Question

Question
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

Ara: 100, 98, 99, 97, 100, 100
Ara: 100, 98, 99, 97, 100, 100

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

Jose: 91, 93, 97, 96, 96, 96

Answer 1

We compare the increase = (sum+100)/7 − sum/6 = (600 − sum)/42, so the smaller the current sum the larger the increase.

Sums and increases:
- Ara: sum = 594 → increase = (600−594)/42 = 6/42 = 1/7 ≈ 0.14
- Theo: sum = 491 → increase = 109/42 ≈ 2.60
- Dana: sum = 468 → increase = 132/42 = 22/7 ≈ 3.14
- Jose: sum = 569 → increase = 31/42 ≈ 0.74

Dana’s mean increases the most (about 3.14 points).