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 1.28.
The average deviation from the mean is 1.28.

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 9.6.

Answer 1

To calculate the average deviation from the mean of the dataset {7, 9, 10, 11, 11}, follow these steps:

1. **Calculate the mean:**
\[
\text{Mean} = \frac{\text{Sum of data}}{\text{Number of data points}} = \frac{7 + 9 + 10 + 11 + 11}{5} = \frac{48}{5} = 9.6
\]

2. **Calculate the absolute deviations 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: \(|11 - 9.6| = 1.4\)

3. **Sum the absolute deviations:**
\[
2.6 + 0.6 + 0.4 + 1.4 + 1.4 = 6.4
\]

4. **Calculate the average deviation:**
\[
\text{Average Deviation} = \frac{\text{Sum of absolute deviations}}{\text{Number of data points}} = \frac{6.4}{5} = 1.28
\]

Therefore, the average deviation from the mean is **1.28**.

The correct answer from the provided options is:
**The average deviation from the mean is 1.28.**