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?(1 point)
Responses

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 9.6.
The average deviation from the mean is 9.6.

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 6.4.

Answer 1

To calculate the average deviation from the mean, we will first need to determine the mean of the dataset, then calculate the absolute deviations from the mean, and finally find the average of those deviations.

1. **Calculate the Mean**:
- The dataset is {7, 9, 10, 11, 11}.
- Mean = (7 + 9 + 10 + 11 + 11) / 5 = 48 / 5 = 9.6.

2. **Calculate the Absolute Deviations from the Mean**:
- Deviation for 7: |7 - 9.6| = 2.6
- Deviation for 9: |9 - 9.6| = 0.6
- Deviation for 10: |10 - 9.6| = 0.4
- Deviation for 11: |11 - 9.6| = 1.4
- Deviation for 11: |11 - 9.6| = 1.4

3. **Calculate the Average of These Absolute Deviations**:
- Total of absolute deviations = 2.6 + 0.6 + 0.4 + 1.4 + 1.4 = 6.4.
- Average deviation = Total of absolute deviations / Number of data points = 6.4 / 5 = 1.28.

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

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