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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

55
55

82.9
82.9

8.29
8.29

5.5

1 answer

To calculate the mean absolute deviation (MAD) of Lucia's Spanish quiz grades, we follow these steps:

  1. Calculate the mean of the grades. The grades are: 74, 81, 86, 92, 74, 85, 90, 89, 78, 80.

    First, find the sum of the grades: \[ 74 + 81 + 86 + 92 + 74 + 85 + 90 + 89 + 78 + 80 = 839 \] Next, find the mean: \[ \text{Mean} = \frac{839}{10} = 83.9 \]

  2. Calculate the absolute deviations from the mean. Now, we subtract the mean from each grade and take the absolute value:

    • |74 - 83.9| = | -9.9| = 9.9
    • |81 - 83.9| = | -2.9| = 2.9
    • |86 - 83.9| = | 2.1| = 2.1
    • |92 - 83.9| = | 8.1| = 8.1
    • |74 - 83.9| = | -9.9| = 9.9
    • |85 - 83.9| = | 1.1| = 1.1
    • |90 - 83.9| = | 6.1| = 6.1
    • |89 - 83.9| = | 5.1| = 5.1
    • |78 - 83.9| = | -5.9| = 5.9
    • |80 - 83.9| = | -3.9| = 3.9

    The absolute deviations are: 9.9, 2.9, 2.1, 8.1, 9.9, 1.1, 6.1, 5.1, 5.9, 3.9

  3. Calculate the mean of these absolute deviations. Sum of absolute deviations: \[ 9.9 + 2.9 + 2.1 + 8.1 + 9.9 + 1.1 + 6.1 + 5.1 + 5.9 + 3.9 = 54.1 \]

    Now, find the mean of these absolute deviations: \[ \text{MAD} = \frac{54.1}{10} = 5.41 \]

Considering the options provided, none of the choices (55, 82.9, 8.29, 5.5) directly match the calculated 5.41.

However, since 5.41 is approximately equal to 5.5, the closest choice available is:

5.5