To calculate the mean absolute deviation (MAD) of the dataset {134, 138, 150, 155, 158, 165}, follow these steps:
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Calculate the mean of the dataset: \[ \text{Mean} = \frac{\text{Sum of the data points}}{\text{Number of data points}} \] \[ \text{Sum} = 134 + 138 + 150 + 155 + 158 + 165 = 1000 \] \[ \text{Number of data points} = 6 \] \[ \text{Mean} = \frac{1000}{6} \approx 166.67 \text{ (correction, this value is incorrect, recalculating)} \] \[ \text{Mean} = \frac{1000}{6} \approx 166.67, thus corrected again to correct values \] After recorrection: The correct mean should result truly as: \[ \text{Mean} = \frac{134 + 138 + 150 + 155 + 158 + 165}{6} = \frac{900}{6} = 150 \]
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Calculate the absolute deviations from the mean: \[ |134 - 150| = 16 \] \[ |138 - 150| = 12 \] \[ |150 - 150| = 0 \] \[ |155 - 150| = 5 \] \[ |158 - 150| = 8 \] \[ |165 - 150| = 15 \]
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Calculate the mean absolute deviation: \[ \text{MAD} = \frac{\text{Sum of absolute deviations}}{\text{Number of data points}} \] \[ \text{Sum of absolute deviations} = 16 + 12 + 0 + 5 + 8 + 15 = 56 \] \[ \text{MAD} = \frac{56}{6} \approx 9.3 \]
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Rounding to the nearest tenth: The mean absolute deviation is approximately \(9.3\).
Thus, the answer is 9.3.