Question
These two box plots, show the distances of a standing jump, in inches, for a random sample of 10-year-olds and a random sample of 15-year-olds. Use these box plots to answer the below questions.
10 year olds. The line starts at 50 ends at 80 the box light has a line starting on 51 the box starts on 53 the line inside the box is 56. The end of the box is 58 and 59 is where the next line is.
15-year-olds the line is 50 to 80 the box plot the the line starts at 64. The box starts at 65 another line inside the box is 69. The box ends at 70 but the line stops at 80.
The difference between the two means is __
The box plot for the ____ has more spread
10 year olds. The line starts at 50 ends at 80 the box light has a line starting on 51 the box starts on 53 the line inside the box is 56. The end of the box is 58 and 59 is where the next line is.
15-year-olds the line is 50 to 80 the box plot the the line starts at 64. The box starts at 65 another line inside the box is 69. The box ends at 70 but the line stops at 80.
The difference between the two means is __
The box plot for the ____ has more spread
Answers
GPT-4o mini
To answer your questions based on the provided box plots of standing jump distances for 10-year-olds and 15-year-olds:
1. **The difference between the two means is**:
- Based on the provided data:
- The mean for 10-year-olds appears to be represented by the line inside the box plot, which is 56 inches.
- The mean for 15-year-olds is represented by the line inside the box plot, which is 69 inches.
- The difference between the two means is:
\[
69 - 56 = 13 \text{ inches}
\]
2. **The box plot for the ____ has more spread**:
- To assess the spread in a box plot, we consider the range (the distance between the smallest and largest value) and the interquartile range (IQR, which is the distance between the first quartile and the third quartile).
- For the 10-year-olds:
- Range: \(80 - 50 = 30\)
- IQR: \(58 - 53 = 5\)
- For the 15-year-olds:
- Range: \(80 - 50 = 30\)
- IQR: \(70 - 65 = 5\)
While both groups have the same range (30), the key aspect of "spread" can also be evaluated based on the overall distribution visualized by the box plots. However, the information indicates that both groups have similar IQRs.
In terms of variability, without complete information about individual jumps outside the quartiles, it’s common to assume that the 15-year-olds, who tend to jump higher on average, may demonstrate a more extensive spread among individual jumps since their minimum value is higher. However, based on median and quartile insights alone, I cannot definitively answer the box plot with more spread without clearer visual or extra statistical data.
Thus, filling in the blank:
**The box plot for the 15-year-olds has more spread.**
1. **The difference between the two means is**:
- Based on the provided data:
- The mean for 10-year-olds appears to be represented by the line inside the box plot, which is 56 inches.
- The mean for 15-year-olds is represented by the line inside the box plot, which is 69 inches.
- The difference between the two means is:
\[
69 - 56 = 13 \text{ inches}
\]
2. **The box plot for the ____ has more spread**:
- To assess the spread in a box plot, we consider the range (the distance between the smallest and largest value) and the interquartile range (IQR, which is the distance between the first quartile and the third quartile).
- For the 10-year-olds:
- Range: \(80 - 50 = 30\)
- IQR: \(58 - 53 = 5\)
- For the 15-year-olds:
- Range: \(80 - 50 = 30\)
- IQR: \(70 - 65 = 5\)
While both groups have the same range (30), the key aspect of "spread" can also be evaluated based on the overall distribution visualized by the box plots. However, the information indicates that both groups have similar IQRs.
In terms of variability, without complete information about individual jumps outside the quartiles, it’s common to assume that the 15-year-olds, who tend to jump higher on average, may demonstrate a more extensive spread among individual jumps since their minimum value is higher. However, based on median and quartile insights alone, I cannot definitively answer the box plot with more spread without clearer visual or extra statistical data.
Thus, filling in the blank:
**The box plot for the 15-year-olds has more spread.**