To find the mean absolute deviation (MAD) of the dataset, you follow these steps:
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Calculate the Mean: You mentioned that the mean is \( 8 \).
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Find the Absolute Deviations: Calculate the absolute deviation of each data point from the mean. The absolute deviation for a data point \( x \) is calculated as \( |x - \text{mean}| \).
Given the dataset \( (5.8, 7, 8.1, 9.2, 9.9) \):
- For \( 5.8 \): \( |5.8 - 8| = | -2.2 | = 2.2 \)
- For \( 7 \): \( |7 - 8| = | -1 | = 1 \)
- For \( 8.1 \): \( |8.1 - 8| = |0.1| = 0.1 \)
- For \( 9.2 \): \( |9.2 - 8| = |1.2| = 1.2 \)
- For \( 9.9 \): \( |9.9 - 8| = |1.9| = 1.9 \)
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Average the Absolute Deviations: To find the mean absolute deviation, sum up the absolute deviations and divide by the number of observations.
Sum of absolute deviations: \[ 2.2 + 1 + 0.1 + 1.2 + 1.9 = 6.4 \]
Number of observations = 5
Mean Absolute Deviation: \[ \text{MAD} = \frac{6.4}{5} = 1.28 \]
Thus, the mean absolute deviation of the dataset is \( \boxed{1.28} \).