Question
Jacob is practicing the 100 meter dash. the data show his times in seconds.
14,13,13.5,16,14,15.5,14.5
which box plot shows the distribution of the data
what is the interquaertile range (IQR) for Jacob's date set?
14,13,13.5,16,14,15.5,14.5
which box plot shows the distribution of the data
what is the interquaertile range (IQR) for Jacob's date set?
Answers
GPT-4o mini
To analyze Jacob's data set, we first need to determine some key statistics that will help us in creating a box plot, including finding the quartiles and the interquartile range (IQR).
1. **Sort the Data**: First, we sort the times in ascending order:
- 13, 13.5, 14, 14, 14.5, 15.5, 16
2. **Find the Quartiles**:
- **Median (Q2)**: The median (Q2) is the middle value. In this case, with 7 data points, the median is the 4th value:
- Q2 = 14
- **First Quartile (Q1)**: This is the median of the first half of the data (the lower half). The lower half is 13, 13.5, and 14:
- Q1 = 13.5
- **Third Quartile (Q3)**: This is the median of the second half of the data (the upper half). The upper half is 14, 14.5, 15.5, and 16:
- Q3 = 14.5
3. **Calculate the IQR**:
- IQR = Q3 - Q1 = 14.5 - 13.5 = 1
4. **Summary of Key Statistics**:
- Q1 = 13.5
- Q2 (Median) = 14
- Q3 = 14.5
- IQR = 1
5. **Box Plot**: When you create a box plot, you will mark the minimum value (13), the first quartile (13.5), the median (14), the third quartile (14.5), and the maximum value (16). You would see:
- A box from Q1 (13.5) to Q3 (14.5) with a line at Q2 (14).
- Whiskers extending to the minimum (13) and maximum (16).
In summary, the interquartile range (IQR) for Jacob's data set is **1**. You can use this information to illustrate the box plot accordingly!
1. **Sort the Data**: First, we sort the times in ascending order:
- 13, 13.5, 14, 14, 14.5, 15.5, 16
2. **Find the Quartiles**:
- **Median (Q2)**: The median (Q2) is the middle value. In this case, with 7 data points, the median is the 4th value:
- Q2 = 14
- **First Quartile (Q1)**: This is the median of the first half of the data (the lower half). The lower half is 13, 13.5, and 14:
- Q1 = 13.5
- **Third Quartile (Q3)**: This is the median of the second half of the data (the upper half). The upper half is 14, 14.5, 15.5, and 16:
- Q3 = 14.5
3. **Calculate the IQR**:
- IQR = Q3 - Q1 = 14.5 - 13.5 = 1
4. **Summary of Key Statistics**:
- Q1 = 13.5
- Q2 (Median) = 14
- Q3 = 14.5
- IQR = 1
5. **Box Plot**: When you create a box plot, you will mark the minimum value (13), the first quartile (13.5), the median (14), the third quartile (14.5), and the maximum value (16). You would see:
- A box from Q1 (13.5) to Q3 (14.5) with a line at Q2 (14).
- Whiskers extending to the minimum (13) and maximum (16).
In summary, the interquartile range (IQR) for Jacob's data set is **1**. You can use this information to illustrate the box plot accordingly!