Mean Absolute Deviation Quick Check
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Question
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
To find the mean absolute deviation, we first need to calculate the mean of Lucia's grades:
(74 + 81 + 86 + 92 + 74 + 85 + 90 + 89 + 78 + 80) / 10 = 825 / 10 = 82.5
Next, we calculate the absolute deviations from the mean for each grade:
|74 - 82.5| = 8.5
|81 - 82.5| = 1.5
|86 - 82.5| = 3.5
|92 - 82.5| = 9.5
|74 - 82.5| = 8.5
|85 - 82.5| = 2.5
|90 - 82.5| = 7.5
|89 - 82.5| = 6.5
|78 - 82.5| = 4.5
|80 - 82.5| = 2.5
Now, we find the average of these absolute deviations:
(8.5 + 1.5 + 3.5 + 9.5 + 8.5 + 2.5 + 7.5 + 6.5 + 4.5 + 2.5) / 10 = 55 / 10 = 5.5
Therefore, the mean absolute deviation of Lucia's Spanish quiz grades is 5.5.