Question
A dot plot titled Age of Eagles going from 7 to 12. 7 has 1 dot, 8 has 2 dots, 9 has 4 dots, 10 has 2 dots, 11 has 3 dots, 12 has 2 dots. A dot plot titled Age of Lions going from 7 to 12. 7 has 0 dots, 8 has 0 dots, 9 has 2 dots, 10 has 2 dots, 11 has 5 dots, 12 has 4 dots.
The dot plots show the ages of players on two soccer teams. Which statements are true? Check all that apply.
The Lions have more variability in the ages of their players.
The Eagles have more variability in the ages of their players.
The Lions have more players.
The Eagles have more players.
The mean of the ages of Lions is less than the mean of the ages of Eagles.
The dot plots show the ages of players on two soccer teams. Which statements are true? Check all that apply.
The Lions have more variability in the ages of their players.
The Eagles have more variability in the ages of their players.
The Lions have more players.
The Eagles have more players.
The mean of the ages of Lions is less than the mean of the ages of Eagles.
Answers
GPT-4o mini
To analyze the given dot plots for the two soccer teams (Eagles and Lions), we'll summarize the data and calculate totals and means.
### Ages and Frequencies:
**Eagles:**
- Age 7: 1 dot
- Age 8: 2 dots
- Age 9: 4 dots
- Age 10: 2 dots
- Age 11: 3 dots
- Age 12: 2 dots
- **Total Players (Eagles):** 1 + 2 + 4 + 2 + 3 + 2 = 14 players
**Lions:**
- Age 7: 0 dots
- Age 8: 0 dots
- Age 9: 2 dots
- Age 10: 2 dots
- Age 11: 5 dots
- Age 12: 4 dots
- **Total Players (Lions):** 0 + 0 + 2 + 2 + 5 + 4 = 13 players
### Calculating Mean Ages:
**Mean Age of Eagles:**
\[
\text{Mean} = \frac{(7 \times 1) + (8 \times 2) + (9 \times 4) + (10 \times 2) + (11 \times 3) + (12 \times 2)}{14}
\]
\[
= \frac{7 + 16 + 36 + 20 + 33 + 24}{14} = \frac{136}{14} \approx 9.71
\]
**Mean Age of Lions:**
\[
\text{Mean} = \frac{(7 \times 0) + (8 \times 0) + (9 \times 2) + (10 \times 2) + (11 \times 5) + (12 \times 4)}{13}
\]
\[
= \frac{0 + 0 + 18 + 20 + 55 + 48}{13} = \frac{141}{13} \approx 10.85
\]
### Evaluating Each Statement:
1. **The Lions have more variability in the ages of their players.**
- To determine variability, look at the spread of ages. The Eagles have ages from 7 to 12, while the Lions range from 9 to 12 (no players younger than 9). Since Eagles have a wider range, they likely have more variability.
- **False**
2. **The Eagles have more variability in the ages of their players.**
- As determined above, the Eagles have a wider range of ages (7 to 12).
- **True**
3. **The Lions have more players.**
- Eagles: 14 players, Lions: 13 players.
- **False**
4. **The Eagles have more players.**
- As stated above, the Eagles have 14 players compared to the Lions' 13.
- **True**
5. **The mean of the ages of Lions is less than the mean of the ages of Eagles.**
- Mean age of Lions (10.85) is greater than that of Eagles (9.71).
- **False**
### Conclusion:
The true statements from the above analysis are:
- The Eagles have more variability in the ages of their players.
- The Eagles have more players.
### Ages and Frequencies:
**Eagles:**
- Age 7: 1 dot
- Age 8: 2 dots
- Age 9: 4 dots
- Age 10: 2 dots
- Age 11: 3 dots
- Age 12: 2 dots
- **Total Players (Eagles):** 1 + 2 + 4 + 2 + 3 + 2 = 14 players
**Lions:**
- Age 7: 0 dots
- Age 8: 0 dots
- Age 9: 2 dots
- Age 10: 2 dots
- Age 11: 5 dots
- Age 12: 4 dots
- **Total Players (Lions):** 0 + 0 + 2 + 2 + 5 + 4 = 13 players
### Calculating Mean Ages:
**Mean Age of Eagles:**
\[
\text{Mean} = \frac{(7 \times 1) + (8 \times 2) + (9 \times 4) + (10 \times 2) + (11 \times 3) + (12 \times 2)}{14}
\]
\[
= \frac{7 + 16 + 36 + 20 + 33 + 24}{14} = \frac{136}{14} \approx 9.71
\]
**Mean Age of Lions:**
\[
\text{Mean} = \frac{(7 \times 0) + (8 \times 0) + (9 \times 2) + (10 \times 2) + (11 \times 5) + (12 \times 4)}{13}
\]
\[
= \frac{0 + 0 + 18 + 20 + 55 + 48}{13} = \frac{141}{13} \approx 10.85
\]
### Evaluating Each Statement:
1. **The Lions have more variability in the ages of their players.**
- To determine variability, look at the spread of ages. The Eagles have ages from 7 to 12, while the Lions range from 9 to 12 (no players younger than 9). Since Eagles have a wider range, they likely have more variability.
- **False**
2. **The Eagles have more variability in the ages of their players.**
- As determined above, the Eagles have a wider range of ages (7 to 12).
- **True**
3. **The Lions have more players.**
- Eagles: 14 players, Lions: 13 players.
- **False**
4. **The Eagles have more players.**
- As stated above, the Eagles have 14 players compared to the Lions' 13.
- **True**
5. **The mean of the ages of Lions is less than the mean of the ages of Eagles.**
- Mean age of Lions (10.85) is greater than that of Eagles (9.71).
- **False**
### Conclusion:
The true statements from the above analysis are:
- The Eagles have more variability in the ages of their players.
- The Eagles have more players.