To determine whose mean test score will increase the most after scoring 100 on their latest math test, we need to calculate the mean scores for each individual before and after the test.
Step 1: Calculate mean scores before the new test
Dana's scores: 68, 74, 83, 80, 81, 82
Mean = (68 + 74 + 83 + 80 + 81 + 82) / 6
Mean = 468 / 6 = 78
Theo's scores: 84, 88, 81, 85, 77, 76
Mean = (84 + 88 + 81 + 85 + 77 + 76) / 6
Mean = 491 / 6 ≈ 81.83
Ara's scores: 100, 98, 99, 97, 100, 100
Mean = (100 + 98 + 99 + 97 + 100 + 100) / 6
Mean = 594 / 6 = 99
Jose's scores: 91, 93, 97, 96, 96, 96
Mean = (91 + 93 + 97 + 96 + 96 + 96) / 6
Mean = 569 / 6 ≈ 94.83
Step 2: Calculate mean scores after the new test (with a score of 100)
Dana's new mean:
New scores: 68, 74, 83, 80, 81, 82, 100
Mean = (68 + 74 + 83 + 80 + 81 + 82 + 100) / 7
Mean = 468 + 100 / 7 = 568 / 7 ≈ 81.14
Increase = 81.14 - 78 = 3.14
Theo's new mean:
New scores: 84, 88, 81, 85, 77, 76, 100
Mean = (84 + 88 + 81 + 85 + 77 + 76 + 100) / 7
Mean = 491 + 100 / 7 = 591 / 7 ≈ 84.43
Increase = 84.43 - 81.83 ≈ 2.6
Ara's new mean:
New scores: 100, 98, 99, 97, 100, 100, 100
Mean = (100 + 98 + 99 + 97 + 100 + 100 + 100) / 7
Mean = 594 + 100 / 7 = 694 / 7 ≈ 99.14
Increase = 99.14 - 99 = 0.14
Jose's new mean:
New scores: 91, 93, 97, 96, 96, 96, 100
Mean = (91 + 93 + 97 + 96 + 96 + 96 + 100) / 7
Mean = 569 + 100 / 7 = 669 / 7 ≈ 95.57
Increase = 95.57 - 94.83 ≈ 0.74
Step 3: Compare increases
- Dana: Increase of ≈ 3.14
- Theo: Increase of ≈ 2.6
- Ara: Increase of ≈ 0.14
- Jose: Increase of ≈ 0.74
Conclusion
Dana's mean test score will increase the most after scoring 100 on the latest math test.