Question
Two soccer teams are tied for the league championship going into the final game of the season. The list below shows the number of goals each scored by each team in its last eight games.
Team A : 1,2,3,3,3,3,4,5
team B: 2,2,2,3,3,4,4,4
Which of the following statements, best describes graph of the teams goal score data
There will be some overlap because the difference of the means a small and the quotient of the main absolute deviation is close to one
There will be some overlap because the difference of the means zero, but the quote of the mean absolute deviation is not one
There will be almost complete over loud because the difference of the means is zero and the quotient of the main absolute deviation is one
There will be no overlap because the difference of the means as much greater than the quotient of the main absolute deviation
Team A : 1,2,3,3,3,3,4,5
team B: 2,2,2,3,3,4,4,4
Which of the following statements, best describes graph of the teams goal score data
There will be some overlap because the difference of the means a small and the quotient of the main absolute deviation is close to one
There will be some overlap because the difference of the means zero, but the quote of the mean absolute deviation is not one
There will be almost complete over loud because the difference of the means is zero and the quotient of the main absolute deviation is one
There will be no overlap because the difference of the means as much greater than the quotient of the main absolute deviation
Answers
GPT-4o mini
To analyze the problem, let's start by calculating the means and the mean absolute deviations for both teams.
### Team A Goals
Data: 1, 2, 3, 3, 3, 3, 4, 5
- **Mean (average):**
\[
\text{Mean} = \frac{1 + 2 + 3 + 3 + 3 + 3 + 4 + 5}{8} = \frac{24}{8} = 3
\]
- **Mean Absolute Deviation (MAD):**
\[
\text{MAD} = \frac{|1-3| + |2-3| + |3-3| + |3-3| + |3-3| + |3-3| + |4-3| + |5-3|}{8}
\]
\[
= \frac{2 + 1 + 0 + 0 + 0 + 0 + 1 + 2}{8} = \frac{6}{8} = 0.75
\]
### Team B Goals
Data: 2, 2, 2, 3, 3, 4, 4, 4
- **Mean (average):**
\[
\text{Mean} = \frac{2 + 2 + 2 + 3 + 3 + 4 + 4 + 4}{8} = \frac{24}{8} = 3
\]
- **Mean Absolute Deviation (MAD):**
\[
= \frac{|2-3| + |2-3| + |2-3| + |3-3| + |3-3| + |4-3| + |4-3| + |4-3|}{8}
\]
\[
= \frac{1 + 1 + 1 + 0 + 0 + 1 + 1 + 1}{8} = \frac{5}{8} = 0.625
\]
Now, let's summarize our findings:
- **Mean of Team A:** 3
- **Mean of Team B:** 3
- **Difference of the Means:** \(3 - 3 = 0\)
- **MAD of Team A:** 0.75
- **MAD of Team B:** 0.625
- **Quotient of the MADs:**
\[
\frac{0.75}{0.625} = 1.2
\]
### Conclusion:
- The difference of the means is 0 (they have the same average goals).
- The quotient of the mean absolute deviations is approximately 1.2 (not equal to 1).
Thus, the statement that best describes the situation is:
**"There will be some overlap because the difference of the means is zero, but the quotient of the mean absolute deviation is not one."**
### Team A Goals
Data: 1, 2, 3, 3, 3, 3, 4, 5
- **Mean (average):**
\[
\text{Mean} = \frac{1 + 2 + 3 + 3 + 3 + 3 + 4 + 5}{8} = \frac{24}{8} = 3
\]
- **Mean Absolute Deviation (MAD):**
\[
\text{MAD} = \frac{|1-3| + |2-3| + |3-3| + |3-3| + |3-3| + |3-3| + |4-3| + |5-3|}{8}
\]
\[
= \frac{2 + 1 + 0 + 0 + 0 + 0 + 1 + 2}{8} = \frac{6}{8} = 0.75
\]
### Team B Goals
Data: 2, 2, 2, 3, 3, 4, 4, 4
- **Mean (average):**
\[
\text{Mean} = \frac{2 + 2 + 2 + 3 + 3 + 4 + 4 + 4}{8} = \frac{24}{8} = 3
\]
- **Mean Absolute Deviation (MAD):**
\[
= \frac{|2-3| + |2-3| + |2-3| + |3-3| + |3-3| + |4-3| + |4-3| + |4-3|}{8}
\]
\[
= \frac{1 + 1 + 1 + 0 + 0 + 1 + 1 + 1}{8} = \frac{5}{8} = 0.625
\]
Now, let's summarize our findings:
- **Mean of Team A:** 3
- **Mean of Team B:** 3
- **Difference of the Means:** \(3 - 3 = 0\)
- **MAD of Team A:** 0.75
- **MAD of Team B:** 0.625
- **Quotient of the MADs:**
\[
\frac{0.75}{0.625} = 1.2
\]
### Conclusion:
- The difference of the means is 0 (they have the same average goals).
- The quotient of the mean absolute deviations is approximately 1.2 (not equal to 1).
Thus, the statement that best describes the situation is:
**"There will be some overlap because the difference of the means is zero, but the quotient of the mean absolute deviation is not one."**