Question
Logan wants to move to a new city. He gathered graphs of temperatures for two different cities. Which statements about the data sets shown are true?
City A
A box-and-whisker plot. The whiskers have a range of 10 and the box has a range of 3.
City B
A box-and-whisker plot. The whiskers have a range of 18.5 and the box has a range of 9.5.
City A is likely to have a colder temperatures because the interquartile range is smaller than that of City B.
City A is likely to have temperatures that remain fairly constant year round because it has a compact interquartile range compared to that of City B.
City A is likely to have very hot days and extreme temperatures because the mean is larger than that of City B.
City B is likely to have more warm days than City A because the maximum value is greater.
City B is likely to have more extreme temperatures with colder days in winter and hotter days in summer because the range is greater than that of A.
City B is likely to have more lower temperatures than City A because the median for City B is lower.
City A
A box-and-whisker plot. The whiskers have a range of 10 and the box has a range of 3.
City B
A box-and-whisker plot. The whiskers have a range of 18.5 and the box has a range of 9.5.
City A is likely to have a colder temperatures because the interquartile range is smaller than that of City B.
City A is likely to have temperatures that remain fairly constant year round because it has a compact interquartile range compared to that of City B.
City A is likely to have very hot days and extreme temperatures because the mean is larger than that of City B.
City B is likely to have more warm days than City A because the maximum value is greater.
City B is likely to have more extreme temperatures with colder days in winter and hotter days in summer because the range is greater than that of A.
City B is likely to have more lower temperatures than City A because the median for City B is lower.
Answers
GPT-4o mini
To evaluate the statements about the temperature data of City A and City B based on their box-and-whisker plots, we can analyze the given characteristics of each city:
1. **City A**:
- Whiskers have a range of 10
- Box has a range of 3 (Interquartile Range, IQR)
2. **City B**:
- Whiskers have a range of 18.5
- Box has a range of 9.5 (Interquartile Range, IQR)
Let's assess each statement:
1. **"City A is likely to have colder temperatures because the interquartile range is smaller than that of City B."**
- **False**: A smaller interquartile range indicates less variability in the middle 50% of the data, but it does not necessarily mean that the temperatures are colder. It is possible for City A to have higher temperatures overall with a smaller variability.
2. **"City A is likely to have temperatures that remain fairly constant year-round because it has a compact interquartile range compared to that of City B."**
- **True**: A smaller interquartile range suggests that the temperatures in City A are more consistent and less spread out compared to City B, which shows more variability.
3. **"City A is likely to have very hot days and extreme temperatures because the mean is larger than that of City B."**
- **Not Evaluatable**: The statement mentions the mean without providing numerical data about the means of both cities. Therefore, this cannot be assessed as true or false based on the given information.
4. **"City B is likely to have more warm days than City A because the maximum value is greater."**
- **True**: If City B has a higher maximum temperature, it suggests that City B can reach higher temperatures than City A, possibly leading to more days categorized as warm.
5. **"City B is likely to have more extreme temperatures with colder days in winter and hotter days in summer because the range is greater than that of A."**
- **True**: A greater range suggests that City B experiences more variability, which often correlates with more extreme temperatures—both colder and hotter.
6. **"City B is likely to have more lower temperatures than City A because the median for City B is lower."**
- **Not Evaluatable**: The statement about median values is not provided in the initial information, so the truth of this statement cannot be determined.
In summary, the true statements are:
- City A is likely to have temperatures that remain fairly constant year-round because it has a compact interquartile range compared to that of City B.
- City B is likely to have more warm days than City A because the maximum value is greater.
- City B is likely to have more extreme temperatures with colder days in winter and hotter days in summer because the range is greater than that of A.
1. **City A**:
- Whiskers have a range of 10
- Box has a range of 3 (Interquartile Range, IQR)
2. **City B**:
- Whiskers have a range of 18.5
- Box has a range of 9.5 (Interquartile Range, IQR)
Let's assess each statement:
1. **"City A is likely to have colder temperatures because the interquartile range is smaller than that of City B."**
- **False**: A smaller interquartile range indicates less variability in the middle 50% of the data, but it does not necessarily mean that the temperatures are colder. It is possible for City A to have higher temperatures overall with a smaller variability.
2. **"City A is likely to have temperatures that remain fairly constant year-round because it has a compact interquartile range compared to that of City B."**
- **True**: A smaller interquartile range suggests that the temperatures in City A are more consistent and less spread out compared to City B, which shows more variability.
3. **"City A is likely to have very hot days and extreme temperatures because the mean is larger than that of City B."**
- **Not Evaluatable**: The statement mentions the mean without providing numerical data about the means of both cities. Therefore, this cannot be assessed as true or false based on the given information.
4. **"City B is likely to have more warm days than City A because the maximum value is greater."**
- **True**: If City B has a higher maximum temperature, it suggests that City B can reach higher temperatures than City A, possibly leading to more days categorized as warm.
5. **"City B is likely to have more extreme temperatures with colder days in winter and hotter days in summer because the range is greater than that of A."**
- **True**: A greater range suggests that City B experiences more variability, which often correlates with more extreme temperatures—both colder and hotter.
6. **"City B is likely to have more lower temperatures than City A because the median for City B is lower."**
- **Not Evaluatable**: The statement about median values is not provided in the initial information, so the truth of this statement cannot be determined.
In summary, the true statements are:
- City A is likely to have temperatures that remain fairly constant year-round because it has a compact interquartile range compared to that of City B.
- City B is likely to have more warm days than City A because the maximum value is greater.
- City B is likely to have more extreme temperatures with colder days in winter and hotter days in summer because the range is greater than that of A.