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 6.4.
The average deviation from the mean is 6.4.

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 0.16.

Answer 1

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

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

2. Calculate the absolute deviations from the mean:
- For 7: \( |7 - 9.6| = 2.6 \)
- For 9: \( |9 - 9.6| = 0.6 \)
- For 10: \( |10 - 9.6| = 0.4 \)
- For 11: \( |11 - 9.6| = 1.4 \) (note there are two 11’s)
- For the other 11: \( |11 - 9.6| = 1.4 \)

3. Calculate the sum of the absolute deviations:
\[
\text{Sum of absolute deviations} = 2.6 + 0.6 + 0.4 + 1.4 + 1.4 = 6.4
\]

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

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

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