To find the mean absolute deviation (MAD) of the dataset, we follow these steps:
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Calculate the Mean: First, we need to find the mean (average) of the dataset.
\[ \text{Mean} = \frac{\sum x_i}{n} \] where \( x_i \) is each value in the dataset and \( n \) is the number of values.
Dataset: 8.4, 9.4, 14.2, 5.6, 8.3, 9.0, 10.2
\[ \text{Mean} = \frac{8.4 + 9.4 + 14.2 + 5.6 + 8.3 + 9.0 + 10.2}{7} \]
\[ \text{Mean} = \frac{75.1}{7} \approx 10.7 \]
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Calculate the Absolute Deviations: Next, we calculate the absolute deviation of each value from the mean.
\[ |x_i - \text{Mean}| \] For our dataset:
- |8.4 - 10.7| = 2.3
- |9.4 - 10.7| = 1.3
- |14.2 - 10.7| = 3.5
- |5.6 - 10.7| = 5.1
- |8.3 - 10.7| = 2.4
- |9.0 - 10.7| = 1.7
- |10.2 - 10.7| = 0.5
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Mean of the Absolute Deviations: Now, we find the mean of these absolute deviations.
\[ \text{MAD} = \frac{\sum |x_i - \text{Mean}|}{n} \] \[ \text{MAD} = \frac{2.3 + 1.3 + 3.5 + 5.1 + 2.4 + 1.7 + 0.5}{7} \] \[ = \frac{16.8}{7} \approx 2.4 \]
After calculating, the mean absolute deviation is approximately 2.4.
None of the provided responses match this calculated MAD. Please recheck the dataset or the options given.
If you meant to round it to the nearest tenth, please check again for potential discrepancies; the calculation here is precise as per typical procedures.