Question

Lucia has been recording her grades on her Spanish quizzes. The following is a list of her grades:

74, 81, 86, 92, 74, 85, 90, 89, 78, 80

Determine the mean absolute deviation of Lucia’s Spanish quiz grades.

(1 point)
Responses

82.9

5.5

55

8.29

Answer 1

To calculate the mean absolute deviation, follow these steps:

1. Find the mean of Lucia's grades:
(74 + 81 + 86 + 92 + 74 + 85 + 90 + 89 + 78 + 80) / 10 = 829 / 10 = 82.9

2. Calculate the absolute difference for each grade from the mean:
|74-82.9| = 8.9
|81-82.9| = 1.9
|86-82.9| = 3.1
|92-82.9| = 9.1
|74-82.9| = 8.9
|85-82.9| = 2.1
|90-82.9| = 7.1
|89-82.9| = 6.1
|78-82.9| = 4.9
|80-82.9| = 2.9

3. Find the mean of these absolute differences:
(8.9 + 1.9 + 3.1 + 9.1 + 8.9 + 2.1 + 7.1 + 6.1 + 4.9 + 2.9) / 10 = 55 / 10 = 5.5

Therefore, the mean absolute deviation of Lucia's Spanish quiz grades is 5.5.