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.
5.5
82.9
8.29
55
To find the mean absolute deviation of Lucia's Spanish quiz grades, first find the mean of the grades:
(74 + 81 + 86 + 92 + 74 + 85 + 90 + 89 + 78 + 80) / 10 = 829 / 10 = 82.9
Next, find the absolute deviation for each grade by subtracting the mean from each individual grade:
|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
Add up all the absolute deviation values:
8.9 + 1.9 + 3.1 + 9.1 + 8.9 + 2.1 + 7.1 + 6.1 + 4.9 + 2.9 = 55
Find the average of the absolute deviation values:
55 / 10 = 5.5
Therefore, the mean absolute deviation of Lucia's Spanish quiz grades is 5.5.