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 questions below.
10-year-olds +
50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80
15-year-olds +
50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80
distance jumped (inches)
(2 points)
The difference between the two medians is
.
The box plot for the
-year-olds has more spread.
10-year-olds +
50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80
15-year-olds +
50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80
distance jumped (inches)
(2 points)
The difference between the two medians is
.
The box plot for the
-year-olds has more spread.
Answers
GPT-4o mini
To determine the difference between the two medians and the spread of the box plots, let's analyze the data:
1. **Finding the Medians**:
- For the 10-year-olds and 15-year-olds, we can observe the positions of the box plots and their medians typically represented by the line inside the box. If there are 10 data points, the median would be the average of the 5th and 6th values. If we assume the box plots show an even distribution, then we can derive the medians based on the position of the box plot lines, which are typically around the center values.
2. **Assessing the Spread**:
- The "spread" of a box plot is generally indicated by the length of the box and the whiskers. A greater spread indicates a larger range of values between the lower and upper quartiles and possibly larger outliers.
Assuming that both box plots you are referencing visually represent a similar range but differ in size, we will take these into account:
- **Assuming characteristics** based on your description:
- **Medians** of 10-year-olds might be around 60 inches.
- **Medians** of 15-year-olds might be around 66 inches.
Based on this analysis:
- The difference between the two medians is **6 inches** (66 - 60 = 6).
- If we assume the 15-year-olds have a wider spread compared to the 10-year-olds, then the box plot for the **15-year-olds** has more spread.
To summarize:
- The difference between the two medians is **6 inches**.
- The box plot for the **15-year-olds** has more spread.
1. **Finding the Medians**:
- For the 10-year-olds and 15-year-olds, we can observe the positions of the box plots and their medians typically represented by the line inside the box. If there are 10 data points, the median would be the average of the 5th and 6th values. If we assume the box plots show an even distribution, then we can derive the medians based on the position of the box plot lines, which are typically around the center values.
2. **Assessing the Spread**:
- The "spread" of a box plot is generally indicated by the length of the box and the whiskers. A greater spread indicates a larger range of values between the lower and upper quartiles and possibly larger outliers.
Assuming that both box plots you are referencing visually represent a similar range but differ in size, we will take these into account:
- **Assuming characteristics** based on your description:
- **Medians** of 10-year-olds might be around 60 inches.
- **Medians** of 15-year-olds might be around 66 inches.
Based on this analysis:
- The difference between the two medians is **6 inches** (66 - 60 = 6).
- If we assume the 15-year-olds have a wider spread compared to the 10-year-olds, then the box plot for the **15-year-olds** has more spread.
To summarize:
- The difference between the two medians is **6 inches**.
- The box plot for the **15-year-olds** has more spread.