Tom and Abby wanted to see whose grades were the closest to their final grade after their last unit test.

Question

Tom and Abby wanted to see whose grades were the closest to their final grade after their last unit test.

For Tom’s 5 lesson/test grades he has: 74, 65, 88, 90, 100, 75

For Abby’s 5 lesson/test grades she has: 77, 78, 80, 80, 90, 93.

Feel free to use the worksheet to show your work, or complete all work on your own paper. Either way, all work must be shown. If needed, round to the nearest tenths place.

Question 1: What is the mean or average percent for both Tom and Abby’s overall unit grade?

Question 2: What is the MAD of Tom and Abby’s unit grade?

Question 3: Which student’s (Tom or Abby) grades were the closest to their overall average? For this student, what could this mean about their grades? Make sure to answer both parts of this question.

Answer 1

To find the mean or average percent for both Tom and Abby's overall unit grades, we need to find the average of their test scores.

For Tom:
Mean = (74 + 65 + 88 + 90 + 100 + 75) / 6
Mean = 492 / 6
Mean ≈ 82

For Abby:
Mean = (77 + 78 + 80 + 80 + 90 + 93) / 6
Mean = 498 / 6
Mean ≈ 83.2

So the mean or average percent for Tom's overall unit grade is approximately 82, and for Abby, it is approximately 83.2.

To find the MAD (Mean Absolute Deviation) of Tom and Abby's unit grade, we need to calculate the average deviation from the mean of their test scores.

For Tom:
Deviation from mean = |74 - 82| + |65 - 82| + |88 - 82| + |90 - 82| + |100 - 82| + |75 - 82|
Deviation from mean = 8 + 17 + 6 + 8 + 18 + 7
Deviation from mean = 64

MAD = 64/6
MAD ≈ 10.7

For Abby:
Deviation from mean = |77 - 83.2| + |78 - 83.2| + |80 - 83.2| + |80 - 83.2| + |90 - 83.2| + |93 - 83.2|
Deviation from mean = 6.2 + 5.2 + 3.2 + 3.2 + 6.8 + 9.8
Deviation from mean ≈ 34.4

MAD = 34.4/6
MAD ≈ 5.7

So the MAD of Tom's unit grade is approximately 10.7, and for Abby, it is approximately 5.7.

To determine which student's grades were closest to their overall average, we need to compare their MAD values. The student with the smaller MAD value has grades that are closer to their overall average.

In this case, Abby has a smaller MAD value of approximately 5.7, which means her grades were closer to her overall average compared to Tom. This could mean that Abby's performance on different tests was more consistent and stable compared to Tom, who had larger deviations from his average.