To determine whose mean test score will increase the most after scoring 100 on their latest test, we can calculate the mean score for each individual before the latest test and then figure out the new mean after adding the 100.
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Theo's scores:
- Previous scores: 84, 88, 81, 85, 77, 76
- Mean before: \((84 + 88 + 81 + 85 + 77 + 76) / 6 = 82.83\)
- New mean after test: \((82.83 \times 6 + 100) / 7 = 85.33\)
- Increase in mean: \(85.33 - 82.83 = 2.50\)
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Aram's scores:
- Previous scores: 100, 98, 99, 97, 100, 100
- Mean before: \((100 + 98 + 99 + 97 + 100 + 100) / 6 = 99\)
- New mean after test: \((99 \times 6 + 100) / 7 = 99.43\)
- Increase in mean: \(99.43 - 99 = 0.43\)
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Dana's scores:
- Previous scores: 68, 74, 83, 80, 81, 82
- Mean before: \((68 + 74 + 83 + 80 + 81 + 82) / 6 = 77.17\)
- New mean after test: \((77.17 \times 6 + 100) / 7 = 80.17\)
- Increase in mean: \(80.17 - 77.17 = 3.00\)
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Jose's scores:
- Previous scores: 91, 93, 97, 96, 96, 96
- Mean before: \((91 + 93 + 97 + 96 + 96 + 96) / 6 = 94.33\)
- New mean after test: \((94.33 \times 6 + 100) / 7 = 95.33\)
- Increase in mean: \(95.33 - 94.33 = 1.00\)
Now, let's summarize the increase in mean for each person:
- Theo: 2.50
- Aram: 0.43
- Dana: 3.00
- Jose: 1.00
Conclusion: Dana will have the largest increase in mean test score, which is \(3.00\).