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 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 for the dataset {7, 9, 10, 11, 11}, we first need to find the mean, then calculate the deviations from the mean, take the absolute value of those deviations, and finally compute the average of those absolute deviations.

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

2. **Calculate the deviations from the mean:**
\[
|7 - 9.6| = 2.6
\]
\[
|9 - 9.6| = 0.6
\]
\[
|10 - 9.6| = 0.4
\]
\[
|11 - 9.6| = 1.4
\]
\[
|11 - 9.6| = 1.4
\]

3. **Create the list of absolute deviations:**
The absolute deviations are {2.6, 0.6, 0.4, 1.4, 1.4}.

4. **Calculate the average of the absolute deviations:**
\[
\text{Average Deviation} = \frac{2.6 + 0.6 + 0.4 + 1.4 + 1.4}{5} = \frac{6.4}{5} = 1.28
\]

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

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