To calculate the average deviation from the mean for the dataset {23, 24, 26, 27, 28, 30, 31}, we first need to find the mean of the dataset.
- Calculate the mean:
\[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} \]
\[ \text{Sum} = 23 + 24 + 26 + 27 + 28 + 30 + 31 = 189 \]
\[ \text{Number of values} = 7 \]
\[ \text{Mean} = \frac{189}{7} = 27 \]
- Calculate the absolute deviations from the mean:
\[ |23 - 27| = 4 \] \[ |24 - 27| = 3 \] \[ |26 - 27| = 1 \] \[ |27 - 27| = 0 \] \[ |28 - 27| = 1 \] \[ |30 - 27| = 3 \] \[ |31 - 27| = 4 \]
- Sum of absolute deviations:
\[ 4 + 3 + 1 + 0 + 1 + 3 + 4 = 16 \]
- Calculate the average deviation:
\[ \text{Average Deviation} = \frac{\text{Sum of absolute deviations}}{\text{Number of values}} = \frac{16}{7} \approx 2.285714286 \]
- Round the answer to the nearest hundredth:
\[ \text{Average Deviation} \approx 2.29 \]
Therefore, the average deviation from the mean is \( \boxed{2.29} \).