To calculate the average deviation from the mean, we first need to find the mean (average) of the dataset and then compute the average of the absolute deviations from the mean.
- Calculate the mean:
The dataset is {7, 9, 10, 11, 11}.
Mean \( \mu \) is calculated as follows:
\[ \mu = \frac{\text{Sum of all values}}{\text{Number of values}} = \frac{7 + 9 + 10 + 11 + 11}{5} = \frac{48}{5} = 9.6 \]
- Calculate the absolute deviations from the mean:
Next, we calculate the absolute deviation of each value from the mean:
- For 7: \( |7 - 9.6| = 2.6 \)
- For 9: \( |9 - 9.6| = 0.6 \)
- For 10: \( |10 - 9.6| = 0.4 \)
- For 11: \( |11 - 9.6| = 1.4 \)
- For 11: \( |11 - 9.6| = 1.4 \)
- Calculate the average of the absolute deviations:
Now, we find the average of these absolute deviations:
\[ \text{Average deviation} = \frac{2.6 + 0.6 + 0.4 + 1.4 + 1.4}{5} = \frac{6.4}{5} = 1.28 \]
Thus, the average deviation from the mean is 1.28.
The correct response is: The average deviation from the mean is 1.28.