Question

Five friends recorded the number of action figures each friend has. The following is the dataset they recorded: {7,9,10,11,11}
. Which of the following correctly calculates the average deviation from the mean number of action figures?


Responses

The average deviation from the mean is 6.4.
The average deviation from the mean is 6.4.

The average deviation from the mean is 0.16.
The average deviation from the mean is 0.16.

The average deviation from the mean is 1.28.
The average deviation from the mean is 1.28.

The average deviation from the mean is 9.6.

Answer 1

To calculate the average deviation from the mean, we first need to find the mean of the dataset {7, 9, 10, 11, 11}.

1. **Calculate the Mean (Average)**:
\[
\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} = \frac{7 + 9 + 10 + 11 + 11}{5} = \frac{48}{5} = 9.6
\]

2. **Calculate the Absolute Deviations from the Mean**:
Now, we'll find the absolute deviations of each data point from the mean (9.6):
- 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 the second 11: \( |11 - 9.6| = 1.4 \)

3. **Calculate the Average Deviation**:
To find the average deviation, sum these absolute deviations and divide by the number of values:
\[
\text{Sum of absolute deviations} = 2.6 + 0.6 + 0.4 + 1.4 + 1.4 = 6.4
\]
\[
\text{Average Deviation} = \frac{6.4}{5} = 1.28
\]

Therefore, the average deviation from the mean number of action figures is **1.28**.

The correct response is:
**The average deviation from the mean is 1.28.**