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What is the mean absolute deviation of the deviations 15, -6, 12, 8, -18, and -4 units?

  1. 8.5 units

  2. 10.5 units

  3. 12.5 units

  4. 15.0 units

The correct answer is: 10.5 units

To determine the mean absolute deviation, you first need to calculate the absolute values of each of the deviations provided. This involves converting negative values to positive values, which results in the following absolute deviations: 15, 6, 12, 8, 18, and 4. Next, you would find the mean of these absolute deviations. To do this, sum the absolute values: 15 + 6 + 12 + 8 + 18 + 4 = 63. Then, divide this sum by the number of observations, which in this case is 6: 63 / 6 = 10.5. Thus, the mean absolute deviation of the deviations is 10.5 units, making this the correct answer. This metric is useful for understanding how spread out the deviations are from the mean of a given dataset, indicating variability or dispersion in the data.