To find the mean absolute deviation (MAD) of the dataset \({5.8, 7, 8.1, 9.2, 9.9}\), we first need to calculate the absolute deviations from the mean, and then find the average of those absolute deviations.
Given that the mean of the dataset is 8, we can proceed with the following steps:
- Calculate the absolute deviations from the mean:
\[ |5.8 - 8| = | -2.2 | = 2.2 \] \[ |7 - 8| = | -1 | = 1 \] \[ |8.1 - 8| = |0.1| = 0.1 \] \[ |9.2 - 8| = |1.2| = 1.2 \] \[ |9.9 - 8| = |1.9| = 1.9 \]
- Compile the absolute deviations:
\[ {2.2, 1, 0.1, 1.2, 1.9} \]
- Calculate the mean of the absolute deviations. First, sum the absolute deviations:
\[ 2.2 + 1 + 0.1 + 1.2 + 1.9 = 6.4 \]
- Since there are 5 values in the dataset, divide the total by 5 to find the mean absolute deviation:
\[ \text{MAD} = \frac{6.4}{5} = 1.28 \]
Thus, the mean absolute deviation of the dataset is \(\boxed{1.28}\).