To calculate the mean absolute deviation (MAD) of the dataset \( 204, 211, 216, 300, 426, 567, 680 \), follow these steps:
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Calculate the mean of the dataset: \[ \text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}} \] \[ \text{Sum} = 204 + 211 + 216 + 300 + 426 + 567 + 680 = 2104 \] \[ \text{Number of data points} = 7 \] \[ \text{Mean} = \frac{2104}{7} \approx 300.57142857 \] Rounding to three decimal places, the mean is \( 300.571 \).
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Calculate the absolute deviations from the mean: \[ |204 - 300.571| \approx 96.571 \] \[ |211 - 300.571| \approx 89.571 \] \[ |216 - 300.571| \approx 84.571 \] \[ |300 - 300.571| \approx 0.571 \] \[ |426 - 300.571| \approx 125.429 \] \[ |567 - 300.571| \approx 266.429 \] \[ |680 - 300.571| \approx 379.429 \]
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Calculate the mean of the absolute deviations: \[ \text{Sum of absolute deviations} \approx 96.571 + 89.571 + 84.571 + 0.571 + 125.429 + 266.429 + 379.429 \approx 1042.571 \] \[ \text{Mean Absolute Deviation} = \frac{1042.571}{7} \approx 149. Mine \]
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Round the answer to the nearest tenth: The mean absolute deviation rounded to the nearest tenth is \( 149.0 \).
Thus, the Mean Absolute Deviation of the dataset is approximately \( \boxed{149.0} \).