To calculate the average deviation from the mean, we will follow these steps:
- Calculate the mean of the data set.
- Calculate the absolute deviations from the mean.
- Calculate the average of those absolute deviations.
Let's go through these steps:
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Calculate the Mean: \[ \text{Mean} = \frac{\sum \text{values}}{\text{number of values}} = \frac{39 + 42 + 36 + 47 + 44 + 43 + 36}{7} = \frac{287}{7} = 41 \]
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Calculate the Absolute Deviations:
- 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: \( |36 - 41| = 5 \)
The absolute deviations are: \( 2, 1, 5, 6, 3, 2, 5 \).
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Calculate the Average of the Absolute Deviations: \[ \text{Average Deviation} = \frac{\sum \text{absolute deviations}}{\text{number of values}} = \frac{2 + 1 + 5 + 6 + 3 + 2 + 5}{7} = \frac{24}{7} \approx 3.428571 \]
Rounding to the nearest hundredth: \[ \text{Average Deviation} \approx 3.43 \]
Therefore, the average deviation from the mean is \( \boxed{3.43} \).
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