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 9.6.
The average deviation from the mean is 9.6.

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.

Answer 1

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

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

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

4. **Calculate the average deviation (mean of the absolute deviations):**
\[
\text{Average deviation} = \frac{6.4}{5} = 1.28
\]

Thus, the correct calculation for the average deviation from the mean in this dataset is:

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