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?
a Dana: 68, 74, 83, 80, 81, 82
b Ara: 100, 98, 99, 97, 100, 100
c Jose: 91, 93, 97, 96, 96, 96
d Theo: 84, 88, 81, 85, 77, 76
@bot answer the question and thank you for answering it
Based on the given information, Ara's mean test score will increase the most because they had the highest scores on the previous six tests. Therefore, getting a perfect score on the latest math test will have the biggest impact on their overall mean test score.
You're welcome!
Are you sure the answer you got is correct?
I apologize for my error in the previous response. The correct answer is actually Dana.
To calculate the change in mean test score, we need to find the mean of each student's previous six test scores and then compare it to the mean of their seven test scores including the latest math test. Here are the calculations:
- Dana: Mean of previous 6 tests = (68+74+83+80+81+82)/6 = 77.33
New mean of 7 tests = (68+74+83+80+81+82+100)/7 = 81.14
Change in mean = 81.14 - 77.33 = 3.81
- Ara: Mean of previous 6 tests = (100+98+99+97+100+100)/6 = 99.00
New mean of 7 tests = (100+98+99+97+100+100+100)/7 = 99.29
Change in mean = 99.29 - 99.00 = 0.29
- Jose: Mean of previous 6 tests = (91+93+97+96+96+96)/6 = 95.17
New mean of 7 tests = (91+93+97+96+96+96+100)/7 = 95.71
Change in mean = 95.71 - 95.17 = 0.54
- Theo: Mean of previous 6 tests = (84+88+81+85+77+76)/6 = 82.00
New mean of 7 tests = (84+88+81+85+77+76+100)/7 = 84.86
Change in mean = 84.86 - 82.00 = 2.86
Therefore, Dana's mean test score will increase the most with a change of 3.81.
Dana is the correct answer right?
Yes, Dana is the correct answer. My apologies for the confusion earlier.
To determine whose mean test score will increase the most, we need to calculate the mean test score for each of the students on their previous six tests and compare the differences.
Let's calculate the mean test scores for each student:
a. Dana:
Mean test score = (68 + 74 + 83 + 80 + 81 + 82) / 6 = 78
b. Ara:
Mean test score = (100 + 98 + 99 + 97 + 100 + 100) / 6 = 98.33
c. Jose:
Mean test score = (91 + 93 + 97 + 96 + 96 + 96) / 6 = 95.5
d. Theo:
Mean test score = (84 + 88 + 81 + 85 + 77 + 76) / 6 = 82.83
Now, let's calculate the increase in mean test scores for each student by subtracting their previous mean test score from 100 (since they all got 100% on their latest math test):
a. Dana: Increase = 100 - 78 = 22
b. Ara: Increase = 100 - 98.33 = 1.67
c. Jose: Increase = 100 - 95.5 = 4.5
d. Theo: Increase = 100 - 82.83 = 17.17
Comparing the differences, we can see that Dana's mean test score will increase the most, with an increase of 22. Therefore, the answer is option a) Dana.