To determine whose mean test score will increase the most after adding a score of 100 to their previous test scores, we first calculate the mean for each of Theo, Ara, Jose, and Dana based on their past six tests, and then see how adding a perfect score changes their means.
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Jose's scores: 91, 93, 97, 96, 96, 96
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Mean = (91 + 93 + 97 + 96 + 96 + 96) / 6
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Mean = 569 / 6
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Mean = 94.83 (approximately)
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New mean after adding 100:
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New Mean = (569 + 100) / 7
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New Mean = 669 / 7
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New Mean = 95.57 (approximately)
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Increase in mean: 95.57 - 94.83 = 0.74
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Dana's scores: 68, 74, 83, 80, 81, 82
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Mean = (68 + 74 + 83 + 80 + 81 + 82) / 6
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Mean = 468 / 6
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Mean = 78
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New mean after adding 100:
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New Mean = (468 + 100) / 7
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New Mean = 568 / 7
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New Mean = 81.14 (approximately)
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Increase in mean: 81.14 - 78 = 3.14
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Theo's scores: 84, 88, 81, 85, 77, 76
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Mean = (84 + 88 + 81 + 85 + 77 + 76) / 6
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Mean = 491 / 6
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Mean = 81.83 (approximately)
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New mean after adding 100:
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New Mean = (491 + 100) / 7
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New Mean = 591 / 7
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New Mean = 84.43 (approximately)
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Increase in mean: 84.43 - 81.83 = 2.6
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Ara's scores: 100, 98, 99, 97, 100, 100
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Mean = (100 + 98 + 99 + 97 + 100 + 100) / 6
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Mean = 594 / 6
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Mean = 99
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New mean after adding 100:
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New Mean = (594 + 100) / 7
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New Mean = 694 / 7
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New Mean = 99.14 (approximately)
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Increase in mean: 99.14 - 99 = 0.14
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Now let's summarize the increases:
- Jose: 0.74
- Dana: 3.14
- Theo: 2.6
- Ara: 0.14
The mean test score that will increase the most is Dana's, with an increase of 3.14.