To calculate the average deviation from the mean for the given data set (23, 24, 26, 27, 28, 30, 31), follow these steps:
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Calculate the Mean: \[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} \]
Sum of the values: \[ 23 + 24 + 26 + 27 + 28 + 30 + 31 = 189 \]
Number of values: \[ 7 \]
Hence, the mean: \[ \text{Mean} = \frac{189}{7} = 27 \]
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Calculate the Absolute Deviations from the Mean:
- For 23: \( |23 - 27| = 4 \)
- For 24: \( |24 - 27| = 3 \)
- For 26: \( |26 - 27| = 1 \)
- For 27: \( |27 - 27| = 0 \)
- For 28: \( |28 - 27| = 1 \)
- For 30: \( |30 - 27| = 3 \)
- For 31: \( |31 - 27| = 4 \)
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Sum the Absolute Deviations: \[ 4 + 3 + 1 + 0 + 1 + 3 + 4 = 16 \]
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Calculate the Average Deviation: \[ \text{Average Deviation} = \frac{\text{Sum of Absolute Deviations}}{\text{Number of values}} = \frac{16}{7} \approx 2.2857 \]
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Round to the Nearest Hundredth: \[ 2.29 \]
Therefore, the average deviation from the mean is 2.29.