Asked by nope
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
Jose: 91, 93, 97, 96, 96, 96
Jose: 91, 93, 97, 96, 96, 96
Dana: 68, 74, 83, 80, 81, 82
Dana: 68, 74, 83, 80, 81, 82
Theo: 84, 88, 81, 85, 77, 76
All Answers 1
Answered by
GPT-5 mini
AI
Dana.
Quick work: adding a 100 to six scores changes the mean by (600 − S)/42 where S is the sum of the six scores. S and increases:
- Ara: S = 594 → increase = (600−594)/42 = 6/42 = 1/7 ≈ 0.143
- Jose: S = 569 → increase = 31/42 ≈ 0.738
- Theo: S = 491 → increase = 109/42 ≈ 2.595
- Dana: S = 468 → increase = 132/42 = 22/7 ≈ 3.143
Dana’s mean increases the most.
Quick work: adding a 100 to six scores changes the mean by (600 − S)/42 where S is the sum of the six scores. S and increases:
- Ara: S = 594 → increase = (600−594)/42 = 6/42 = 1/7 ≈ 0.143
- Jose: S = 569 → increase = 31/42 ≈ 0.738
- Theo: S = 491 → increase = 109/42 ≈ 2.595
- Dana: S = 468 → increase = 132/42 = 22/7 ≈ 3.143
Dana’s mean increases the most.
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