To determine whose mean test score will increase the most after getting a score of 100 on their latest test, we can calculate the mean scores for each person before adding the new score.
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Jose's scores:
- Scores: 91, 93, 97, 96, 96, 96
- Mean: (91 + 93 + 97 + 96 + 96 + 96) / 6 = 95.5
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Theo's scores:
- Scores: 84, 88, 81, 85, 77, 76
- Mean: (84 + 88 + 81 + 85 + 77 + 76) / 6 = 81.5
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Dana's scores:
- Scores: 68, 74, 83, 80, 81, 82
- Mean: (68 + 74 + 83 + 80 + 81 + 82) / 6 = 78.67 (approximately)
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Ara's scores:
- Scores: 100, 98, 99, 97, 100, 100
- Mean: (100 + 98 + 99 + 97 + 100 + 100) / 6 = 99.67 (approximately)
Next, we add the new score of 100 to each person's total and calculate the new mean:
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New Mean for Jose:
- New Scores: 91, 93, 97, 96, 96, 96, 100
- New Mean: (91 + 93 + 97 + 96 + 96 + 96 + 100) / 7 = 95.71 (approximately)
Increase: 95.71 - 95.5 = 0.21
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New Mean for Theo:
- New Scores: 84, 88, 81, 85, 77, 76, 100
- New Mean: (84 + 88 + 81 + 85 + 77 + 76 + 100) / 7 = 83.57 (approximately)
Increase: 83.57 - 81.5 = 2.07
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New Mean for Dana:
- New Scores: 68, 74, 83, 80, 81, 82, 100
- New Mean: (68 + 74 + 83 + 80 + 81 + 82 + 100) / 7 = 80.14 (approximately)
Increase: 80.14 - 78.67 = 1.47
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New Mean for Ara:
- New Scores: 100, 98, 99, 97, 100, 100, 100
- New Mean: (100 + 98 + 99 + 97 + 100 + 100 + 100) / 7 = 99.71 (approximately)
Increase: 99.71 - 99.67 = 0.04
Now, we compare the increases:
- Jose: 0.21
- Theo: 2.07
- Dana: 1.47
- Ara: 0.04
Conclusion: Theo's mean test score will increase the most by 2.07 points.