To find out whose mean test score will increase the most after scoring 100 percent on their latest math test, we will calculate the mean score for each individual before and after adding the score of 100.
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Calculate the mean for each student before the latest test:
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Jose:
- Scores: 91, 93, 97, 96, 96, 96
- Mean = (91 + 93 + 97 + 96 + 96 + 96) / 6 = 95.5
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Ara:
- Scores: 100, 98, 99, 97, 100, 100
- Mean = (100 + 98 + 99 + 97 + 100 + 100) / 6 = 99.67
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Dana:
- Scores: 68, 74, 83, 80, 81, 82
- Mean = (68 + 74 + 83 + 80 + 81 + 82) / 6 = 78.67
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Theo:
- Scores: 84, 88, 81, 85, 77, 76
- Mean = (84 + 88 + 81 + 85 + 77 + 76) / 6 = 80.5
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Calculate the new mean for each student after adding the score of 100:
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Jose:
- New Mean = (91 + 93 + 97 + 96 + 96 + 96 + 100) / 7 = 95.714
- Increase = 95.714 - 95.5 = 0.214
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Ara:
- New Mean = (100 + 98 + 99 + 97 + 100 + 100 + 100) / 7 = 99.71
- Increase = 99.71 - 99.67 = 0.04
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Dana:
- New Mean = (68 + 74 + 83 + 80 + 81 + 82 + 100) / 7 = 80.14
- Increase = 80.14 - 78.67 = 1.47
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Theo:
- New Mean = (84 + 88 + 81 + 85 + 77 + 76 + 100) / 7 = 84.14
- Increase = 84.14 - 80.5 = 3.64
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Determine who has the largest increase in mean score:
- Jose: Increase = 0.214
- Ara: Increase = 0.04
- Dana: Increase = 1.47
- Theo: Increase = 3.64
Conclusion: Theo's mean test score will increase the most, by 3.64 points.