https://file.aiquickdraw.com/mathbot/file/17289287929831k3b1nzi.jpg

Let's analyze the box-and-whisker diagram and evaluate the statements.

### Box-and-Whisker Diagram Analysis:
1. **Median (middle line of the box)**: Located around 250 mm.
2. **Interquartile Range (IQR)**: The difference between the upper quartile (right edge of the box) and the lower quartile (left edge of the box). From the diagram:
   - **Q3 (Upper quartile)**: Approximately 325 mm.
   - **Q1 (Lower quartile)**: Approximately 210 mm.
   - **IQR**: \( 325 \, \text{mm} - 210 \, \text{mm} = 115 \, \text{mm} \).

3. **Whiskers**:
   - The lower whisker extends to about 140 mm.
   - The upper whisker extends to about 400 mm.

### Statement Evaluations:
1. **The interquartile range is 115 mm.**
   - True. Based on the IQR calculation above, \( Q3 - Q1 = 115 \, \text{mm} \).

2. **Half the plants have height above 250 mm.**
   - False. The median (250 mm) divides the data into two halves, so half of the plants are below 250 mm and half are above.

3. **There are more plants with heights between 250 mm and 325 mm than between 210 mm and 250 mm.**
   - False. Both sections (250 mm to 325 mm and 210 mm to 250 mm) represent equal proportions of the dataset, as they both form one quarter of the data.

4. **There are twice as many plants with heights between 130 mm and 210 mm as between 210 mm and 250 mm.**
   - False. The range between 130 mm and 210 mm corresponds to the left whisker and part of the box, which is less than the range between 210 mm and 250 mm (part of the box).

### Correct Answer:
- **The interquartile range is 115 mm.** (True)

Would you like further details on any part of the solution?

### Follow-up Questions:
1. How is the interquartile range helpful in understanding data spread?
2. What is the significance of the median in a box plot?
3. How can we use a box-and-whisker plot to detect outliers?
4. Can you explain the difference between quartiles and percentiles?
5. How can whiskers in the plot help interpret the overall data distribution?

### Tip:
In a box-and-whisker plot, the IQR is a key indicator of variability, as it contains the middle 50% of the data points.

Which of the following statements are true? The interquartile range is 115 mm, Half the plants have height above 250 mm, There are more plants with heights between 250 mm and 325 mm than between 210 mm and 250 mm, There are twice as many plants with heights between 130 mm and 210 mm as between 210 mm and 250 mm.

Analyze a box-and-whisker plot to determine the interquartile range, median, and the distribution of data points. The problem includes calculations of IQR, understanding data spread, and comparison of plant heights. Suitable for students in Grades 8-10.

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