase for Dana: 81.143 - 78 = 3.143
New mean for Jose: New Scores: 91, 93, 97, 96, 96, 96, 100 New Mean = (569 + 100) / 7 = 669 / 7 ≈ 95.571
Mean increase for Jose: 95.571 - 94.833 ≈ 0.738
New mean for Theo: New Scores: 84, 88, 81, 85, 77, 76, 100 New Mean = (491 + 100) / 7 = 591 / 7 ≈ 84.429
Mean increase for Theo: 84.429 - 81.833 ≈ 2.596
Now we compare the mean increases:
- Ara: 0.143
- Dana: 3.143
- Jose: 0.738
- Theo: 2.596
Dana's mean test score increases the most by 3.143 points.
Thus, the answer is Dana.