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 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.

Answer 1

To calculate the average deviation from the mean, we will first need to find the mean of the dataset {7, 9, 10, 11, 11}, and then determine the absolute deviations from the mean. Finally, we will calculate 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 absolute deviations from the mean:**

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

The absolute deviations are: {2.6, 0.6, 0.4, 1.4, 1.4}.

3. **Calculate the average of the absolute deviations:**

\[
\text{Average Deviation} = \frac{2.6 + 0.6 + 0.4 + 1.4 + 1.4}{5} = \frac{6.4}{5} = 1.28
\]

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

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