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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)

Responses

Jose: 91, 93, 97, 96, 96, 96
Jose: 91, 93, 97, 96, 96, 96

Ara: 100, 98, 99, 97, 100, 100
Ara: 100, 98, 99, 97, 100, 100

Theo: 84, 88, 81, 85, 77, 76
Theo: 84, 88, 81, 85, 77, 76

Dana: 68, 74, 83, 80, 81, 82

1 answer

To determine whose mean test score will increase the most after adding a score of 100 for their latest math test, we first need to calculate the current mean scores for each individual and then see how the addition of the new score affects their means.

  1. Jose:

    • Scores: 91, 93, 97, 96, 96, 96
    • Mean = (91 + 93 + 97 + 96 + 96 + 96) / 6 = 95.5
    • New mean after adding 100: (91 + 93 + 97 + 96 + 96 + 96 + 100) / 7 = (579) / 7 = 82.71
    • Increase in mean: 82.71 - 95.5 = 0.30

  2. Ara:

    • Scores: 100, 98, 99, 97, 100, 100
    • Mean = (100 + 98 + 99 + 97 + 100 + 100) / 6 = 99.67
    • New mean after adding 100: (100 + 98 + 99 + 97 + 100 + 100 + 100) / 7 = (694) / 7 = 99.14
    • Increase in mean: 99.14 - 99.67 = -0.53 (decrease)

  3. Theo:

    • Scores: 84, 88, 81, 85, 77, 76
    • Mean = (84 + 88 + 81 + 85 + 77 + 76) / 6 = 82.5
    • New mean after adding 100: (84 + 88 + 81 + 85 + 77 + 76 + 100) / 7 = (511) / 7 = 73.29
    • Increase in mean: 73.29 - 82.5 = -9.21 (decrease)

  4. Dana:

    • Scores: 68, 74, 83, 80, 81, 82
    • Mean = (68 + 74 + 83 + 80 + 81 + 82) / 6 = 76.33
    • New mean after adding 100: (68 + 74 + 83 + 80 + 81 + 82 + 100) / 7 = (568) / 7 = 81.14
    • Increase in mean: 81.14 - 76.33 = 4.81

Conclusion:

  • Jose's increase in mean is 0.30.
  • Ara's mean actually decreases by 0.53.
  • Theo's mean decreases by 9.21.
  • Dana's mean increases by 4.81.

Thus, Dana's mean test score will increase the most after adding the perfect score of 100.