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To calculate who's mean test score will increase the most, we need to calculate the average of their previous six test scores and then find the difference between that average and their latest test score.
Tina:
Average of previous scores = (60+65+75+85+90+92)/6 = 77.83
Increase in mean test score = 100 - 77.83 = 22.17
Ben:
Average of previous scores = (90+92+93+95+97+90)/6 = 92.83
Increase in mean test score = 100 - 92.83 = 7.17
Miguel:
Average of previous scores = (80+82+90+85+86+84)/6 = 83.83
Increase in mean test score = 100 - 83.83 = 16.17
Shaya:
Average of previous scores = (70+80+75+85+90+95)/6 = 81.67
Increase in mean test score = 100 - 81.67 = 18.33
Therefore, Shaya's mean test score will increase the most at 18.33 points.