To calculate the average deviation from the mean for the dataset {39, 42, 36, 47, 44, 43, 36}, follow these steps:
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Calculate the mean (average): \[ \text{Mean} = \frac{39 + 42 + 36 + 47 + 44 + 43 + 36}{7} = \frac{287}{7} = 41 \]
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Calculate the absolute deviations from the mean:
- For 39: \(|39 - 41| = 2\)
- For 42: \(|42 - 41| = 1\)
- For 36: \(|36 - 41| = 5\)
- For 47: \(|47 - 41| = 6\)
- For 44: \(|44 - 41| = 3\)
- For 43: \(|43 - 41| = 2\)
- For 36: \(|36 - 41| = 5\)
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List of absolute deviations: \[ 2, 1, 5, 6, 3, 2, 5 \]
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Calculate the average of the absolute deviations: \[ \text{Average deviation} = \frac{2 + 1 + 5 + 6 + 3 + 2 + 5}{7} = \frac{24}{7} \approx 3.43 \]
Therefore, the average deviation from the mean for the dataset is approximately \(3.43\).