Theo, Ara, Jose, and Dana all got 100 percent on their latest math test. Their scores on the previous six tests are listed. Whose mean test score will increase the most?
A. Dana: 68, 74, 83, 80, 81, 82
B. Jose: 91, 93, 97, 96, 96, 96
C. Theo: 84, 88, 81, 85, 77, 76
D. Ara: 100, 98, 99, 97, 100, 100
Since all four students got 100 percent on their latest math test, their mean test scores will all increase by the same amount. Therefore, the previous test scores are irrelevant and the answer is the same for all four students. The mean test score will increase by the same amount for all of them. Answer: all of them.
To determine whose mean test score will increase the most, we need to calculate the mean test score for each person before and after their latest math test.
Let's calculate the mean test scores for each person before their latest math test:
A. Dana: (68 + 74 + 83 + 80 + 81 + 82) / 6 = 78.0
B. Jose: (91 + 93 + 97 + 96 + 96 + 96) / 6 = 95.5
C. Theo: (84 + 88 + 81 + 85 + 77 + 76) / 6 = 82.0
D. Ara: (100 + 98 + 99 + 97 + 100 + 100) / 6 = 98.3
Now let's calculate the mean test scores for each person after their latest math test (assuming they got 100% in their latest test):
A. Dana: (68 + 74 + 83 + 80 + 81 + 82 + 100) / 7 = 82.9
B. Jose: (91 + 93 + 97 + 96 + 96 + 96 + 100) / 7 = 95.9
C. Theo: (84 + 88 + 81 + 85 + 77 + 76 + 100) / 7 = 85.0
D. Ara: (100 + 98 + 99 + 97 + 100 + 100 + 100) / 7 = 99.3
Now let's calculate the difference between the mean test scores before and after for each person:
A. Dana: 82.9 - 78.0 = 4.9
B. Jose: 95.9 - 95.5 = 0.4
C. Theo: 85.0 - 82.0 = 3.0
D. Ara: 99.3 - 98.3 = 1.0
Based on the calculations, Dana's mean test score increased the most, by 4.9 points, which means the correct answer is A. Dana.