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

Question

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

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

Responses

8.29
8.29

5.5
5.5

82.9
82.9

55

Answer 1

The correct answer is 5.5.

To calculate the mean absolute deviation, first find the mean of Lucia's grades:

(74 + 81 + 86 + 92 + 74 + 85 + 90 + 89 + 78 + 80) / 10 = 83.9

Next, find the absolute deviation of each grade from the mean:

|74 - 83.9| = 9.9
|81 - 83.9| = 2.9
|86 - 83.9| = 2.1
|92 - 83.9| = 8.1
|74 - 83.9| = 9.9
|85 - 83.9| = 1.1
|90 - 83.9| = 6.1
|89 - 83.9| = 5.1
|78 - 83.9| = 5.9
|80 - 83.9| = 3.9

Then, find the average of these absolute deviations:

(9.9 + 2.9 + 2.1 + 8.1 + 9.9 + 1.1 + 6.1 + 5.1 + 5.9 + 3.9) / 10 = 5.5

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