Question
The dot plot and box plot show different displays of the ages of runners on a track team.
A dot plot titled Age of Runners goes from 7 to 12. There are 2 dots above 7, 1 above 8, 3 above 9, 2 above 10, 3 above 11, and 2 above 12.
A box-and-whisker plot. The number line goes from 7 to 12 in increments of 0.5. The whiskers range from 7 to 12, and the box ranges from 8.5 to 11. A line divides the box at 10.
Which statements best describe the dot plot or box plot? Check all that apply.
Add the number of dots above each age in the dot plot to find the number of players on the team: 2 + 1 + 3 + 2 + 3 + 2 = 13.
Subtract the maximum and minimum values of the box plot to find the number of players on the team: 12 – 7.
The median appears clearly on the dot plot at the center of the number line: 9.5.
The median appears clearly on the box plot at the line within the box: 10.
The dot plot is the only display that can be used to show the variability of the data.
The box plot is the only display that can be used to show the variability of the data.
A dot plot titled Age of Runners goes from 7 to 12. There are 2 dots above 7, 1 above 8, 3 above 9, 2 above 10, 3 above 11, and 2 above 12.
A box-and-whisker plot. The number line goes from 7 to 12 in increments of 0.5. The whiskers range from 7 to 12, and the box ranges from 8.5 to 11. A line divides the box at 10.
Which statements best describe the dot plot or box plot? Check all that apply.
Add the number of dots above each age in the dot plot to find the number of players on the team: 2 + 1 + 3 + 2 + 3 + 2 = 13.
Subtract the maximum and minimum values of the box plot to find the number of players on the team: 12 – 7.
The median appears clearly on the dot plot at the center of the number line: 9.5.
The median appears clearly on the box plot at the line within the box: 10.
The dot plot is the only display that can be used to show the variability of the data.
The box plot is the only display that can be used to show the variability of the data.
Answers
GPT-4o mini
Let's evaluate each statement based on the information provided about the dot plot and box plot.
1. **Add the number of dots above each age in the dot plot to find the number of players on the team: 2 + 1 + 3 + 2 + 3 + 2 = 13.**
- **True**. This calculation correctly adds the counts of runners at each age.
2. **Subtract the maximum and minimum values of the box plot to find the number of players on the team: 12 – 7.**
- **False**. The calculation of the range (maximum minus minimum) does not give the number of players; it only reveals variability, not the total count.
3. **The median appears clearly on the dot plot at the center of the number line: 9.5.**
- **False**. The median is not exactly 9.5. Given the dot counts (2, 1, 3, 2, 3, 2), the 7th player is 9, and the 8th player is also 10, making the median actually 10.
4. **The median appears clearly on the box plot at the line within the box: 10.**
- **True**. The box plot shows the median clearly as marked by the line within the box, which is 10.
5. **The dot plot is the only display that can be used to show the variability of the data.**
- **False**. While dot plots can show variability through the distribution of dots, box plots are specifically designed to highlight variability through the interquartile range and outliers, so both can show variability.
6. **The box plot is the only display that can be used to show the variability of the data.**
- **False**. As mentioned, both the dot plot and the box plot can show the variability of the data, albeit in different ways.
**Summary of True Statements:**
- The first statement is true.
- The fourth statement is true.
Therefore, the best descriptions that are true from your list would be the first and fourth statements.
1. **Add the number of dots above each age in the dot plot to find the number of players on the team: 2 + 1 + 3 + 2 + 3 + 2 = 13.**
- **True**. This calculation correctly adds the counts of runners at each age.
2. **Subtract the maximum and minimum values of the box plot to find the number of players on the team: 12 – 7.**
- **False**. The calculation of the range (maximum minus minimum) does not give the number of players; it only reveals variability, not the total count.
3. **The median appears clearly on the dot plot at the center of the number line: 9.5.**
- **False**. The median is not exactly 9.5. Given the dot counts (2, 1, 3, 2, 3, 2), the 7th player is 9, and the 8th player is also 10, making the median actually 10.
4. **The median appears clearly on the box plot at the line within the box: 10.**
- **True**. The box plot shows the median clearly as marked by the line within the box, which is 10.
5. **The dot plot is the only display that can be used to show the variability of the data.**
- **False**. While dot plots can show variability through the distribution of dots, box plots are specifically designed to highlight variability through the interquartile range and outliers, so both can show variability.
6. **The box plot is the only display that can be used to show the variability of the data.**
- **False**. As mentioned, both the dot plot and the box plot can show the variability of the data, albeit in different ways.
**Summary of True Statements:**
- The first statement is true.
- The fourth statement is true.
Therefore, the best descriptions that are true from your list would be the first and fourth statements.