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:
\[ \text{Mean} = \frac{\text{Sum of all data}}{\text{Number of data points}} \]
Sum of the data:
\[ 23 + 24 + 26 + 27 + 28 + 30 + 31 = 189 \]
Number of data points:
\[ 7 \]
\[ \text{Mean} = \frac{189}{7} = 27 \]
- Calculate the absolute deviations from the mean:
Next, we find the absolute deviations from the mean (27):
\[ |23 - 27| = 4 \] \[ |24 - 27| = 3 \] \[ |26 - 27| = 1 \] \[ |27 - 27| = 0 \] \[ |28 - 27| = 1 \] \[ |30 - 27| = 3 \] \[ |31 - 27| = 4 \]
The absolute deviations are: 4, 3, 1, 0, 1, 3, 4.
- Calculate the average of these absolute deviations:
Sum of absolute deviations:
\[ 4 + 3 + 1 + 0 + 1 + 3 + 4 = 16 \]
Now, we divide by the number of data points:
\[ \text{Average Deviation} = \frac{16}{7} \approx 2.285714285714286 \]
Rounding to the nearest hundredth:
\[ \text{Average Deviation} \approx 2.29 \]
Thus, the average deviation from the mean is approximately 2.29.