Question
A survey was conducted on ice cream sales. An ice cream shop was randomly selected, and the sales amounts from 12 summer days and 12 spring days were analyzed. The statistics from the sales of the ice cream shop are shown below.
Spring Summer
First Quartile $1,900 $2,500
Second Quartile (Median) $2,325 $3,100
Third Quartile $2,800 $3,850
Based on these samples, what generalization can be made?
A.
At least $2,400 of ice cream was sold for over half the days in spring and summer.
B.
Not enough information is provided to draw any of these conclusions.
C.
The largest amount of money was made on a summer day.
D.
More than $2,300 of ice cream was sold for at least half the days in spring and summer.
Spring Summer
First Quartile $1,900 $2,500
Second Quartile (Median) $2,325 $3,100
Third Quartile $2,800 $3,850
Based on these samples, what generalization can be made?
A.
At least $2,400 of ice cream was sold for over half the days in spring and summer.
B.
Not enough information is provided to draw any of these conclusions.
C.
The largest amount of money was made on a summer day.
D.
More than $2,300 of ice cream was sold for at least half the days in spring and summer.
Answers
Answered by
GPT-4o mini
To analyze the statements based on the provided quartile data for both spring and summer sales, let’s consider what each option implies in relation to the median and quartiles.
1. **In the spring:**
- The median (Q2) is $2,325, which means that over half (50%) of the days had sales greater than or equal to $2,325.
2. **In the summer:**
- The median (Q2) is $3,100, which means that over half (50%) of the days had sales greater than or equal to $3,100.
Now, let's evaluate the options:
A. **At least $2,400 of ice cream was sold for over half the days in spring and summer.**
- This statement is not necessarily true. In spring, the median sales were $2,325, indicating that over half the days had sales below $2,400. Thus, A is incorrect.
B. **Not enough information is provided to draw any of these conclusions.**
- We have provided data and can analyze it. Therefore, this option is not correct.
C. **The largest amount of money was made on a summer day.**
- While we see the third quartile sales for summer ($3,850), which is likely higher than most spring sales, without specific information about maximum sales, we cannot definitively conclude this. Thus, C is inconclusive.
D. **More than $2,300 of ice cream was sold for at least half the days in spring and summer.**
- In spring, the median is $2,325, which means over half the days had sales greater than or equal to this amount. In summer, the median sales are $3,100, which is also above $2,300. Hence, more than $2,300 of ice cream was sold for at least half the days in spring and summer.
Based on this analysis, the best generalization we can make is:
**D. More than $2,300 of ice cream was sold for at least half the days in spring and summer.**
1. **In the spring:**
- The median (Q2) is $2,325, which means that over half (50%) of the days had sales greater than or equal to $2,325.
2. **In the summer:**
- The median (Q2) is $3,100, which means that over half (50%) of the days had sales greater than or equal to $3,100.
Now, let's evaluate the options:
A. **At least $2,400 of ice cream was sold for over half the days in spring and summer.**
- This statement is not necessarily true. In spring, the median sales were $2,325, indicating that over half the days had sales below $2,400. Thus, A is incorrect.
B. **Not enough information is provided to draw any of these conclusions.**
- We have provided data and can analyze it. Therefore, this option is not correct.
C. **The largest amount of money was made on a summer day.**
- While we see the third quartile sales for summer ($3,850), which is likely higher than most spring sales, without specific information about maximum sales, we cannot definitively conclude this. Thus, C is inconclusive.
D. **More than $2,300 of ice cream was sold for at least half the days in spring and summer.**
- In spring, the median is $2,325, which means over half the days had sales greater than or equal to this amount. In summer, the median sales are $3,100, which is also above $2,300. Hence, more than $2,300 of ice cream was sold for at least half the days in spring and summer.
Based on this analysis, the best generalization we can make is:
**D. More than $2,300 of ice cream was sold for at least half the days in spring and summer.**