Question
A survey was conducted on the salaries of 30 randomly selected households in two different cities. Fifteen of the people surveyed resided in Cartisia, while the other 15 resided in Pascalville.
Cartisia Pascalville
First Quartile $38,000 $45,000
Second Quartile (Median) $50,000 $68,000
Third Quartile $68,000 $77,000
Based on the samples, what generalization can be made?
A.
At least half of the household incomes in both towns are $50,000 or greater.
B.
The median in Cartisia is $18,000 more than in Pascalville.
C.
At least half of the household incomes in both towns are $50,000 or less.
D.
Not enough information is provided to draw any of these conclusions.
Cartisia Pascalville
First Quartile $38,000 $45,000
Second Quartile (Median) $50,000 $68,000
Third Quartile $68,000 $77,000
Based on the samples, what generalization can be made?
A.
At least half of the household incomes in both towns are $50,000 or greater.
B.
The median in Cartisia is $18,000 more than in Pascalville.
C.
At least half of the household incomes in both towns are $50,000 or less.
D.
Not enough information is provided to draw any of these conclusions.
Answers
Answered by
GPT-4o mini
Based on the provided salary data for the two cities, we can analyze the options given in the question.
1. **Option A:** "At least half of the household incomes in both towns are $50,000 or greater."
- This is true for Cartisia because the median (second quartile) is $50,000, so half of the incomes are at least $50,000. However, this is not true for Pascalville, where the median income is $68,000, indicating that half of the incomes are at least $68,000, which is greater than $50,000. Therefore, this statement is valid.
2. **Option B:** "The median in Cartisia is $18,000 more than in Pascalville."
- This is false because the median in Cartisia is $50,000, and the median in Pascalville is $68,000. In fact, the median in Cartisia is $18,000 less than in Pascalville.
3. **Option C:** "At least half of the household incomes in both towns are $50,000 or less."
- This is false for Cartisia because the second quartile (median) indicates that half of the incomes are $50,000 or greater. For Pascalville, since the median is $68,000, this statement is also not true for Pascalville.
4. **Option D:** "Not enough information is provided to draw any of these conclusions."
- This is incorrect because we have sufficient information to evaluate the statements.
Based on this analysis, the only true statement is **Option A.** Therefore, the correct answer is:
**A. At least half of the household incomes in both towns are $50,000 or greater.**
1. **Option A:** "At least half of the household incomes in both towns are $50,000 or greater."
- This is true for Cartisia because the median (second quartile) is $50,000, so half of the incomes are at least $50,000. However, this is not true for Pascalville, where the median income is $68,000, indicating that half of the incomes are at least $68,000, which is greater than $50,000. Therefore, this statement is valid.
2. **Option B:** "The median in Cartisia is $18,000 more than in Pascalville."
- This is false because the median in Cartisia is $50,000, and the median in Pascalville is $68,000. In fact, the median in Cartisia is $18,000 less than in Pascalville.
3. **Option C:** "At least half of the household incomes in both towns are $50,000 or less."
- This is false for Cartisia because the second quartile (median) indicates that half of the incomes are $50,000 or greater. For Pascalville, since the median is $68,000, this statement is also not true for Pascalville.
4. **Option D:** "Not enough information is provided to draw any of these conclusions."
- This is incorrect because we have sufficient information to evaluate the statements.
Based on this analysis, the only true statement is **Option A.** Therefore, the correct answer is:
**A. At least half of the household incomes in both towns are $50,000 or greater.**