To determine whose mean test score will increase the most after receiving a score of 100 on the latest math test, we will first calculate the current mean scores for each student and then find their new mean after including the latest test score.
Step 1: Calculate the current means.
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Dana:
- Scores: 68, 74, 83, 80, 81, 82
- Total = 68 + 74 + 83 + 80 + 81 + 82 = 468
- Mean = 468 / 6 = 78
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Jose:
- Scores: 91, 93, 97, 96, 96, 96
- Total = 91 + 93 + 97 + 96 + 96 + 96 = 569
- Mean = 569 / 6 = 94.8333 (approximately 94.83)
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Theo:
- Scores: 84, 88, 81, 85, 77, 76
- Total = 84 + 88 + 81 + 85 + 77 + 76 = 491
- Mean = 491 / 6 = 81.8333 (approximately 81.83)
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Ara:
- Scores: 100, 98, 99, 97, 100, 100
- Total = 100 + 98 + 99 + 97 + 100 + 100 = 594
- Mean = 594 / 6 = 99
Step 2: Calculate the new means after adding a score of 100.
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Dana:
- New Total = 468 + 100 = 568
- New Mean = 568 / 7 = 81.142857 (approximately 81.14)
- Increase = 81.14 - 78 = 3.14
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Jose:
- New Total = 569 + 100 = 669
- New Mean = 669 / 7 = 95.571429 (approximately 95.57)
- Increase = 95.57 - 94.83 = 0.74
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Theo:
- New Total = 491 + 100 = 591
- New Mean = 591 / 7 = 84.428571 (approximately 84.43)
- Increase = 84.43 - 81.83 = 2.60
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Ara:
- New Total = 594 + 100 = 694
- New Mean = 694 / 7 = 99.142857 (approximately 99.14)
- Increase = 99.14 - 99 = 0.14
Step 3: Determine whose mean increases the most.
- Dana: Increase = 3.14
- Jose: Increase = 0.74
- Theo: Increase = 2.60
- Ara: Increase = 0.14
The largest increase in mean test score is for Dana, with an increase of 3.14.