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: \[ \text{Mean} = \frac{\text{sum of the dataset}}{\text{number of values}} \]
Sum of the dataset: \[ 23 + 24 + 26 + 27 + 28 + 30 + 31 = 189 \]
Number of values: \[ 7 \]
Thus, the mean is: \[ \text{Mean} = \frac{189}{7} = 27 \]
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Calculate the Deviations from the Mean: Now find the absolute deviation from the mean for each value:
- |23 - 27| = 4
- |24 - 27| = 3
- |26 - 27| = 1
- |27 - 27| = 0
- |28 - 27| = 1
- |30 - 27| = 3
- |31 - 27| = 4
The absolute deviations are: {4, 3, 1, 0, 1, 3, 4}
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Calculate the Average Deviation: Average deviation is calculated as the mean of the absolute deviations: \[ \text{Average Deviation} = \frac{\text{sum of absolute deviations}}{\text{number of values}} \]
Sum of the absolute deviations: \[ 4 + 3 + 1 + 0 + 1 + 3 + 4 = 16 \]
Thus, the average deviation is: \[ \text{Average Deviation} = \frac{16}{7} \approx 2.285714 \]
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Round to Nearest Hundredth: Rounding 2.285714 to the nearest hundredth gives: \[ 2.29 \]
The average deviation from the mean is 2.29.