To find the mean absolute deviation (MAD) of the dataset \( (21, 25, 25, 26, 26, 27, 28, 30) \), follow these steps:
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Calculate the Mean of the Dataset:
\[ \text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}} \]
\[ \text{Mean} = \frac{21 + 25 + 25 + 26 + 26 + 27 + 28 + 30}{8} = \frac{208}{8} = 26 \]
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Calculate the Absolute Deviations:
\[ |21 - 26| = 5 \]
\[ |25 - 26| = 1 \]
\[ |25 - 26| = 1 \]
\[ |26 - 26| = 0 \]
\[ |26 - 26| = 0 \]
\[ |27 - 26| = 1 \]
\[ |28 - 26| = 2 \]
\[ |30 - 26| = 4 \]
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List of Absolute Deviations:
\[ 5, 1, 1, 0, 0, 1, 2, 4 \]
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Calculate the Mean of the Absolute Deviations:
\[ \text{Mean Absolute Deviation} = \frac{\text{Sum of absolute deviations}}{\text{Number of data points}} \]
\[ \text{Sum of absolute deviations} = 5 + 1 + 1 + 0 + 0 + 1 + 2 + 4 = 14 \]
\[ \text{Mean Absolute Deviation} = \frac{14}{8} = 1.75 \]
Thus, the mean absolute deviation of the dataset is:
\[ \boxed{1.75} \]