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? (1 point)
Theo: 84, 88, 81, 85, 77, 76
Ara: 100, 98, 99, 97, 100, 100
Jose: 91, 93, 97, 96, 96, 96
Dana: 68, 74, 83, 80, 81, 82
To find whose mean test score will increase the most, we need to calculate the mean (average) test score for each student up until now, and compare it to their current mean test score.
Theo: (84 + 88 + 81 + 85 + 77 + 76) / 6 = 82.8
Ara: (100 + 98 + 99 + 97 + 100 + 100) / 6 = 98.3
Jose: (91 + 93 + 97 + 96 + 96 + 96) / 6 = 94.8
Dana: (68 + 74 + 83 + 80 + 81 + 82) / 6 = 78.0
Since all four students got 100% on their latest test, their new mean test scores would be:
Theo: (84 + 88 + 81 + 85 + 77 + 76 + 100) / 7 ≈ 85.43
Ara: (100 + 98 + 99 + 97 + 100 + 100 + 100) / 7 = 99.29
Jose: (91 + 93 + 97 + 96 + 96 + 96 + 100) / 7 = 95.86
Dana: (68 + 74 + 83 + 80 + 81 + 82 + 100) / 7 ≈ 82.57
The student whose mean test score will increase the most is Theo, with an increase of approximately 2.63 points.