https://file.aiquickdraw.com/mathbot/file/1728240515055k3e513cj.jpg

To create a box plot based on the data in the image, we need to understand the components and place them correctly on the provided axis:

### Given Data:
- **Lower Quartile (Q1)**: 27
- **Median (Q2)**: 35
- **Interquartile Range (IQR)**: 22
- **Longest Time (Maximum)**: 57
- **Range**: 41 (This suggests the minimum value is `57 - 41 = 16`)

### Steps to Create the Box Plot:
1. **Identify the Quartiles and Whiskers:**
   - Minimum (Lower Whisker): 16
   - Q1 (Lower Quartile): 27
   - Q2 (Median): 35
   - Q3 (Upper Quartile): This can be calculated as \( Q1 + IQR = 27 + 22 = 49 \)
   - Maximum (Upper Whisker): 57

2. **Construct the Box Plot:**
   - The box should extend from Q1 (27) to Q3 (49).
   - The median line should be drawn at 35.
   - The whiskers should extend from the minimum value (16) to the maximum value (57).

3. **Plotting on the Provided Axis:**
   - Mark 16 as the starting point for the lower whisker.
   - Mark 27 as the beginning of the box (Q1).
   - Draw a line at 35 for the median (Q2).
   - Mark 49 as the end of the box (Q3).
   - Mark 57 as the end point for the upper whisker.

### Final Box Plot Representation:
To construct the box plot, you would need to sketch:
- A box from 27 to 49 with a vertical line at 35.
- Whiskers from 16 to 27 and from 49 to 57.

If you need any help visualizing or verifying your drawing, feel free to ask! 

Would you like further details or help with related questions? Here are some possible extensions:

1. What are the steps to calculate the interquartile range given Q1 and Q3?
2. How can you determine if a value is an outlier in a box plot?
3. Why is the median important in a box plot?
4. How would the box plot change if the maximum waiting time was 65 minutes instead of 57?
5. What information can we infer about data spread using the range and interquartile range?

**Tip**: Remember that the box in a box plot represents the interquartile range (middle 50% of the data), which helps identify how data is distributed around the median.

Copy the axis below. Draw a box plot to represent the information in the table, which includes lower quartile, longest time, median, range, and interquartile range.

Learn how to draw a box plot using quartiles, median, and interquartile range. This problem involves calculating and plotting the minimum, lower quartile, median, upper quartile, and maximum values on a given axis. Suitable for students in Grades 7-9.

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