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
14,13,13.5,16,14,15.5,14.5
which box plot shows the distribution of the data
Answers
GPT-4o mini
To create a box plot (also known as a whisker plot) for Jacob's 100 meter dash times, we first need to organize the data and calculate the necessary statistics for the box plot.
Here are the steps to create the box plot:
1. **Organize the Data**: Sort the times in ascending order.
- Sorted times: 13, 13.5, 14, 14, 14.5, 15.5, 16
2. **Calculate the Quartiles**:
- **Minimum (Min)**: The smallest value = 13
- **Maximum (Max)**: The largest value = 16
- **Median (Q2)**: The middle value of the sorted list. Since there are 7 values, the median is the 4th value: 14
- **First Quartile (Q1)**: The median of the first half of the data (13, 13.5, 14). The median of this set is 13.5.
- **Third Quartile (Q3)**: The median of the second half of the data (14, 14.5, 15.5, 16). The median of this set is 14.5.
3. **Summarize the Values**:
- Minimum (Min): 13
- First Quartile (Q1): 13.5
- Median (Q2): 14
- Third Quartile (Q3): 14.5
- Maximum (Max): 16
4. **Draw the Box Plot**:
- The box will extend from Q1 (13.5) to Q3 (14.5) with a line at the median (14).
- Whiskers will extend from the minimum (13) to the first quartile (13.5) and from the third quartile (14.5) to the maximum (16).
The final box plot will resemble a rectangular box with whiskers extending out to the minimum and maximum values.
If you're trying to find the correct representation among options, look for a box that spans from 13.5 to 14.5, with a line at 14 and whiskers reaching out to 13 and 16. The box plot should clearly indicate these statistics.
Here are the steps to create the box plot:
1. **Organize the Data**: Sort the times in ascending order.
- Sorted times: 13, 13.5, 14, 14, 14.5, 15.5, 16
2. **Calculate the Quartiles**:
- **Minimum (Min)**: The smallest value = 13
- **Maximum (Max)**: The largest value = 16
- **Median (Q2)**: The middle value of the sorted list. Since there are 7 values, the median is the 4th value: 14
- **First Quartile (Q1)**: The median of the first half of the data (13, 13.5, 14). The median of this set is 13.5.
- **Third Quartile (Q3)**: The median of the second half of the data (14, 14.5, 15.5, 16). The median of this set is 14.5.
3. **Summarize the Values**:
- Minimum (Min): 13
- First Quartile (Q1): 13.5
- Median (Q2): 14
- Third Quartile (Q3): 14.5
- Maximum (Max): 16
4. **Draw the Box Plot**:
- The box will extend from Q1 (13.5) to Q3 (14.5) with a line at the median (14).
- Whiskers will extend from the minimum (13) to the first quartile (13.5) and from the third quartile (14.5) to the maximum (16).
The final box plot will resemble a rectangular box with whiskers extending out to the minimum and maximum values.
If you're trying to find the correct representation among options, look for a box that spans from 13.5 to 14.5, with a line at 14 and whiskers reaching out to 13 and 16. The box plot should clearly indicate these statistics.