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)
To find the mean absolute deviation, we first need to find the mean of the grades:
Mean = (74 + 81 + 86 + 92 + 74 + 85 + 90 + 89 + 78 + 80) / 10
Mean = 839 / 10
Mean = 83.9
Next, we find the absolute deviation for each grade by subtracting the mean from each grade and taking the absolute value:
|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
Now, we find the mean of these absolute deviations:
Mean absolute deviation = (9.9 + 2.9 + 2.1 + 8.1 + 9.9 + 1.1 + 6.1 + 5.1 + 5.9 + 3.9) / 10
Mean absolute deviation = 55.9 / 10
Mean absolute deviation = 5.59
Therefore, the mean absolute deviation of Lucia's Spanish quiz grades is 5.59.