To calculate the average deviation from the mean for the dataset {23, 24, 26, 27, 28, 30, 31}, follow these steps:
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Calculate the mean of the dataset: \[ \text{Mean} = \frac{23 + 24 + 26 + 27 + 28 + 30 + 31}{7} = \frac{189}{7} = 27 \]
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Calculate the deviations from the mean:
- Deviation for 23: \( 23 - 27 = -4 \)
- Deviation for 24: \( 24 - 27 = -3 \)
- Deviation for 26: \( 26 - 27 = -1 \)
- Deviation for 27: \( 27 - 27 = 0 \)
- Deviation for 28: \( 28 - 27 = 1 \)
- Deviation for 30: \( 30 - 27 = 3 \)
- Deviation for 31: \( 31 - 27 = 4 \)
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Take the absolute values of the deviations:
- Absolute deviation for 23: \( | -4 | = 4 \)
- Absolute deviation for 24: \( | -3 | = 3 \)
- Absolute deviation for 26: \( | -1 | = 1 \)
- Absolute deviation for 27: \( | 0 | = 0 \)
- Absolute deviation for 28: \( | 1 | = 1 \)
- Absolute deviation for 30: \( | 3 | = 3 \)
- Absolute deviation for 31: \( | 4 | = 4 \)
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Sum the absolute deviations: \[ 4 + 3 + 1 + 0 + 1 + 3 + 4 = 16 \]
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Calculate the average deviation: \[ \text{Average Deviation} = \frac{\text{Sum of Absolute Deviations}}{\text{Number of Data Points}} = \frac{16}{7} \approx 2.2857 \]
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Round to the nearest hundredth: \[ \text{Average Deviation} \approx 2.29 \]
Finally, since you requested a solid number answer without decimals, the final average deviation is:
2 (the integer part of 2.29).