To find the mean absolute deviation (MAD) of the dataset \({5.8, 7, 8.1, 9.2, 9.9}\) with a mean of \(8\), follow these steps:
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Calculate the absolute deviations from the mean:
- 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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List the absolute deviations: \({2.2, 1, 0.1, 1.2, 1.9}\)
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Calculate the mean of these absolute deviations: \[ \text{Mean Absolute Deviation} = \frac{2.2 + 1 + 0.1 + 1.2 + 1.9}{5} \]
First, sum the absolute deviations: \[ 2.2 + 1 + 0.1 + 1.2 + 1.9 = 6.4 \]
Then, divide by the number of data points: \[ \text{Mean Absolute Deviation} = \frac{6.4}{5} = 1.28 \]
Thus, the mean absolute deviation of the dataset is \(\boxed{1.28}\).