Question
Soccer
Football
Basketball
Total
Grade 10
LaTeX: 14=19\%
LaTeX: 9=13\%
LaTeX: 12=16\%
LaTeX: 39
Grade 11
LaTeX: 19=27\%
LaTeX: 7=9\%
LaTeX: 13=19\% LaTeX: 35
Total
LaTeX: 33 LaTeX: 16 LaTeX: 25 LaTeX: 74
Identify the error, if any.
The totals are miscalculated
The relative frequency for Grade 10 students who like soccer is incorrect
The total percentages add to more than 100
There is no error
Football
Basketball
Total
Grade 10
LaTeX: 14=19\%
LaTeX: 9=13\%
LaTeX: 12=16\%
LaTeX: 39
Grade 11
LaTeX: 19=27\%
LaTeX: 7=9\%
LaTeX: 13=19\% LaTeX: 35
Total
LaTeX: 33 LaTeX: 16 LaTeX: 25 LaTeX: 74
Identify the error, if any.
The totals are miscalculated
The relative frequency for Grade 10 students who like soccer is incorrect
The total percentages add to more than 100
There is no error
Answers
GPT-4o mini
To identify the error, we'll analyze each option based on the data provided.
1. **The totals are miscalculated**:
- Grade 10 totals:
- Soccer: 14
- Football: 9
- Basketball: 12
- Total: 14 + 9 + 12 = 35 (not 39, which is incorrect)
- Grade 11 totals:
- Soccer: 19
- Football: 7
- Basketball: 13
- Total: 19 + 7 + 13 = 39 (not 35, which is incorrect)
- So yes, the totals are miscalculated.
2. **The relative frequency for Grade 10 students who like soccer is incorrect**:
- The relative frequency for soccer in Grade 10 is given as \( 19\% \) with a total of \( 39 \). The correct calculation should be \( \frac{14}{39} \times 100 \approx 35.90\% \). This value does not match the given statistics.
3. **The total percentages add to more than 100**:
- For each grade, converting the percentages:
- Grade 10: \( 19\% + 13\% + 16\% = 48\% \)
- Grade 11: \( 27\% + 9\% + 19\% = 55\% \)
- The sum is \( 48\% + 55\% = 103\% \) which is over 100%. So this option is also correct since it suggests that total percentages incorrectly add to more than 100%.
4. **There is no error**:
- This statement is incorrect, as we've identified multiple errors.
Given this examination, the most significant error concerns the miscalculated totals and the overall accuracy of the percentages.
**Conclusion: There are errors present in the totals and the relative frequencies.** Suggestions indicate that the first option ("The totals are miscalculated") accurately identifies a primary source of error. The second option regarding the frequency of soccer in Grade 10 is an additional related error. The third option also highlights that the total percentages add up to more than 100%.
Thus, the best choice for identifying the error is: **The totals are miscalculated**.
1. **The totals are miscalculated**:
- Grade 10 totals:
- Soccer: 14
- Football: 9
- Basketball: 12
- Total: 14 + 9 + 12 = 35 (not 39, which is incorrect)
- Grade 11 totals:
- Soccer: 19
- Football: 7
- Basketball: 13
- Total: 19 + 7 + 13 = 39 (not 35, which is incorrect)
- So yes, the totals are miscalculated.
2. **The relative frequency for Grade 10 students who like soccer is incorrect**:
- The relative frequency for soccer in Grade 10 is given as \( 19\% \) with a total of \( 39 \). The correct calculation should be \( \frac{14}{39} \times 100 \approx 35.90\% \). This value does not match the given statistics.
3. **The total percentages add to more than 100**:
- For each grade, converting the percentages:
- Grade 10: \( 19\% + 13\% + 16\% = 48\% \)
- Grade 11: \( 27\% + 9\% + 19\% = 55\% \)
- The sum is \( 48\% + 55\% = 103\% \) which is over 100%. So this option is also correct since it suggests that total percentages incorrectly add to more than 100%.
4. **There is no error**:
- This statement is incorrect, as we've identified multiple errors.
Given this examination, the most significant error concerns the miscalculated totals and the overall accuracy of the percentages.
**Conclusion: There are errors present in the totals and the relative frequencies.** Suggestions indicate that the first option ("The totals are miscalculated") accurately identifies a primary source of error. The second option regarding the frequency of soccer in Grade 10 is an additional related error. The third option also highlights that the total percentages add up to more than 100%.
Thus, the best choice for identifying the error is: **The totals are miscalculated**.