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.

Question

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 0.4.
The average deviation from the mean is 0.4.

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 0.67.
The average deviation from the mean is 0.67.

The average deviation from the mean is 0.2.

Answer 1

To calculate the average deviation from the mean, we need to follow these steps:

1. Calculate the Mean: Sum the number of goals and divide by the total number of games.
2. Find the Absolute Deviations: For each data point, find the absolute difference between it and the mean.
3. Calculate the Average Deviation: Sum the absolute deviations and divide by the number of data points.

Since the specific number of goals scored by Soccer Team B is not provided, I'll illustrate the process conceptually:

Let's say Soccer Team B's goals per game are represented as follows (these numbers are hypothetical; you would replace them with the actual data points you have):

• Goals Scored: 2, 3, 1, 4, 5, 2, 3, 4, 1, 2 (as an example)
• Total Goals = 2 + 3 + 1 + 4 + 5 + 2 + 3 + 4 + 1 + 2 = 27
• Number of Games = 10
• Mean = Total Goals / Number of Games = 27 / 10 = 2.7

Next, be sure to calculate the absolute deviations:

• |2 - 2.7| = 0.7
• |3 - 2.7| = 0.3
• |1 - 2.7| = 1.7
• |4 - 2.7| = 1.3
• |5 - 2.7| = 2.3
• |2 - 2.7| = 0.7
• |3 - 2.7| = 0.3
• |4 - 2.7| = 1.3
• |1 - 2.7| = 1.7
• |2 - 2.7| = 0.7

Sum of Absolute Deviations = 0.7 + 0.3 + 1.7 + 1.3 + 2.3 + 0.7 + 0.3 + 1.3 + 1.7 + 0.7 = 10.2

Finally, to find the average deviation:

Average Deviation = Total Absolute Deviations / Number of Goals = 10.2 / 10 = 1.02

Since the actual data is not provided in the question, the average deviation obtained might differ. You would substitute the numbers you have to get the actual average deviation.

Looking at the response options provided:

1. The average deviation from the mean is 0.4.
2. The average deviation from the mean is 2.5.
3. The average deviation from the mean is 0.67.
4. The average deviation from the mean is 0.2.

Please choose from the options after you plug in your specific goal data into the mentioned steps, or let me know if you have the exact goal numbers for more specific assistance!

Answer 2

0-0 dots 1-0doys 2-2dots 3-6dots 4-2dots 5-0dots

Answer 3

Thank you for providing the data. Based on your input, we have the following information about the number of goals scored per game by Soccer Team B:

• 0 goals scored in 0 games (0 dots)
• 1 goal scored in 0 games (0 dots)
• 2 goals scored in 2 games (2 dots)
• 3 goals scored in 6 games (6 dots)
• 4 goals scored in 2 games (2 dots)
• 5 goals scored in 0 games (0 dots)

We will calculate the average deviation from the mean number of goals per game:

Step 1: Calculate the total number of games

\[ \text{Total games} = 0 + 0 + 2 + 6 + 2 + 0 = 10 \]

Step 2: Calculate the total number of goals

\[ \text{Total goals} = (0 \times 0) + (1 \times 0) + (2 \times 2) + (3 \times 6) + (4 \times 2) + (5 \times 0) \] \[ = 0 + 0 + 4 + 18 + 8 + 0 = 30 \]

Step 3: Calculate the mean number of goals per game

\[ \text{Mean} = \frac{\text{Total goals}}{\text{Total games}} = \frac{30}{10} = 3 \]

Step 4: Calculate the absolute deviations from the mean

Now we find the absolute deviations for each number of goals:

• For 0 goals:
  • Absolute deviation = \(|0 - 3| \times 0 = 0\)
• For 1 goal:
  • Absolute deviation = \(|1 - 3| \times 0 = 0\)
• For 2 goals:
  • Absolute deviation = \(|2 - 3| \times 2 = 1 \times 2 = 2\)
• For 3 goals:
  • Absolute deviation = \(|3 - 3| \times 6 = 0 \times 6 = 0\)
• For 4 goals:
  • Absolute deviation = \(|4 - 3| \times 2 = 1 \times 2 = 2\)
• For 5 goals:
  • Absolute deviation = \(|5 - 3| \times 0 = 0\)

Step 5: Sum the absolute deviations

\[ \text{Total absolute deviations} = 0 + 0 + 2 + 0 + 2 + 0 = 4 \]

Step 6: Calculate the average deviation

\[ \text{Average deviation} = \frac{\text{Total absolute deviations}}{\text{Total games}} = \frac{4}{10} = 0.4 \]

Conclusion

The average deviation from the mean number of goals per game scored by Soccer Team B is 0.4.

Therefore, the correct response is: The average deviation from the mean is 0.4.