To calculate the Mean Absolute Deviation (MAD) of the dataset \(2, 6, 8, 12, 12\), follow these steps:
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Find the mean of the dataset.
\[ \text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}} = \frac{2 + 6 + 8 + 12 + 12}{5} = \frac{40}{5} = 8 \]
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Find the absolute deviations from the mean.
\[ \begin{align*} |2 - 8| & = | -6 | = 6 \ |6 - 8| & = | -2 | = 2 \ |8 - 8| & = | 0 | = 0 \ |12 - 8| & = | 4 | = 4 \ |12 - 8| & = | 4 | = 4 \ \end{align*} \]
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List of absolute deviations: \[ 6, 2, 0, 4, 4 \]
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Calculate the mean of these absolute deviations:
\[ \text{MAD} = \frac{\text{Sum of absolute deviations}}{\text{Number of data points}} = \frac{6 + 2 + 0 + 4 + 4}{5} = \frac{16}{5} = 3.2 \]
Thus, the Mean Absolute Deviation (MAD) of the dataset is 3.2.