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How is the mean absolute deviation calculated from the deviation values of 12, -8, 15, 17, -22, and -3 units?

1.83

2.57

3.33

12.83

Calculating the mean absolute deviation involves first converting all deviation values to their absolute values. This ensures that the deviations are treated without regard to their direction — whether they are positive or negative.

For the given deviation values of 12, -8, 15, 17, -22, and -3, we will take the absolute values:

- |12| = 12

- |-8| = 8

- |15| = 15

- |17| = 17

- |-22| = 22

- |-3| = 3

Next, we sum these absolute values:

12 + 8 + 15 + 17 + 22 + 3 = 77

To find the mean absolute deviation, we then divide this sum by the number of values. Here, there are 6 deviation values:

Mean Absolute Deviation = Total Absolute Deviation / Number of Deviations

Mean Absolute Deviation = 77 / 6 ≈ 12.83

Thus, the mean absolute deviation is approximately 12.83. This validates the choice of answer, aligning with the correct result from the calculations.

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