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

8.29
8.29

55
55

5.5
5.5

82.9

1 answer

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 = 819 / 10 = 81.9

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

|74 - 81.9| = 7.9
|81 - 81.9| = 0.9
|86 - 81.9| = 4.1
|92 - 81.9| = 10.1
|74 - 81.9| = 7.9
|85 - 81.9| = 3.1
|90 - 81.9| = 8.1
|89 - 81.9| = 7.1
|78 - 81.9| = 3.9
|80 - 81.9| = 1.9

Now, find the mean of these absolute deviations:

(7.9 + 0.9 + 4.1 + 10.1 + 7.9 + 3.1 + 8.1 + 7.1 + 3.9 + 1.9) / 10 = 46.9 / 10 = 4.69

Therefore, the mean absolute deviation of Lucia's Spanish quiz grades is 4.69.