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, 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 deviations from the mean for each value:**

\[
\begin{align*}
7: & \quad |7 - 9.6| = 2.6 \\
9: & \quad |9 - 9.6| = 0.6 \\
10: & \quad |10 - 9.6| = 0.4 \\
11: & \quad |11 - 9.6| = 1.4 \\
11: & \quad |11 - 9.6| = 1.4 \\
\end{align*}
\]

3. **Sum the absolute deviations:**

\[
\text{Sum of deviations} = 2.6 + 0.6 + 0.4 + 1.4 + 1.4 = 6.4
\]

4. **Calculate the average deviation:**

\[
\text{Average deviation} = \frac{\text{Sum of deviations}}{\text{Number of values}} = \frac{6.4}{5} = 1.28
\]

So, the average deviation from the mean is **1.28**. Therefore, the correct response is **"The average deviation from the mean is 1.28."**