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

Dana: 68, 74, 83, 80, 81, 82
Dana: 68, 74, 83, 80, 81, 82

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

Theo: 84, 88, 81, 85, 77, 76

:)

Answer 1

To determine whose mean test score will increase the most after scoring 100% on the latest test, we need to calculate the mean scores for each student both before and after adding the latest test score.

**Step 1: Calculate the mean scores before the latest test.**

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

2. **Dana:**
Scores: 68, 74, 83, 80, 81, 82
Sum = 68 + 74 + 83 + 80 + 81 + 82 = 468
Mean = 468 / 6 = 78

3. **Jose:**
Scores: 91, 93, 97, 96, 96, 96
Sum = 91 + 93 + 97 + 96 + 96 + 96 = 569
Mean = 569 / 6 = 94.83 (approximately)

4. **Theo:**
Scores: 84, 88, 81, 85, 77, 76
Sum = 84 + 88 + 81 + 85 + 77 + 76 = 491
Mean = 491 / 6 = 81.83 (approximately)

**Step 2: Calculate the new mean scores after adding the latest test score (100).**

1. **Ara:**
New sum = 594 + 100 = 694
New mean = 694 / 7 ≈ 99.14

Increase = 99.14 - 99 = 0.14

2. **Dana:**
New sum = 468 + 100 = 568
New mean = 568 / 7 ≈ 81.14

Increase = 81.14 - 78 = 3.14

3. **Jose:**
New sum = 569 + 100 = 669
New mean = 669 / 7 ≈ 95.57

Increase = 95.57 - 94.83 ≈ 0.74

4. **Theo:**
New sum = 491 + 100 = 591
New mean = 591 / 7 ≈ 84.43

Increase = 84.43 - 81.83 ≈ 2.60

**Step 3: Summary of increases:**

- Ara: +0.14
- Dana: +3.14
- Jose: +0.74
- Theo: +2.60

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