To find the mean absolute deviation (MAD) of the dataset \(8.4, 9.4, 14.2, 5.6, 8.3, 9.0, 10.2\), we will follow these steps:
- Calculate the mean of the dataset.
- Calculate the absolute deviations from the mean for each data point.
- Calculate the mean of these absolute deviations.
Step 1: Calculate the mean
\[ \text{Mean} = \frac{8.4 + 9.4 + 14.2 + 5.6 + 8.3 + 9.0 + 10.2}{7} = \frac{65.1}{7} \approx 9.3 \]
Step 2: Calculate the absolute deviations from the mean
\[ \begin{align*} |8.4 - 9.3| & = | -0.9 | = 0.9 \ |9.4 - 9.3| & = | 0.1 | = 0.1 \ |14.2 - 9.3| & = | 4.9 | = 4.9 \ |5.6 - 9.3| & = | -3.7 | = 3.7 \ |8.3 - 9.3| & = | -1.0 | = 1.0 \ |9.0 - 9.3| & = | -0.3 | = 0.3 \ |10.2 - 9.3| & = | 0.9 | = 0.9 \ \end{align*} \]
Step 3: Calculate the mean of these absolute deviations
\[ \text{Mean Absolute Deviation} = \frac{0.9 + 0.1 + 4.9 + 3.7 + 1.0 + 0.3 + 0.9}{7} = \frac{11.8}{7} \approx 1.6857 \]
Rounding this to the nearest tenth gives us:
\[ \text{MAD} \approx 1.7 \]
Therefore, the mean absolute deviation of the dataset is 1.7.