Question
The box plots show the number of hours of television a group of middle school students and a group of elementary school students watch each week.
Middle School Students
2 box plots. The number line goes from 0 to 10. For middle school students, the whiskers range from 1 to 9, and the box ranges from 2 to 7. A line divides the box at 4. For elementary school students, the whiskers range from 1 to 9, and the box ranges from 4 to 7. A line divides the box at 5.5.
Elementary School Students
Which are true statements when comparing the data in the box plots? Select three choices.
The data for elementary school are more consistent than those for middle school.
More of the data for middle school lie closer to the median than the data for elementary school.
About 50% of elementary school students watch between 4 and 7 hours of television each week.
About one-half of middle school students watch less than 2 hours of television each week.
On average, middle school students watch less television than elementary school students each week.
Middle School Students
2 box plots. The number line goes from 0 to 10. For middle school students, the whiskers range from 1 to 9, and the box ranges from 2 to 7. A line divides the box at 4. For elementary school students, the whiskers range from 1 to 9, and the box ranges from 4 to 7. A line divides the box at 5.5.
Elementary School Students
Which are true statements when comparing the data in the box plots? Select three choices.
The data for elementary school are more consistent than those for middle school.
More of the data for middle school lie closer to the median than the data for elementary school.
About 50% of elementary school students watch between 4 and 7 hours of television each week.
About one-half of middle school students watch less than 2 hours of television each week.
On average, middle school students watch less television than elementary school students each week.
Answers
Answered by
GPT-4o mini
Based on the description of the box plots for both groups, we can analyze the statements provided. Here are the relevant details:
1. **Middle School Students:**
- Whiskers range from 1 to 9.
- Box ranges from 2 to 7.
- Median (line in the box) is at 4.
2. **Elementary School Students:**
- Whiskers range from 1 to 9.
- Box ranges from 4 to 7.
- Median (line in the box) is at 5.5.
Now let's evaluate the statements:
1. **The data for elementary school are more consistent than those for middle school.**
- **True:** The range of the box for elementary school (4 to 7) indicates that the middle 50% of the data lies in a narrower range than for middle school (2 to 7). This suggests that the elementary school data is more consistent.
2. **More of the data for middle school lie closer to the median than the data for elementary school.**
- **False:** The box for the elementary school (4 to 7) indicates that a significant portion of the data is very close to the median (5.5), while the middle school data (2 to 7) has a wider spread, indicating greater variability.
3. **About 50% of elementary school students watch between 4 and 7 hours of television each week.**
- **True:** The box plot indicates that the interquartile range (IQR) for elementary school students is from 4 to 7, which contains the middle 50% of the data.
4. **About one-half of middle school students watch less than 2 hours of television each week.**
- **False:** The box plot for middle school students shows that the lower quartile starts at 2 hours, indicating that 25% of students watch less than that.
5. **On average, middle school students watch less television than elementary school students each week.**
- **False:** The median for middle school students is 4, while the median for elementary school students is 5.5, indicating that elementary students watch more on average.
Based on this analysis, the three true statements are:
1. The data for elementary school are more consistent than those for middle school.
2. About 50% of elementary school students watch between 4 and 7 hours of television each week.
3. More of the data for middle school lie closer to the median than the data for elementary school. (This statement is actually false. We have only two true statements.)
So the correct answers are:
1. The data for elementary school are more consistent than those for middle school.
2. About 50% of elementary school students watch between 4 and 7 hours of television each week.
1. **Middle School Students:**
- Whiskers range from 1 to 9.
- Box ranges from 2 to 7.
- Median (line in the box) is at 4.
2. **Elementary School Students:**
- Whiskers range from 1 to 9.
- Box ranges from 4 to 7.
- Median (line in the box) is at 5.5.
Now let's evaluate the statements:
1. **The data for elementary school are more consistent than those for middle school.**
- **True:** The range of the box for elementary school (4 to 7) indicates that the middle 50% of the data lies in a narrower range than for middle school (2 to 7). This suggests that the elementary school data is more consistent.
2. **More of the data for middle school lie closer to the median than the data for elementary school.**
- **False:** The box for the elementary school (4 to 7) indicates that a significant portion of the data is very close to the median (5.5), while the middle school data (2 to 7) has a wider spread, indicating greater variability.
3. **About 50% of elementary school students watch between 4 and 7 hours of television each week.**
- **True:** The box plot indicates that the interquartile range (IQR) for elementary school students is from 4 to 7, which contains the middle 50% of the data.
4. **About one-half of middle school students watch less than 2 hours of television each week.**
- **False:** The box plot for middle school students shows that the lower quartile starts at 2 hours, indicating that 25% of students watch less than that.
5. **On average, middle school students watch less television than elementary school students each week.**
- **False:** The median for middle school students is 4, while the median for elementary school students is 5.5, indicating that elementary students watch more on average.
Based on this analysis, the three true statements are:
1. The data for elementary school are more consistent than those for middle school.
2. About 50% of elementary school students watch between 4 and 7 hours of television each week.
3. More of the data for middle school lie closer to the median than the data for elementary school. (This statement is actually false. We have only two true statements.)
So the correct answers are:
1. The data for elementary school are more consistent than those for middle school.
2. About 50% of elementary school students watch between 4 and 7 hours of television each week.