Theo, Ara, Jose and Dana all got 100 percent on their latest math test. Their scores on the previous six tests are listed. Whose means test score will increase the most?
Dana 68,74,83,80,81,82
Theo 84,88,81,85,77,76
Ara. 100,98,99,97,100, 100
Jose 91,93,97,96,96,96
Ara's mean test score will increase the most as they have been consistently scoring in the high 90s and 100s, while Dana's scores have been fluctuating and Theo's scores have been lower. Jose's scores have also been consistent, but not as high as Ara's.
To find out whose mean test score will increase the most, we need to calculate the mean (average) test score for each person's previous six tests and compare the differences.
Let's calculate the mean test scores for each person as follows:
1. Mean test score for Dana: (68 + 74 + 83 + 80 + 81 + 82) / 6 = 448 / 6 = 74.67
2. Mean test score for Theo: (84 + 88 + 81 + 85 + 77 + 76) / 6 = 491 / 6 = 81.83
3. Mean test score for Ara: (100 + 98 + 99 + 97 + 100 + 100) / 6 = 594 / 6 = 99
4. Mean test score for Jose: (91 + 93 + 97 + 96 + 96 + 96) / 6 = 569 / 6 = 94.83
Now let's calculate the increase in mean test scores for each person by subtracting their previous mean test scores from 100% (since they all got 100% on their latest test):
1. Increase in mean test score for Dana: 100 - 74.67 = 25.33
2. Increase in mean test score for Theo: 100 - 81.83 = 18.17
3. Increase in mean test score for Ara: 100 - 99 = 1
4. Increase in mean test score for Jose: 100 - 94.83 = 5.17
Therefore, Dana's mean test score will increase the most, with an increase of 25.33.