To calculate the mean absolute deviation (MAD) of the dataset, follow these steps:
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Calculate the Mean: First, find the mean of the dataset.
- Sum of the dataset: \( 204 + 211 + 216 + 300 + 426 + 567 + 680 = 2104 \)
- Number of data points: 7
- Mean \( \mu \): \[ \mu = \frac{\text{Sum}}{\text{Number of Data Points}} = \frac{2104}{7} \approx 300.5714 \]
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Calculate the Absolute Deviations: Find the absolute deviation of each data point from the mean.
- \( |204 - 300.5714| \approx 96.5714 \)
- \( |211 - 300.5714| \approx 89.5714 \)
- \( |216 - 300.5714| \approx 84.5714 \)
- \( |300 - 300.5714| \approx 0.5714 \)
- \( |426 - 300.5714| \approx 125.4286 \)
- \( |567 - 300.5714| \approx 266.4286 \)
- \( |680 - 300.5714| \approx 379.4286 \)
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Sum of Absolute Deviations: Calculate the sum of all the absolute deviations. \[ 96.5714 + 89.5714 + 84.5714 + 0.5714 + 125.4286 + 266.4286 + 379.4286 \approx 433.5714 + 125.4286 + 266.4286 + 379.4286 \approx 679.4286 \]
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Calculate the Mean Absolute Deviation: Divide the sum of absolute deviations by the number of data points. \[ \text{MAD} = \frac{\text{Sum of Absolute Deviations}}{\text{Number of Data Points}} = \frac{679.4286}{7} \approx 97.0427 \]
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Round the Result: Round the result to the nearest tenth. \[ \text{MAD} \approx 97.0 \]
Therefore, the mean absolute deviation of the dataset \( 204, 211, 216, 300, 426, 567, 680 \) is approximately 97.0.