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
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.