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?
Theo: 84, 88, 81, 85, 77, 76
Jose: 91, 93, 97, 96, 96, 96
Ara: 100, 98, 99, 97, 100, 100
Dana: 68, 74, 83, 80, 81, 82
Dana's mean test score will increase the most because she had the lowest scores out of the four students. Getting a perfect score on the latest test will have a greater impact on her overall mean compared to the other students who already had high scores.
is the answer dana?
Yes, that is correct! Dana's mean test score will increase the most.
To find out whose mean test score will increase the most, we need to calculate the mean for each person's previous test scores and compare it to their mean including the latest test.
Theo's mean (previous): (84 + 88 + 81 + 85 + 77 + 76) / 6 = 82.8
Theo's mean (including latest): (82.8 + 100) / 7 = 85.1
Jose's mean (previous): (91 + 93 + 97 + 96 + 96 + 96) / 6 = 95.8
Jose's mean (including latest): (95.8 + 100) / 7 = 96.4
Ara's mean (previous): (100 + 98 + 99 + 97 + 100 + 100) / 6 = 99.2
Ara's mean (including latest): (99.2 + 100) / 7 = 99.4
Dana's mean (previous): (68 + 74 + 83 + 80 + 81 + 82) / 6 = 77.3
Dana's mean (including latest): (77.3 + 100) / 7 = 81.0
Comparing the mean scores, we can see that Ara's mean score will increase the most, from 99.2 to 99.4, an increase of 0.2. Therefore, Ara's mean test score will increase the most.