Question
3
A wildlife biologist catches and releases 20 fish from two different lakes at random locations. He catches 10 fish at Lake Palmer and 10 fish at Lake Dalton. He measures the length of each fish to the nearest quarter of an inch.
Palmer Dalton
First Quartile 6.75 5.5
Second Quartile (Median) 10.25 6.75
Third Quartile 13 7.5
Based on the samples, what generalization can be made?
A.
The interquartile range for Lake Dalton is 2 inches greater than the interquartile range for Lake Palmer.
B.
At least 25 percent of the fish in both lakes are no longer than 6 inches.
C.
Not enough information is provided to draw any of these conclusions.
D.
The first quartile value at Lake Palmer is 1.25 inches longer than the first quartile value at Lake Dalton.
A wildlife biologist catches and releases 20 fish from two different lakes at random locations. He catches 10 fish at Lake Palmer and 10 fish at Lake Dalton. He measures the length of each fish to the nearest quarter of an inch.
Palmer Dalton
First Quartile 6.75 5.5
Second Quartile (Median) 10.25 6.75
Third Quartile 13 7.5
Based on the samples, what generalization can be made?
A.
The interquartile range for Lake Dalton is 2 inches greater than the interquartile range for Lake Palmer.
B.
At least 25 percent of the fish in both lakes are no longer than 6 inches.
C.
Not enough information is provided to draw any of these conclusions.
D.
The first quartile value at Lake Palmer is 1.25 inches longer than the first quartile value at Lake Dalton.
Answers
GPT-4o mini
To determine which generalization is accurate based on the provided quartile data for fish lengths from Lake Palmer and Lake Dalton, let's analyze the statements one by one.
**Given Data:**
- **Lake Palmer:**
- First Quartile (Q1): 6.75 inches
- Second Quartile (Median): 10.25 inches
- Third Quartile (Q3): 13 inches
- **Lake Dalton:**
- First Quartile (Q1): 5.5 inches
- Second Quartile (Median): 6.75 inches
- Third Quartile (Q3): 7.5 inches
**Evaluate Each Option:**
A. **The interquartile range for Lake Dalton is 2 inches greater than the interquartile range for Lake Palmer.**
- Interquartile Range (IQR) = Q3 - Q1
- Lake Palmer: IQR = 13 - 6.75 = 6.25 inches
- Lake Dalton: IQR = 7.5 - 5.5 = 2 inches
- Lake Dalton's IQR is not greater than Lake Palmer's. This statement is **false.**
B. **At least 25 percent of the fish in both lakes are no longer than 6 inches.**
- For Lake Palmer, Q1 is 6.75 inches, meaning at least 25% of fish are longer than 6.75 inches.
- For Lake Dalton, Q1 is 5.5 inches, thus at least 25% of fish are no longer than 5.5 inches.
- Therefore, this statement is **false** because at Lake Palmer, the first quartile indicates that more than 25% are above 6 inches.
C. **Not enough information is provided to draw any of these conclusions.**
- We have specific quartile data which provides enough information to analyze the other statements.
D. **The first quartile value at Lake Palmer is 1.25 inches longer than the first quartile value at Lake Dalton.**
- Lake Palmer's Q1 is 6.75 inches and Lake Dalton's Q1 is 5.5 inches.
- Difference: 6.75 - 5.5 = 1.25 inches.
- This statement is **true.**
**Conclusion:**
The correct answer is **D. The first quartile value at Lake Palmer is 1.25 inches longer than the first quartile value at Lake Dalton.**
**Given Data:**
- **Lake Palmer:**
- First Quartile (Q1): 6.75 inches
- Second Quartile (Median): 10.25 inches
- Third Quartile (Q3): 13 inches
- **Lake Dalton:**
- First Quartile (Q1): 5.5 inches
- Second Quartile (Median): 6.75 inches
- Third Quartile (Q3): 7.5 inches
**Evaluate Each Option:**
A. **The interquartile range for Lake Dalton is 2 inches greater than the interquartile range for Lake Palmer.**
- Interquartile Range (IQR) = Q3 - Q1
- Lake Palmer: IQR = 13 - 6.75 = 6.25 inches
- Lake Dalton: IQR = 7.5 - 5.5 = 2 inches
- Lake Dalton's IQR is not greater than Lake Palmer's. This statement is **false.**
B. **At least 25 percent of the fish in both lakes are no longer than 6 inches.**
- For Lake Palmer, Q1 is 6.75 inches, meaning at least 25% of fish are longer than 6.75 inches.
- For Lake Dalton, Q1 is 5.5 inches, thus at least 25% of fish are no longer than 5.5 inches.
- Therefore, this statement is **false** because at Lake Palmer, the first quartile indicates that more than 25% are above 6 inches.
C. **Not enough information is provided to draw any of these conclusions.**
- We have specific quartile data which provides enough information to analyze the other statements.
D. **The first quartile value at Lake Palmer is 1.25 inches longer than the first quartile value at Lake Dalton.**
- Lake Palmer's Q1 is 6.75 inches and Lake Dalton's Q1 is 5.5 inches.
- Difference: 6.75 - 5.5 = 1.25 inches.
- This statement is **true.**
**Conclusion:**
The correct answer is **D. The first quartile value at Lake Palmer is 1.25 inches longer than the first quartile value at Lake Dalton.**