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

To determine whose mean test score will increase the most after scoring 100 on their latest test, we first need to calculate the current mean scores for Theo, Ara, Dana, and Jose based on their previous six test scores.

**Calculating the mean for each student:**

1. **Ara:**
- Scores: 100, 98, 99, 97, 100, 100
- Mean = (100 + 98 + 99 + 97 + 100 + 100) / 6 = 594 / 6 = 99

2. **Theo:**
- Scores: 84, 88, 81, 85, 77, 76
- Mean = (84 + 88 + 81 + 85 + 77 + 76) / 6 = 491 / 6 ≈ 81.83

3. **Dana:**
- Scores: 68, 74, 83, 80, 81, 82
- Mean = (68 + 74 + 83 + 80 + 81 + 82) / 6 = 468 / 6 = 78

4. **Jose:**
- Scores: 91, 93, 97, 96, 96, 96
- Mean = (91 + 93 + 97 + 96 + 96 + 96) / 6 = 569 / 6 ≈ 94.83

**Calculating the new mean with the latest test score of 100:**

1. **Ara:**
- New mean = (594 + 100) / 7 = 694 / 7 ≈ 99.14
- Increase = 99.14 - 99 = 0.14

2. **Theo:**
- New mean = (491 + 100) / 7 = 591 / 7 ≈ 84.43
- Increase = 84.43 - 81.83 ≈ 2.60

3. **Dana:**
- New mean = (468 + 100) / 7 = 568 / 7 ≈ 81.14
- Increase = 81.14 - 78 = 3.14

4. **Jose:**
- New mean = (569 + 100) / 7 = 669 / 7 ≈ 95.57
- Increase = 95.57 - 94.83 ≈ 0.74

**Summary of increases:**
- Ara: 0.14
- Theo: 2.60
- Dana: 3.14
- Jose: 0.74

**Conclusion:**
Dana's mean test score will increase the most by approximately 3.14.