Question

Theo, Ara , Jose and Dana all got 100 percent on their latest math test. Their scores on previous six tests are listed. Whose mean test scores will increase the most?

Theo: 84, 88, 81, 85, 77, 76
Ara: 100, 98, 99, 97, 100, 100
Dana: 68, 74, 83, 80, 81, 82
Jose: 91, 93, 97, 96, 96, 96

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine whose mean test score will increase the most, we need to calculate the average of each student's previous six test scores and then compare it to their average with the 100% included.

Theo's average without the 100% included: (84 + 88 + 81 + 85 + 77 + 76)/6 = 81.83
Theo's average with the 100% included: (84 + 88 + 81 + 85 + 77 + 76 + 100)/7 ≈ 85.57
Increase in Theo's average: 85.57 - 81.83 = 3.74

Ara's average without the 100% included: (100 + 98 + 99 + 97 + 100 + 100)/6 ≈ 98.33
Ara's average with the 100% included: (100 + 98 + 99 + 97 + 100 + 100 + 100)/7 ≈ 99.33
Increase in Ara's average: 99.33 - 98.33 = 1

Dana's average without the 100% included: (68 + 74 + 83 + 80 + 81 + 82)/6 ≈ 78.0
Dana's average with the 100% included: (68 + 74 + 83 + 80 + 81 + 82 + 100)/7 ≈ 81.14
Increase in Dana's average: 81.14 - 78.0 ≈ 3.14

Jose's average without the 100% included: (91 + 93 + 97 + 96 + 96 + 96)/6 ≈ 95.83
Jose's average with the 100% included: (91 + 93 + 97 + 96 + 96 + 96 + 100)/7 ≈ 95.71
Increase in Jose's average: 95.71 - 95.83 ≈ -0.12

Therefore, Dana's mean test score will increase the most out of the four students.