To calculate the average deviation from the mean, we can follow these steps:
- Calculate the mean (average) of the data set.
- Calculate the deviations from the mean for each data point.
- Take the absolute value of each deviation.
- Calculate the average of these absolute deviations.
Given the dataset: {7, 9, 10, 11, 11}
Step 1: Calculate the Mean
\[ \text{Mean} = \frac{(7 + 9 + 10 + 11 + 11)}{5} = \frac{48}{5} = 9.6 \]
Step 2: Calculate the Deviations from the Mean
For each data point, subtract 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: \( |11 - 9.6| = 1.4 \) (this applies twice, since there are two 11s)
Step 3: Take the Absolute Value of Each Deviation
The absolute deviations are:
- 2.6, 0.6, 0.4, 1.4, 1.4
Step 4: Calculate the Average of the 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.
So the correct response is:
- The average deviation from the mean is 1.28.