Question

Five friends recorded the number of action figures each friend has. The following is the dataset they recorded: {7,9,10,11,11}
{
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 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.

Answer 1

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

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:**
\[
|7 - 9.6| = 2.6
\]
\[
|9 - 9.6| = 0.6
\]
\[
|10 - 9.6| = 0.4
\]
\[
|11 - 9.6| = 1.4
\]
\[
|11 - 9.6| = 1.4
\]

3. **Sum of Absolute Deviations:**
\[
\text{Sum of Absolute Deviations} = 2.6 + 0.6 + 0.4 + 1.4 + 1.4 = 6.4
\]

4. **Calculate the Average Deviation:**
\[
\text{Average Deviation} = \frac{\text{Sum of Absolute Deviations}}{\text{number of values}} = \frac{6.4}{5} = 1.28
\]

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

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