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

Question

. 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 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.

Answer 1

To calculate the average deviation from the mean, we first need to find the mean of the dataset and then calculate the absolute deviations from the mean. Finally, we will find 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: \[ |7 - 9.6| = | -2.6 | = 2.6 \] \[ |9 - 9.6| = | -0.6 | = 0.6 \] \[ |10 - 9.6| = |0.4| = 0.4 \] \[ |11 - 9.6| = |1.4| = 1.4 \] \[ |11 - 9.6| = |1.4| = 1.4 \]

3. List the absolute deviations: \( {2.6, 0.6, 0.4, 1.4, 1.4} \)

4. 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.

The correct response is: The average deviation from the mean is 1.28.