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 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 for the dataset {7, 9, 10, 11, 11}, we can 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.

- For 7: |7 - 9.6| = 2.6
- For 9: |9 - 9.6| = 0.6
- For 10: |10 - 9.6| = 0.4
- For 11: |11 - 9.6| = 1.4
- For 11: |11 - 9.6| = 1.4 (same value as above)

3. Sum the absolute deviations.

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

4. Calculate the average deviation.

\[
\text{Average deviation} = \frac{6.4}{5} = 1.28
\]

So, the correct answer is:

The average deviation from the mean is 1.28.