To find the average deviation from the mean for the numbers 7, 9, 10, 11, and 11, we'll follow these steps:
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Calculate the mean (average) of the numbers.
\[ \text{Mean} = \frac{7 + 9 + 10 + 11 + 11}{5} = \frac{48}{5} = 9.6 \]
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Calculate the absolute deviations from the mean for each number:
- For 7: \(|7 - 9.6| = | -2.6| = 2.6\)
- For 9: \(|9 - 9.6| = |-0.6| = 0.6\)
- For 10: \(|10 - 9.6| = |0.4| = 0.4\)
- For 11: \(|11 - 9.6| = |1.4| = 1.4\)
- For 11 (again): \(|11 - 9.6| = |1.4| = 1.4\)
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Calculate the average of these absolute deviations:
First, add up the absolute deviations: \[ 2.6 + 0.6 + 0.4 + 1.4 + 1.4 = 6.4 \]
Now, divide by the number of data points (which is 5): \[ \text{Average Deviation} = \frac{6.4}{5} = 1.28 \]
Thus, the average deviation from the mean is \(1.28\). Therefore, the answer is:
1.28