Question

A horizontal number line with arrows at both ends is titled at the top as Soccer Team B. Below the line is the title, Number of Goals per Game. The line is numbered 0 to 5 in increments of 1 and has a total of 10 closed points plotted.
0 = 0
1 = 0
2 = 2
3 = 6
4 = 2
5 = 0
Which of the following correctly calculates the average deviation from the mean number of goals per game scored by soccer team B?

(1 point)
Responses

The average deviation from the mean is 0.67.
The average deviation from the mean is 0.67.

The average deviation from the mean is 2.5.
The average deviation from the mean is 2.5.

The average deviation from the mean is 0.4.
The average deviation from the mean is 0.4.

The average deviation from the mean is 0.2.
The average deviation from the mean is 0.2.

Answer 1

To calculate the average deviation from the mean number of goals per game scored by Soccer Team B, follow these steps:

1. **Calculate the mean**:
To find the mean number of goals per game, we need to multiply each goal value by its corresponding frequency (the number of games scored at that goal level), sum those products, and then divide by the total number of games.

Given:
- 0 goals: 0 games
- 1 goal: 0 games
- 2 goals: 2 games
- 3 goals: 6 games
- 4 goals: 2 games
- 5 goals: 0 games

The total number of games is:
\[
0 + 0 + 2 + 6 + 2 + 0 = 10
\]

Now, calculate the total goals scored:
\[
(0 \times 0) + (1 \times 0) + (2 \times 2) + (3 \times 6) + (4 \times 2) + (5 \times 0) = 0 + 0 + 4 + 18 + 8 + 0 = 30
\]

The mean number of goals per game is:
\[
\text{Mean} = \frac{\text{Total Goals}}{\text{Total Games}} = \frac{30}{10} = 3
\]

2. **Calculate the average deviation**:
Next, we need to find the deviations from the mean for each goal value, take the absolute value of those deviations, and then calculate the average of those absolute deviations.

The deviations and their absolute values:
- For 0 goals: \(|0 - 3| = 3\) (0 games)
- For 1 goal: \(|1 - 3| = 2\) (0 games)
- For 2 goals: \(|2 - 3| = 1\) (2 games)
- For 3 goals: \(|3 - 3| = 0\) (6 games)
- For 4 goals: \(|4 - 3| = 1\) (2 games)
- For 5 goals: \(|5 - 3| = 2\) (0 games)

Now, calculate the total of absolute deviations multiplied by their respective frequencies:
\[
(3 \times 0) + (2 \times 0) + (1 \times 2) + (0 \times 6) + (1 \times 2) + (2 \times 0) = 0 + 0 + 2 + 0 + 2 + 0 = 4
\]

The average deviation is then:
\[
\text{Average Deviation} = \frac{\text{Total Absolute Deviation}}{\text{Total Games}} = \frac{4}{10} = 0.4
\]

Thus, the average deviation from the mean is:

**The average deviation from the mean is 0.4.**