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
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
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
Answers
GPT-4o mini
To determine whose mean test score will increase the most after receiving a perfect score of 100 on the latest test, we first need to calculate the current mean scores for each individual, then find the new mean after adding the perfect score.
1. **Calculate Current Mean Scores:**
- **Ara:**
- Scores: 100, 98, 99, 97, 100, 100
- Total = 100 + 98 + 99 + 97 + 100 + 100 = 594
- Mean = 594 / 6 = 99
- **Jose:**
- Scores: 91, 93, 97, 96, 96, 96
- Total = 91 + 93 + 97 + 96 + 96 + 96 = 569
- Mean = 569 / 6 = 94.8333 (approx. 94.83)
- **Dana:**
- Scores: 68, 74, 83, 80, 81, 82
- Total = 68 + 74 + 83 + 80 + 81 + 82 = 468
- Mean = 468 / 6 = 78
- **Theo:**
- Scores: 84, 88, 81, 85, 77, 76
- Total = 84 + 88 + 81 + 85 + 77 + 76 = 491
- Mean = 491 / 6 = 81.8333 (approx. 81.83)
2. **New Mean After Adding the Perfect Score:**
After each person receives a score of 100:
- **Ara:**
- New Total = 594 + 100 = 694
- New Mean = 694 / 7 = 99.142857 (approx. 99.14)
- Increase = 99.14 - 99 = 0.14
- **Jose:**
- New Total = 569 + 100 = 669
- New Mean = 669 / 7 = 95.571428 (approx. 95.57)
- Increase = 95.57 - 94.83 = 0.74
- **Dana:**
- New Total = 468 + 100 = 568
- New Mean = 568 / 7 = 81.142857 (approx. 81.14)
- Increase = 81.14 - 78 = 3.14
- **Theo:**
- New Total = 491 + 100 = 591
- New Mean = 591 / 7 = 84.428571 (approx. 84.43)
- Increase = 84.43 - 81.83 = 2.6
3. **Determine Who's Mean Increases the Most:**
- Ara's mean increases by **0.14**
- Jose's mean increases by **0.74**
- Dana's mean increases by **3.14**
- Theo's mean increases by **2.6**
**Conclusion:**
Dana's mean test score will increase the most by **3.14 points** after scoring 100 on the latest test.
1. **Calculate Current Mean Scores:**
- **Ara:**
- Scores: 100, 98, 99, 97, 100, 100
- Total = 100 + 98 + 99 + 97 + 100 + 100 = 594
- Mean = 594 / 6 = 99
- **Jose:**
- Scores: 91, 93, 97, 96, 96, 96
- Total = 91 + 93 + 97 + 96 + 96 + 96 = 569
- Mean = 569 / 6 = 94.8333 (approx. 94.83)
- **Dana:**
- Scores: 68, 74, 83, 80, 81, 82
- Total = 68 + 74 + 83 + 80 + 81 + 82 = 468
- Mean = 468 / 6 = 78
- **Theo:**
- Scores: 84, 88, 81, 85, 77, 76
- Total = 84 + 88 + 81 + 85 + 77 + 76 = 491
- Mean = 491 / 6 = 81.8333 (approx. 81.83)
2. **New Mean After Adding the Perfect Score:**
After each person receives a score of 100:
- **Ara:**
- New Total = 594 + 100 = 694
- New Mean = 694 / 7 = 99.142857 (approx. 99.14)
- Increase = 99.14 - 99 = 0.14
- **Jose:**
- New Total = 569 + 100 = 669
- New Mean = 669 / 7 = 95.571428 (approx. 95.57)
- Increase = 95.57 - 94.83 = 0.74
- **Dana:**
- New Total = 468 + 100 = 568
- New Mean = 568 / 7 = 81.142857 (approx. 81.14)
- Increase = 81.14 - 78 = 3.14
- **Theo:**
- New Total = 491 + 100 = 591
- New Mean = 591 / 7 = 84.428571 (approx. 84.43)
- Increase = 84.43 - 81.83 = 2.6
3. **Determine Who's Mean Increases the Most:**
- Ara's mean increases by **0.14**
- Jose's mean increases by **0.74**
- Dana's mean increases by **3.14**
- Theo's mean increases by **2.6**
**Conclusion:**
Dana's mean test score will increase the most by **3.14 points** after scoring 100 on the latest test.